{"id":49394,"date":"2025-07-30T18:06:53","date_gmt":"2025-07-30T10:06:53","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/49394.html"},"modified":"2025-07-30T18:06:53","modified_gmt":"2025-07-30T10:06:53","slug":"%e6%95%b0%e5%ad%a6%e5%ae%b6%e3%80%81%e5%9b%be%e7%81%b5%e6%9c%ba%e3%80%81%e8%ae%a1%e7%ae%97%e7%90%86%e8%ae%ba%e3%80%81%e8%ae%a1%e7%ae%97%e6%9c%ba%e3%80%81%e7%a8%8b%e5%ba%8f%e8%ae%be%e8%ae%a1%e8%af%ad","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/49394.html","title":{"rendered":"\u6570\u5b66\u5bb6\u3001\u56fe\u7075\u673a\u3001\u8ba1\u7b97\u7406\u8bba\u3001\u8ba1\u7b97\u673a\u3001\u7a0b\u5e8f\u8bbe\u8ba1\u8bed\u8a00\u548c\u7f16\u8bd1\u5668"},"content":{"rendered":"<p><span style=\"color:#fe2c24\">Hilbert -&gt; Turing -&gt; Chomsky -&gt; &#8230;<\/span>\u00a0<\/p>\n<h2>1. \u5e0c\u5c14\u4f2f\u7279\u768423\u4e2a\u95ee\u9898&#xff08;1900\u5e74&#xff09;<\/h2>\n<p>\n\u00a0 \u00a0 \u00a0 \u00a0 1900\u5e74&#xff0c;\u5fb7\u56fd\u6570\u5b66\u5bb6\u5927\u536b\u00b7\u5e0c\u5c14\u4f2f\u7279&#xff08;David Hilbert&#xff09;\u5728\u5df4\u9ece\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a\u4e0a\u63d0\u51fa\u4e8623\u4e2a\u672a\u89e3\u51b3\u7684\u6570\u5b66\u95ee\u9898&#xff0c;\u8fd9\u4e9b\u95ee\u9898\u6df1\u523b\u5f71\u54cd\u4e8620\u4e16\u7eaa\u6570\u5b66\u7684\u53d1\u5c55\u65b9\u5411\u3002\u8fd9\u4e9b\u95ee\u9898\u6db5\u76d6\u5e7f\u6cdb\u9886\u57df&#xff0c;\u5305\u62ec\u6570\u8bba\u3001\u4ee3\u6570\u3001\u51e0\u4f55\u3001\u5206\u6790\u3001\u903b\u8f91\u7b49&#xff0c;\u5176\u4e2d\u4e00\u4e9b\u95ee\u9898\u81f3\u4eca\u4ecd\u672a\u5b8c\u5168\u89e3\u51b3&#xff0c;\u800c\u53e6\u4e00\u4e9b\u5219\u50ac\u751f\u4e86\u65b0\u7684\u6570\u5b66\u5206\u652f&#xff08;\u5982\u8ba1\u7b97\u7406\u8bba\u3001\u62d3\u6251\u5b66\u3001\u6570\u7406\u903b\u8f91\u7b49&#xff09;\u3002\u73b0\u5206\u7c7b\u4e0e\u6982\u8ff023\u4e2a\u95ee\u9898\u3002<\/p>\n<\/p>\n<h3>1.1. \u6570\u5b66\u57fa\u7840&#xff08;\u903b\u8f91\u4e0e\u516c\u7406\u5316&#xff09;<\/h3>\n<p>\n<span style=\"color:#4da8ee\">\u95ee\u98981&#xff1a;\u8fde\u7eed\u7edf\u5047\u8bbe&#xff08;CH&#xff09;<\/span><\/p>\n<p>\u5eb7\u6258\u5c14\u63d0\u51fa&#xff1a;\u662f\u5426\u5b58\u5728\u4e00\u4e2a\u57fa\u6570\u4e25\u683c\u4ecb\u4e8e\u53ef\u6570\u65e0\u7a77&#xff08;\u2135\u2080&#xff09;\u548c\u5b9e\u6570\u96c6\u57fa\u6570&#xff08;\u2135\u2081&#xff09;\u4e4b\u95f4\u7684\u96c6\u5408&#xff1f;<\/p>\n<p>\u73b0\u72b6&#xff1a;\u54e5\u5fb7\u5c14&#xff08;1940&#xff09;\u548c\u79d1\u6069&#xff08;1963&#xff09;\u8bc1\u660e&#xff0c;CH\u5728ZFC\u516c\u7406\u7cfb\u7edf\u5185\u65e2\u4e0d\u80fd\u88ab\u8bc1\u660e\u4e5f\u4e0d\u80fd\u88ab\u8bc1\u4f2a&#xff08;\u72ec\u7acb\u4e8eZFC&#xff09;\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u98982&#xff1a;\u7b97\u672f\u516c\u7406\u7684\u4e00\u81f4\u6027<\/span><\/p>\n<p>\u5e0c\u5c14\u4f2f\u7279\u5e0c\u671b\u8bc1\u660e\u6570\u5b66\u516c\u7406\u7cfb\u7edf&#xff08;\u5982\u7b97\u672f&#xff09;\u4e0d\u4f1a\u5bfc\u81f4\u77db\u76fe\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u54e5\u5fb7\u5c14\u4e0d\u5b8c\u5907\u6027\u5b9a\u7406&#xff08;1931&#xff09;\u8bc1\u660e&#xff0c;\u4efb\u4f55\u8db3\u591f\u5f3a\u7684\u516c\u7406\u7cfb\u7edf\u65e0\u6cd5\u81ea\u8bc1\u4e00\u81f4\u6027&#xff0c;\u56fe\u7075\u673a\u7684\u505c\u673a\u95ee\u9898\u8fdb\u4e00\u6b65\u5f3a\u5316\u4e86\u8fd9\u4e00\u7ed3\u8bba\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989810&#xff1a;\u5224\u5b9a\u4e22\u756a\u56fe\u65b9\u7a0b\u7684\u53ef\u89e3\u6027<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u662f\u5426\u5b58\u5728\u901a\u7528\u7b97\u6cd5\u5224\u5b9a\u4efb\u610f\u6574\u7cfb\u6570\u591a\u9879\u5f0f\u65b9\u7a0b\u662f\u5426\u6709\u6574\u6570\u89e3&#xff1f;<\/p>\n<p>\u73b0\u72b6&#xff1a;1970\u5e74&#xff0c;\u9a6c\u8482\u4e9a\u8c22\u7ef4\u5947&#xff08;\u57fa\u4e8e\u56fe\u7075\u673a\u7406\u8bba&#xff09;\u8bc1\u660e\u4e0d\u5b58\u5728\u8fd9\u6837\u7684\u7b97\u6cd5&#xff08;\u5e0c\u5c14\u4f2f\u7279\u7b2c\u5341\u95ee\u9898\u4e0d\u53ef\u89e3&#xff09;\u3002<\/p>\n<h3>1.2. \u4ee3\u6570\u4e0e\u6570\u8bba<\/h3>\n<p>\n<span style=\"color:#4da8ee\">\u95ee\u98983&#xff1a;\u4e24\u4e2a\u7b49\u4f53\u79ef\u591a\u9762\u4f53\u7684\u5256\u5206\u76f8\u7b49\u6027<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7ed9\u5b9a\u4e24\u4e2a\u4f53\u79ef\u76f8\u540c\u7684\u591a\u9762\u4f53&#xff0c;\u80fd\u5426\u901a\u8fc7\u6709\u9650\u5207\u5272\u91cd\u7ec4\u4f7f\u5b83\u4eec\u5168\u7b49&#xff1f;<\/p>\n<p>\u73b0\u72b6&#xff1a;\u5fb7\u6069&#xff08;1900&#xff09;\u7ed9\u51fa\u53cd\u4f8b&#xff0c;\u8868\u660e\u4e0d\u4e00\u5b9a\u6210\u7acb\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u98987&#xff1a;\u67d0\u4e9b\u6570\u7684\u8d85\u8d8a\u6027&#xff08;\u5982<img decoding=\"async\" alt=\"e^\\\\pi\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100646-6889eeb6970a1.png\" \/>\u00a0&#xff09;<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u8bc1\u660e\u67d0\u4e9b\u6570&#xff08;\u5982<img decoding=\"async\" alt=\"2^{\\\\sqrt{2}}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100647-6889eeb70ff26.png\" \/>\u00a0\u3001<img decoding=\"async\" alt=\"e^\\\\pi\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100646-6889eeb6970a1.png\" \/>\u00a0&#xff09;\u662f\u8d85\u8d8a\u6570\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u683c\u5c14\u4e30\u5fb7-\u65bd\u5948\u5fb7\u5b9a\u7406&#xff08;1934&#xff09;\u90e8\u5206\u89e3\u51b3&#xff0c;\u4f46\u4ecd\u6709\u5f00\u653e\u95ee\u9898\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u98989&#xff1a;\u4efb\u610f\u6570\u57df\u4e2d\u7684\u4e92\u53cd\u5f8b\u63a8\u5e7f<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u63a8\u5e7f\u9ad8\u65af\u4e8c\u6b21\u4e92\u53cd\u5f8b\u5230\u66f4\u4e00\u822c\u7684\u6570\u57df\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u963f\u5ef7&#xff08;1927&#xff09;\u63d0\u51fa\u7c7b\u57df\u8bba&#xff0c;\u90e8\u5206\u89e3\u51b3\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989811&#xff1a;\u4e8c\u6b21\u578b\u7406\u8bba<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u4ee3\u6570\u6570\u57df\u4e0a\u7684\u4e8c\u6b21\u578b\u7406\u8bba\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u54c8\u585e&#xff08;1920s&#xff09;\u7b49\u6709\u91cd\u8981\u8d21\u732e&#xff0c;\u4f46\u4ecd\u6709\u8bb8\u591a\u5f00\u653e\u95ee\u9898\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989812&#xff1a;\u963f\u8d1d\u5c14\u57df\u7684\u514b\u7f57\u5185\u514b\u5b9a\u7406\u63a8\u5e7f<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u63a8\u5e7f\u514b\u7f57\u5185\u514b\u7684\u201c\u9752\u6625\u4e4b\u68a6\u201d\u731c\u60f3\u5230\u66f4\u4e00\u822c\u7684\u57df\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u7c7b\u57df\u8bba\u90e8\u5206\u89e3\u51b3&#xff0c;\u4f46\u5b8c\u6574\u63a8\u5e7f\u4ecd\u672a\u5b8c\u6210\u3002<\/p>\n<h3>1.3. \u51e0\u4f55\u4e0e\u62d3\u6251<\/h3>\n<p>\n<span style=\"color:#4da8ee\">\u95ee\u98984&#xff1a;\u6784\u9020\u6240\u6709\u5ea6\u91cf\u51e0\u4f55\u7684\u516c\u7406\u7cfb\u7edf<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u4e0d\u540c\u51e0\u4f55&#xff08;\u6b27\u6c0f\u3001\u975e\u6b27\u3001\u5c04\u5f71\u7b49&#xff09;\u7684\u516c\u7406\u5316\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u62d3\u6251\u5b66\u548c\u5fae\u5206\u51e0\u4f55\u7684\u53d1\u5c55\u90e8\u5206\u89e3\u51b3\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u98985&#xff1a;\u674e\u7fa4\u7684\u62d3\u6251\u6027\u8d28<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u8fde\u7eed\u53d8\u6362\u7fa4&#xff08;\u674e\u7fa4&#xff09;\u662f\u5426\u603b\u662f\u53ef\u5fae&#xff1f;<\/p>\n<p>\u73b0\u72b6&#xff1a;1952\u5e74&#xff0c;\u683c\u91cc\u68ee\u7b49\u8bc1\u660e\u5c40\u90e8\u6b27\u6c0f\u7fa4\u5fc5\u4e3a\u674e\u7fa4&#xff08;\u5e0c\u5c14\u4f2f\u7279\u7b2c\u4e94\u95ee\u9898\u89e3\u51b3&#xff09;\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u98986&#xff1a;\u7269\u7406\u5b66\u7684\u516c\u7406\u5316<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u4e3a\u7269\u7406\u5b66&#xff08;\u7279\u522b\u662f\u6982\u7387\u8bba\u548c\u529b\u5b66&#xff09;\u5efa\u7acb\u4e25\u683c\u7684\u6570\u5b66\u57fa\u7840\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u91cf\u5b50\u529b\u5b66\u3001\u7edf\u8ba1\u529b\u5b66\u7b49\u53d1\u5c55\u90e8\u5206\u89e3\u51b3\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989815&#xff1a;\u4ee3\u6570\u51e0\u4f55\u7684\u8212\u4f2f\u7279\u8ba1\u6570\u6f14\u7b97\u4e25\u683c\u5316<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u4e25\u683c\u5316\u8212\u4f2f\u7279\u7684\u201c\u679a\u4e3e\u51e0\u4f55\u201d\u65b9\u6cd5\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;20\u4e16\u7eaa\u4ee3\u6570\u51e0\u4f55&#xff08;\u683c\u7f57\u6ed5\u8fea\u514b\u7b49&#xff09;\u53d1\u5c55\u540e\u57fa\u672c\u89e3\u51b3\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989818&#xff1a;\u7a7a\u95f4\u586b\u5145\u95ee\u9898&#xff08;\u5bc6\u94fa\u7406\u8bba&#xff09;<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u9ad8\u7ef4\u7a7a\u95f4\u7684\u6700\u5bc6\u5806\u79ef&#xff08;\u5982\u7403\u4f53\u5806\u79ef&#xff09;\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u5f00\u666e\u52d2\u731c\u60f3&#xff08;\u4e09\u7ef4\u7403\u5806\u79ef&#xff0c;1998\u5e74\u8bc1\u660e&#xff09;&#xff0c;\u4f46\u66f4\u9ad8\u7ef4\u4ecd\u672a\u5b8c\u5168\u89e3\u51b3\u3002<\/p>\n<h3>1.4. \u5206\u6790\u4e0e\u65b9\u7a0b<\/h3>\n<p>\n<span style=\"color:#4da8ee\">\u95ee\u98988&#xff1a;\u7d20\u6570\u5206\u5e03&#xff08;\u9ece\u66fc\u731c\u60f3\u3001\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u7b49&#xff09;<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u7d20\u6570\u5206\u5e03&#xff08;\u5982\u9ece\u66fc\u03b6\u51fd\u6570\u7684\u96f6\u70b9&#xff09;\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u9ece\u66fc\u731c\u60f3&#xff08;\u672a\u89e3\u51b3&#xff09;&#xff0c;\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3&#xff08;\u9648\u666f\u6da6\u90e8\u5206\u8bc1\u660e&#xff09;\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989813&#xff1a;\u4e03\u6b21\u65b9\u7a0b\u7684\u89e3&#xff08;\u4e00\u822c\u4e03\u6b21\u65b9\u7a0b\u662f\u5426\u53ef\u7528\u6709\u9650\u8d85\u692d\u5706\u51fd\u6570\u8868\u793a&#xff09;<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u63a8\u5e7f\u692d\u5706\u51fd\u6570\u7406\u8bba\u5230\u66f4\u9ad8\u6b21\u65b9\u7a0b\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u90e8\u5206\u89e3\u51b3&#xff08;\u963f\u8d1d\u5c14\u79ef\u5206\u3001\u4ee3\u6570\u51e0\u4f55&#xff09;\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989816&#xff1a;\u4ee3\u6570\u66f2\u7ebf\u4e0e\u66f2\u9762\u7684\u62d3\u6251<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u4ee3\u6570\u66f2\u7ebf\/\u66f2\u9762\u7684\u6781\u9650\u73af&#xff08;\u5982\u5e0c\u5c14\u4f2f\u7279\u7b2c16\u95ee\u9898&#xff09;\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u52a8\u529b\u7cfb\u7edf\u7814\u7a76\u4ecd\u5728\u8fdb\u884c&#xff0c;\u90e8\u5206\u89e3\u51b3\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989819&#xff1a;\u53d8\u5206\u6cd5\u7684\u89e3\u6790\u89e3<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u62c9\u683c\u6717\u65e5\u65b9\u7a0b\u7684\u89e3\u662f\u5426\u603b\u662f\u89e3\u6790\u7684\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u4f2f\u6069\u65af\u5766\u7b49\u6709\u90e8\u5206\u7ed3\u679c&#xff0c;\u4f46\u4ecd\u6709\u5f00\u653e\u95ee\u9898\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989820&#xff1a;\u504f\u5fae\u5206\u65b9\u7a0b\u8fb9\u503c\u95ee\u9898\u7684\u89e3<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u7269\u7406\u65b9\u7a0b&#xff08;\u5982\u70ed\u65b9\u7a0b\u3001\u6ce2\u52a8\u65b9\u7a0b&#xff09;\u7684\u89e3\u7684\u5b58\u5728\u6027\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u6cdb\u51fd\u5206\u6790\u3001\u7d22\u4f2f\u5217\u592b\u7a7a\u95f4\u7b49\u7406\u8bba\u90e8\u5206\u89e3\u51b3\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989821&#xff1a;\u5177\u6709\u7ed9\u5b9a\u5355\u503c\u7fa4\u7684\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u5fae\u5206\u65b9\u7a0b\u7684\u5355\u503c\u7fa4&#xff08;Monodromy&#xff09;\u95ee\u9898\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u4ee3\u6570\u51e0\u4f55\u548c\u5fae\u5206\u65b9\u7a0b\u7406\u8bba\u90e8\u5206\u89e3\u51b3\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u95ee\u989822&#xff1a;\u89e3\u6790\u5173\u7cfb\u7684\u5355\u503c\u5316<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u591a\u503c\u51fd\u6570&#xff08;\u5982\u590d\u53d8\u51fd\u6570&#xff09;\u7684\u5355\u503c\u8868\u793a\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u5355\u503c\u5316\u5b9a\u7406&#xff08;\u5e9e\u52a0\u83b1\u3001\u514b\u8d1d\u7b49&#xff09;\u90e8\u5206\u89e3\u51b3\u3002<\/p>\n<h3>1.5. \u6570\u5b66\u7269\u7406<\/h3>\n<p>\n<span style=\"color:#4da8ee\">\u95ee\u989823&#xff1a;\u53d8\u5206\u6cd5\u7684\u8fdb\u4e00\u6b65\u53d1\u5c55<\/span><\/p>\n<p>\u95ee\u9898&#xff1a;\u7814\u7a76\u53d8\u5206\u6cd5\u5728\u7269\u7406\u4e2d\u7684\u5e94\u7528&#xff08;\u5982\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406&#xff09;\u3002<\/p>\n<p>\u73b0\u72b6&#xff1a;\u73b0\u4ee3\u7269\u7406&#xff08;\u91cf\u5b50\u573a\u8bba\u3001\u5f26\u8bba&#xff09;\u4ecd\u5728\u53d1\u5c55\u76f8\u5173\u6570\u5b66\u3002<\/p>\n<h3>1.6. \u60c5\u51b5\u603b\u7ed3<\/h3>\n<p>\n<span style=\"color:#fe2c24\">\u5df2\u89e3\u51b3<\/span>&#xff1a;\u95ee\u98983\u30015\u300110\u300115\u300117\u300118&#xff08;\u90e8\u5206&#xff09;\u300121\u300122\u7b49\u3002<\/p>\n<p><span style=\"color:#fe2c24\">\u90e8\u5206\u89e3\u51b3<\/span>&#xff1a;\u95ee\u98981\u30012\u30017\u30018\u30019\u300111\u300116\u300119\u300120\u7b49\u3002<\/p>\n<p><span style=\"color:#fe2c24\">\u672a\u89e3\u51b3<\/span>&#xff1a;\u9ece\u66fc\u731c\u60f3&#xff08;\u95ee\u98988\u4e4b\u4e00&#xff09;\u3001\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3&#xff08;\u95ee\u98988\u4e4b\u4e8c&#xff09;\u3001\u5e0c\u5c14\u4f2f\u7279\u7b2c16\u95ee\u9898\u7684\u5b8c\u6574\u89e3\u7b49\u3002<\/p>\n<p>\u5e0c\u5c14\u4f2f\u7279\u768423\u4e2a\u95ee\u9898\u5851\u9020\u4e86\u73b0\u4ee3\u6570\u5b66\u7684\u683c\u5c40&#xff0c;\u63a8\u52a8\u4e86\u6570\u7406\u903b\u8f91\u3001<span style=\"color:#be191c\">\u8ba1\u7b97\u7406\u8bba<\/span>\u3001\u4ee3\u6570\u51e0\u4f55\u3001\u62d3\u6251\u5b66\u7b49\u9886\u57df\u7684\u9769\u547d\u6027\u53d1\u5c55\u3002<\/p>\n<\/p>\n<h2>2. \u5e0c\u5c14\u4f2f\u727923\u95ee\u9898\u4e0e\u56fe\u7075\u673a\u7684\u5173\u7cfb<\/h2>\n<h3>2.1. \u4e0e\u56fe\u7075\u673a\u76f8\u5173\u7684\u5e0c\u5c14\u4f2f\u7279\u95ee\u9898<\/h3>\n<p>\u4ee5\u4e0b\u95ee\u9898\u4e0e\u8ba1\u7b97\u7406\u8bba\u548c\u56fe\u7075\u673a\u6709\u76f4\u63a5\u6216\u95f4\u63a5\u5173\u8054&#xff1a;<\/p>\n<p>\u7b2c1\u95ee\u9898&#xff08;\u8fde\u7eed\u7edf\u5047\u8bbe&#xff09;<br \/>\n\u5eb7\u6258\u5c14\u7684\u8fde\u7eed\u7edf\u5047\u8bbe&#xff08;CH&#xff09;\u63a2\u8ba8\u65e0\u7a77\u96c6\u5408\u7684\u57fa\u6570\u95ee\u9898\u3002\u56fe\u7075\u673a\u5728\u53ef\u8ba1\u7b97\u6027\u7406\u8bba\u4e2d\u7684\u7814\u7a76&#xff08;\u5982\u505c\u673a\u95ee\u9898&#xff09;\u63ed\u793a\u4e86\u6570\u5b66\u4e2d\u67d0\u4e9b\u547d\u9898\u7684\u4e0d\u53ef\u5224\u5b9a\u6027&#xff0c;\u8fd9\u4e0e\u54e5\u5fb7\u5c14\u4e0d\u5b8c\u5907\u5b9a\u7406\u5171\u540c\u8bf4\u660eCH\u5728ZFC\u516c\u7406\u4f53\u7cfb\u5185\u65e0\u6cd5\u88ab\u8bc1\u660e\u6216\u8bc1\u4f2a\u3002<\/p>\n<p>\u7b2c2\u95ee\u9898&#xff08;\u7b97\u672f\u516c\u7406\u7684\u65e0\u77db\u76fe\u6027&#xff09;<br \/>\n\u5e0c\u5c14\u4f2f\u7279\u5e0c\u671b\u8bc1\u660e\u6570\u5b66\u7cfb\u7edf\u7684\u4e00\u81f4\u6027\u3002\u4f46\u54e5\u5fb7\u5c14\u4e0d\u5b8c\u5907\u5b9a\u7406&#xff08;1931\u5e74&#xff09;\u548c\u56fe\u7075\u7684\u5de5\u4f5c\u8868\u660e&#xff0c;\u4efb\u4f55\u8db3\u591f\u5f3a\u7684\u516c\u7406\u7cfb\u7edf&#xff08;\u5982\u7b97\u672f&#xff09;\u65e0\u6cd5\u81ea\u8bc1\u5176\u4e00\u81f4\u6027\u3002\u56fe\u7075\u673a\u7684\u505c\u673a\u95ee\u9898\u6b63\u662f\u8fd9\u79cd\u4e0d\u53ef\u5224\u5b9a\u6027\u7684\u4f53\u73b0\u3002<\/p>\n<p>\u7b2c10\u95ee\u9898&#xff08;\u4e22\u756a\u56fe\u65b9\u7a0b\u7684\u53ef\u89e3\u6027&#xff09;<br \/>\n\u95ee\u9898&#xff1a;\u662f\u5426\u5b58\u5728\u901a\u7528\u7b97\u6cd5\u5224\u5b9a\u6574\u7cfb\u6570\u591a\u9879\u5f0f\u65b9\u7a0b\u662f\u5426\u6709\u6574\u6570\u89e3&#xff1f;<\/p>\n<p>1970\u5e74&#xff0c;\u9a6c\u8482\u4e9a\u8c22\u7ef4\u5947&#xff08;Yuri Matiyasevich&#xff09;\u57fa\u4e8e\u56fe\u7075\u673a\u3001\u9012\u5f52\u51fd\u6570\u7406\u8bba\u8bc1\u660e\u4e0d\u5b58\u5728\u8fd9\u6837\u7684\u7b97\u6cd5&#xff0c;\u5373\u5e0c\u5c14\u4f2f\u7279\u7b2c\u5341\u95ee\u9898\u4e0d\u53ef\u89e3\u3002<\/p>\n<h3>2.2. \u56fe\u7075\u673a\u4e0e\u5e0c\u5c14\u4f2f\u7279\u7eb2\u9886\u7684\u5173\u8054<\/h3>\n<p>\u00a0 \u00a0 \u5e0c\u5c14\u4f2f\u7279\u7684\u5f62\u5f0f\u4e3b\u4e49\u7eb2\u9886\u8bd5\u56fe\u5c06\u6570\u5b66\u5efa\u7acb\u5728\u6709\u9650\u6b65\u9aa4\u7684\u673a\u68b0\u8bc1\u660e&#xff08;\u5373\u201c\u80fd\u884c\u6027\u201d&#xff09;\u57fa\u7840\u4e0a\u3002\u56fe\u7075\u673a\u7684\u63d0\u51fa&#xff08;1936\u5e74&#xff09;\u4e3a\u6b64\u63d0\u4f9b\u4e86\u7406\u8bba\u6a21\u578b&#xff1a;<\/p>\n<p><span style=\"color:#956fe7\">\u53ef\u8ba1\u7b97\u6027&#xff1a;\u56fe\u7075\u673a\u5f62\u5f0f\u5316\u4e86\u201c\u7b97\u6cd5\u201d\u6982\u5ff5&#xff0c;\u8bc1\u660e\u67d0\u4e9b\u95ee\u9898&#xff08;\u5982\u505c\u673a\u95ee\u9898&#xff09;\u65e0\u6cd5\u901a\u8fc7\u7b97\u6cd5\u89e3\u51b3\u3002<\/span><\/p>\n<p><span style=\"color:#956fe7\">\u4e0d\u5b8c\u5907\u6027&#xff1a;\u7ed3\u5408\u54e5\u5fb7\u5c14\u5b9a\u7406&#xff0c;\u56fe\u7075\u673a\u8868\u660e\u5e0c\u5c14\u4f2f\u7279\u5bfb\u6c42\u7684\u201c\u5b8c\u5907\u4e14\u4e00\u81f4\u7684\u6570\u5b66\u7cfb\u7edf\u201d\u4e0d\u53ef\u80fd\u5b58\u5728\u3002<\/span><\/p>\n<h3>2.3. \u5f71\u54cd\u4e0e\u610f\u4e49<\/h3>\n<p>\n\u56fe\u7075\u673a\u4e3a\u8ba1\u7b97\u673a\u79d1\u5b66\u5960\u5b9a\u57fa\u7840&#xff0c;\u5e0c\u5c14\u4f2f\u7279\u95ee\u9898\u4e2d\u7684\u903b\u8f91\u4e0e\u53ef\u8ba1\u7b97\u6027\u7814\u7a76\u76f4\u63a5\u50ac\u751f\u4e86\u73b0\u4ee3\u8ba1\u7b97\u7406\u8bba(\u8ba1\u7b97\u7406\u8bba\u8bde\u751f)\u3002\u901a\u8fc7\u56fe\u7075\u673a&#xff0c;\u4eba\u4eec\u8ba4\u8bc6\u5230\u6570\u5b66\u4e2d\u5b58\u5728\u672c\u8d28\u4e0a\u4e0d\u53ef\u5224\u5b9a\u7684\u95ee\u9898&#xff08;\u5982\u505c\u673a\u95ee\u9898\u3001\u67d0\u4e9b\u6570\u8bba\u95ee\u9898&#xff09;&#xff0c;\u8fd9\u91cd\u5851\u4e86\u6570\u5b66\u54f2\u5b66&#xff08;\u6570\u5b66\u7684\u8fb9\u754c&#xff09;\u3002<\/p>\n<h3>2.4. \u672a\u89e3\u95ee\u9898\u4e0e\u5ef6\u4f38<\/h3>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u90e8\u5206\u5e0c\u5c14\u4f2f\u7279\u95ee\u9898&#xff08;\u5982\u9ece\u66fc\u731c\u60f3&#xff0c;\u7b2c8\u95ee\u9898\u4e4b\u4e00&#xff09;\u4ecd\u5f85\u89e3\u51b3&#xff0c;\u800c\u56fe\u7075\u673a\u7684\u6982\u5ff5\u88ab\u7528\u4e8e\u7814\u7a76\u8fd9\u4e9b\u95ee\u9898\u7684\u53ef\u8ba1\u7b97\u6027\u3002\u4f8b\u5982&#xff1a;\u662f\u5426\u5b58\u5728\u56fe\u7075\u673a\u53ef\u5224\u5b9a\u7684\u6b65\u9aa4\u9a8c\u8bc1\u9ece\u66fc\u731c\u60f3\u7684\u6240\u6709\u975e\u5e73\u51e1\u96f6\u70b9&#xff1f;<\/p>\n<h3>2.5. \u95ee\u9898\u5c0f\u7ed3<\/h3>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u5e0c\u5c14\u4f2f\u7279\u7684\u7b2c1\u30012\u300110\u95ee\u9898\u4e0e\u56fe\u7075\u673a\u6df1\u523b\u76f8\u5173&#xff0c;\u63ed\u793a\u4e86\u6570\u5b66\u7684\u53ef\u8ba1\u7b97\u8fb9\u754c\u548c\u5f62\u5f0f\u5316\u6781\u9650\u3002\u56fe\u7075\u673a\u4e0d\u4ec5\u662f\u8ba1\u7b97\u673a\u7684\u7406\u8bba\u57fa\u77f3&#xff0c;\u4e5f\u7ec8\u7ed3\u4e86<span style=\"color:#fe2c24\">\u5e0c\u5c14\u4f2f\u7279<\/span>\u5173\u4e8e\u201c\u6570\u5b66\u5b8c\u5168\u5f62\u5f0f\u5316\u201d\u7684\u68a6\u60f3&#xff0c;\u8f6c\u800c\u5f00\u8f9f\u4e86\u53ef\u8ba1\u7b97\u6027\u7406\u8bba\u7684\u65b0\u9886\u57df\u3002<\/p>\n<\/p>\n<h2 style=\"background-color:transparent\">3. \u4e54\u59c6\u65af\u57fa&#xff08;Noam Chomsky&#xff09;\u4e0e\u56fe\u7075\u673a\u548c\u8ba1\u7b97\u7406\u8bba<\/h2>\n<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u5386\u53f2\u5230\u4e86\u4e54\u59c6\u65af\u57fa\u65f6\u4ee3\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u4e54\u59c6\u65af\u57fa&#xff08;1928\u2014&#xff09;\u662f\u7f8e\u56fd\u8457\u540d\u8bed\u8a00\u5b66\u5bb6\u3001\u54f2\u5b66\u5bb6\u3001\u8ba4\u77e5\u79d1\u5b66\u5bb6&#xff0c;\u540c\u65f6\u4e5f\u662f\u8ba1\u7b97\u7406\u8bba\u7684\u91cd\u8981\u5960\u57fa\u4eba\u4e4b\u4e00\u3002\u4ed6\u7684\u5f62\u5f0f\u8bed\u8a00\u7406\u8bba\u4e0e\u56fe\u7075\u673a\u3001\u81ea\u52a8\u673a\u7406\u8bba\u3001\u7a0b\u5e8f\u8bbe\u8ba1\u8bed\u8a00\u3001\u7f16\u8bd1\u5668\u7b49\u9886\u57df\u5bc6\u5207\u76f8\u5173&#xff0c;\u76f4\u63a5\u5f71\u54cd\u8ba1\u7b97\u673a\u79d1\u5b66\u7684\u53d1\u5c55\u3002<\/p>\n<h3>3.1. \u4e54\u59c6\u65af\u57fa\u4e0e\u5f62\u5f0f\u8bed\u8a00&#xff08;\u4e54\u59c6\u65af\u57fa\u8c31\u7cfb&#xff09;<\/h3>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u4e54\u59c6\u65af\u57fa\u57281956\u5e74\u63d0\u51fa\u5f62\u5f0f\u8bed\u8a00\u7684\u5206\u7c7b&#xff08;\u5373\u4e54\u59c6\u65af\u57fa\u8c31\u7cfb&#xff09;&#xff0c;\u5c06\u8bed\u8a00\u5206\u4e3a4\u4e2a\u5c42\u6b21&#xff0c;\u5bf9\u5e94\u4e0d\u540c\u7684\u81ea\u52a8\u673a\u6a21\u578b\u548c\u8ba1\u7b97\u80fd\u529b&#xff1a;<\/p>\n<table>\n<tr>\u8bed\u8a00\u7c7b\u578b\u6587\u6cd5\u89c4\u5219\u81ea\u52a8\u673a\u6a21\u578b\u8ba1\u7b97\u80fd\u529b\u7a0b\u5e8f\u8bbe\u8ba1\u8bed\u8a00\u4f8b\u5b50<\/tr>\n<tbody>\n<tr>\n<td>0\u578b&#xff08;\u9012\u5f52\u53ef\u679a\u4e3e\u8bed\u8a00&#xff09;<\/td>\n<td>\u65e0\u9650\u5236\u6587\u6cd5<\/td>\n<td>\u56fe\u7075\u673a<\/td>\n<td>\u53ef\u8ba1\u7b97\u95ee\u9898&#xff08;\u505c\u673a\u95ee\u9898\u4e0d\u53ef\u89e3&#xff09;<\/td>\n<td>\u7406\u8bba\u4e0a\u53ef\u63cf\u8ff0\u6240\u6709\u8ba1\u7b97<\/td>\n<\/tr>\n<tr>\n<td>1\u578b&#xff08;\u4e0a\u4e0b\u6587\u76f8\u5173\u8bed\u8a00&#xff09;<\/td>\n<td>\u4e0a\u4e0b\u6587\u76f8\u5173\u6587\u6cd5<\/td>\n<td>\u7ebf\u6027\u6709\u754c\u81ea\u52a8\u673a&#xff08;LBA&#xff09;<\/td>\n<td>\u6bd4\u56fe\u7075\u673a\u5f31&#xff0c;\u4f46\u6bd4\u4e0b\u63a8\u81ea\u52a8\u673a\u5f3a<\/td>\n<td>XML\u3001\u81ea\u7136\u8bed\u8a00\u5904\u7406<\/td>\n<\/tr>\n<tr>\n<td>2\u578b&#xff08;\u4e0a\u4e0b\u6587\u65e0\u5173\u8bed\u8a00&#xff09;<\/td>\n<td>\u4e0a\u4e0b\u6587\u65e0\u5173\u6587\u6cd5&#xff08;CFG&#xff09;<\/td>\n<td>\u4e0b\u63a8\u81ea\u52a8\u673a&#xff08;PDA&#xff09;<\/td>\n<td>\u53ef\u88ab\u6808\u5f0f\u673a\u5668\u89e3\u6790<\/td>\n<td>\u5927\u591a\u6570\u7f16\u7a0b\u8bed\u8a00&#xff08;C\u3001Python&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>3\u578b&#xff08;\u6b63\u5219\u8bed\u8a00&#xff09;<\/td>\n<td>\u6b63\u5219\u6587\u6cd5<\/td>\n<td>\u6709\u9650\u72b6\u6001\u81ea\u52a8\u673a&#xff08;FA&#xff09;<\/td>\n<td>\u6700\u7b80\u5355\u7684\u6a21\u5f0f\u5339\u914d<\/td>\n<td>\u6b63\u5219\u8868\u8fbe\u5f0f&#xff08;a*b&#xff09;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 Chomsky \u7684\u5173\u952e\u8d21\u732e\u5728\u4e8e\u8bc1\u660e\u4e86\u4e0d\u540c\u6587\u6cd5\u5bf9\u5e94\u4e0d\u540c\u8ba1\u7b97\u6a21\u578b&#xff0c;\u4e3a\u7f16\u8bd1\u5668\u8bbe\u8ba1\u63d0\u4f9b\u7406\u8bba\u57fa\u7840\u3002\u4f8b\u5982&#xff0c;\u4e0a\u4e0b\u6587\u65e0\u5173\u6587\u6cd5&#xff08;CFG&#xff09; \u662f\u7f16\u7a0b\u8bed\u8a00\u8bed\u6cd5\u5206\u6790&#xff08;\u5982BNF\u8303\u5f0f&#xff09;\u7684\u6838\u5fc3\u3002<\/p>\n<\/p>\n<h3>3.2. \u4e54\u59c6\u65af\u57fa\u4e0e\u56fe\u7075\u673a\u7684\u5173\u7cfb<\/h3>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u56fe\u7075\u673a&#xff08;1936&#xff09;\u662f\u6700\u901a\u7528\u7684\u8ba1\u7b97\u6a21\u578b&#xff0c;\u53ef\u8ba1\u7b97\u6240\u6709\u9012\u5f52\u53ef\u679a\u4e3e\u8bed\u8a00&#xff08;\u4e54\u59c6\u65af\u57fa0\u578b\u8bed\u8a00&#xff09;\u3002<\/p>\n<p>\u4e54\u59c6\u65af\u57fa\u8c31\u7cfb\u63ed\u793a\u4e86\u56fe\u7075\u5b8c\u5907\u6027&#xff0c;\u5373\u4efb\u4f550\u578b\u8bed\u8a00\u5747\u53ef\u7531\u56fe\u7075\u673a\u5904\u7406&#xff08;\u5982\u73b0\u4ee3\u7f16\u7a0b\u8bed\u8a00&#xff09;&#xff1b;\u4e5f\u63ed\u793a\u4e86\u8ba1\u7b97\u9650\u5236&#xff1a;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 <span style=\"color:#4da8ee\">1\u578b\u8bed\u8a00&#xff08;LBA&#xff09;<\/span>\u6bd4\u56fe\u7075\u673a\u5f31&#xff0c;\u4f46\u4ecd\u80fd\u5904\u7406\u590d\u6742\u6a21\u5f0f&#xff08;\u5982\u81ea\u7136\u8bed\u8a00&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 <span style=\"color:#4da8ee\">2\u578b\u8bed\u8a00&#xff08;PDA&#xff09;<\/span>\u5bf9\u5e94\u7f16\u7a0b\u8bed\u8a00\u7684\u8bed\u6cd5\u89e3\u6790&#xff08;\u5982\u7f16\u8bd1\u5668\u524d\u7aef&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 <span style=\"color:#4da8ee\">3\u578b\u8bed\u8a00&#xff08;FA&#xff09;<\/span>\u7528\u4e8e\u8bcd\u6cd5\u5206\u6790&#xff08;\u5982\u6b63\u5219\u8868\u8fbe\u5f0f\u5339\u914d&#xff09;\u3002<\/p>\n<h3>3.3. \u4e54\u59c6\u65af\u57fa\u4e0e\u81ea\u52a8\u673a\u7406\u8bba<\/h3>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u4e54\u59c6\u65af\u57fa\u7684\u5f62\u5f0f\u8bed\u8a00\u5206\u7c7b\u76f4\u63a5\u5bf9\u5e94\u81ea\u52a8\u673a\u5c42\u7ea7&#xff1a;<\/p>\n<table>\n<tr>\u81ea\u52a8\u673a\u8ba1\u7b97\u80fd\u529b\u5e94\u7528<\/tr>\n<tbody>\n<tr>\n<td>\u6709\u9650\u72b6\u6001\u81ea\u52a8\u673a&#xff08;FA&#xff09;<\/td>\n<td>\u6b63\u5219\u8bed\u8a00&#xff08;3\u578b&#xff09;<\/td>\n<td>\u8bcd\u6cd5\u5206\u6790&#xff08;Lex&#xff09;\u3001\u6b63\u5219\u8868\u8fbe\u5f0f<\/td>\n<\/tr>\n<tr>\n<td>\u4e0b\u63a8\u81ea\u52a8\u673a&#xff08;PDA&#xff09;<\/td>\n<td>\u4e0a\u4e0b\u6587\u65e0\u5173\u8bed\u8a00&#xff08;2\u578b&#xff09;<\/td>\n<td>\u8bed\u6cd5\u5206\u6790&#xff08;Yacc\u3001LR\u89e3\u6790&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u7ebf\u6027\u6709\u754c\u81ea\u52a8\u673a&#xff08;LBA&#xff09;<\/td>\n<td>\u4e0a\u4e0b\u6587\u76f8\u5173\u8bed\u8a00&#xff08;1\u578b&#xff09;<\/td>\n<td>\u590d\u6742\u6a21\u5f0f\u8bc6\u522b&#xff08;\u81ea\u7136\u8bed\u8a00\u5904\u7406&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u56fe\u7075\u673a<\/td>\n<td>\u9012\u5f52\u53ef\u679a\u4e3e\u8bed\u8a00&#xff08;0\u578b&#xff09;<\/td>\n<td>\u901a\u7528\u8ba1\u7b97&#xff08;\u7f16\u7a0b\u8bed\u8a00\u3001\u7b97\u6cd5&#xff09;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\n\u5173\u952e\u5f71\u54cd&#xff1a;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u8bcd\u6cd5\u5206\u6790&#xff08;Lexer&#xff09;&#xff1a;\u4f7f\u7528\u6709\u9650\u72b6\u6001\u81ea\u52a8\u673a&#xff08;\u5982Flex&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u8bed\u6cd5\u5206\u6790&#xff08;Parser&#xff09;&#xff1a;\u4f7f\u7528\u4e0b\u63a8\u81ea\u52a8\u673a&#xff08;\u5982Bison\u3001ANTLR&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u7f16\u8bd1\u5668\u8bbe\u8ba1&#xff1a;\u4e54\u59c6\u65af\u57fa\u4f53\u7cfb\u6307\u5bfc\u4e86\u7f16\u8bd1\u539f\u7406\u7684\u5206\u5c42\u5904\u7406&#xff08;\u8bcd\u6cd5\u2192\u8bed\u6cd5\u2192\u8bed\u4e49&#xff09;\u3002<\/p>\n<h3>3.4. \u4e54\u59c6\u65af\u57fa\u4e0e\u7a0b\u5e8f\u8bbe\u8ba1\u8bed\u8a00<\/h3>\n<p>\n\u00a0 \u00a0 \u00a0 \u00a0 \u73b0\u4ee3\u7f16\u7a0b\u8bed\u8a00\u7684\u8bbe\u8ba1\u6df1\u53d7\u4e54\u59c6\u65af\u57fa\u7406\u8bba\u5f71\u54cd\u3002\u8bed\u6cd5\u89c4\u5219\u7684\u5b9a\u4e49&#xff0c;\u4f1a\u4f7f\u7528\u4e54\u59c6\u65af\u57fa\u7684\u7406\u8bba\u3002\u4f8b\u5982&#xff0c;\u5927\u591a\u6570\u8bed\u8a00&#xff08;C\u3001Java\u3001Python&#xff09;\u4f7f\u7528\u4e0a\u4e0b\u6587\u65e0\u5173\u6587\u6cd5&#xff08;CFG&#xff09;\u5b9a\u4e49\u8bed\u6cd5\u3002\u4f8b\u5982&#xff0c;BNF&#xff08;\u5df4\u79d1\u65af\u8303\u5f0f&#xff09;\u7528\u4e8e\u63cf\u8ff0\u7f16\u7a0b\u8bed\u8a00\u7684\u8bed\u6cd5\u89c4\u5219&#xff1a;<\/p>\n<p>&lt;if-statement&gt; ::&#061; &#034;if&#034; &#034;(&#034; &lt;condition&gt; &#034;)&#034; &lt;statement&gt;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u8fd9\u540c\u65f6\u5f71\u54cd\u4e86\u7f16\u8bd1\u5668\u524d\u7aef\u7684\u5b9e\u73b0&#xff0c;\u4f8b\u5982\u8bcd\u6cd5\u5206\u6790&#xff08;\u6b63\u5219\u8868\u8fbe\u5f0f\u2192\u6709\u9650\u81ea\u52a8\u673a&#xff09;\u548c\u8bed\u6cd5\u5206\u6790&#xff08;CFG\u2192\u4e0b\u63a8\u81ea\u52a8\u673a&#xff09;\u7684\u5b9e\u73b0\u3002<\/p>\n<h3>3.5. \u4e54\u59c6\u65af\u57fa\u4e0e\u7f16\u8bd1\u5668<\/h3>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u53ef\u4ee5\u76f4\u8a00&#xff0c;\u4e54\u59c6\u65af\u57fa\u7684\u7406\u8bba\u662f\u7f16\u8bd1\u5668\u6574\u4f53\u6784\u9020\u7684\u6838\u5fc3&#xff1a;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0<span style=\"color:#4da8ee\">\u8bcd\u6cd5\u5206\u6790<\/span>&#xff08;Lexical Analysis&#xff09;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u4f7f\u7528\u6b63\u5219\u8868\u8fbe\u5f0f&#xff08;3\u578b\u8bed\u8a00&#xff09;\u5b9a\u4e49Token&#xff08;\u5982if, while, 123&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u7531\u6709\u9650\u72b6\u6001\u81ea\u52a8\u673a&#xff08;FA&#xff09;\u5b9e\u73b0&#xff08;\u5982Flex\u5de5\u5177&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0<span style=\"color:#4da8ee\">\u8bed\u6cd5\u5206\u6790<\/span>&#xff08;Syntax Analysis&#xff09;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u4f7f\u7528\u4e0a\u4e0b\u6587\u65e0\u5173\u6587\u6cd5&#xff08;2\u578b\u8bed\u8a00&#xff09;\u6784\u5efa\u62bd\u8c61\u8bed\u6cd5\u6811&#xff08;AST&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u7531\u4e0b\u63a8\u81ea\u52a8\u673a&#xff08;PDA&#xff09;\u5b9e\u73b0&#xff08;\u5982Bison\u3001LR\u89e3\u6790\u5668&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0<span style=\"color:#4da8ee\">\u8bed\u4e49\u5206\u6790\u4e0e\u4ee3\u7801\u751f\u6210<\/span><\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0\u66f4\u590d\u6742\u7684\u8bed\u8a00\u7279\u6027&#xff08;\u5982\u7c7b\u578b\u68c0\u67e5&#xff09;\u53ef\u80fd\u6d89\u53ca\u4e0a\u4e0b\u6587\u76f8\u5173&#xff08;1\u578b&#xff09;\u751a\u81f3\u9012\u5f52\u53ef\u679a\u4e3e&#xff08;0\u578b&#xff09;\u95ee\u9898\u3002<\/p>\n<h3>3.6. \u4e54\u59c6\u65af\u57fa\u5bf9\u8ba1\u7b97\u7406\u8bba\u7684\u6df1\u8fdc\u5f71\u54cd<\/h3>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u4e54\u59c6\u65af\u57fa\u5bf9\u8ba1\u7b97\u590d\u6742\u6027\u5de5\u4f5c\u5f71\u54cd\u6df1\u8fdc\u3002\u4e54\u59c6\u65af\u57fa\u8c31\u7cfb\u4e0eP vs NP\u95ee\u9898\u76f8\u5173&#xff08;\u6b63\u5219\u8bed\u8a00\u2208P&#xff0c;\u4e0a\u4e0b\u6587\u65e0\u5173\u8bed\u8a00\u2208P&#xff0c;\u4f46\u67d0\u4e9b0\u578b\u8bed\u8a00\u4e0d\u53ef\u5224\u5b9a&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u4e54\u59c6\u65af\u57fa\u7684\u751f\u6210\u8bed\u6cd5\u7406\u8bba\u5f71\u54cd\u8ba1\u7b97\u673a\u8bed\u8a00\u5b66\u3002\u7f16\u7a0b\u8bed\u8a00\u8bbe\u8ba1&#xff1a;\u51e0\u4e4e\u6240\u6709\u73b0\u4ee3\u8bed\u8a00&#xff08;C\u3001Java\u3001Python&#xff09;\u7684\u8bed\u6cd5\u90fd\u57fa\u4e8e\u4e0a\u4e0b\u6587\u65e0\u5173\u6587\u6cd5&#xff08;CFG&#xff09;\u3002<\/p>\n<h3>3.7. \u95ee\u9898\u603b\u7ed3<\/h3>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u4e54\u59c6\u65af\u57fa\u7684\u5f62\u5f0f\u8bed\u8a00\u7406\u8bba\u4e0e\u81ea\u52a8\u673a\u5206\u7c7b\u5de5\u4f5c&#xff0c;\u5960\u5b9a\u4e86\u7f16\u8bd1\u539f\u7406\u7684\u57fa\u7840&#xff08;\u8bcd\u6cd5\u5206\u6790\u2192\u8bed\u6cd5\u5206\u6790\u2192\u4ee3\u7801\u751f\u6210&#xff09;\u3002\u8fde\u63a5\u4e86\u56fe\u7075\u673a\u3001\u81ea\u52a8\u673a\u4e0e\u7f16\u7a0b\u8bed\u8a00&#xff0c;\u63ed\u793a\u8ba1\u7b97\u80fd\u529b\u7684\u5c42\u6b21\u7ed3\u6784\u3002\u76f4\u63a5\u5f71\u54cd\u7f16\u8bd1\u5668\u8bbe\u8ba1&#xff08;\u5982Lex\/Yacc\u3001ANTLR\u7b49\u5de5\u5177&#xff09;\u3002\u4ed6\u7684\u5de5\u4f5c\u4e0d\u4ec5\u662f\u7406\u8bba\u8ba1\u7b97\u673a\u79d1\u5b66\u7684\u57fa\u77f3&#xff0c;\u4e5f\u76f4\u63a5\u5851\u9020\u4e86\u73b0\u4ee3\u7f16\u7a0b\u8bed\u8a00\u548c\u7f16\u8bd1\u5668\u6280\u672f\u3002<\/p>\n<p>\u00a0<\/p>\n<h2>4.\u00a0 \u56fe\u7075\u673a&#xff08;Turing Machine, TM&#xff09;\u8be6\u89e3<\/h2>\n<p>\n\u00a0 \u00a0 \u00a0 \u00a0 \u56fe\u7075\u673a\u662f\u8ba1\u7b97\u673a\u79d1\u5b66\u7684\u7406\u8bba\u8ba1\u7b97\u6a21\u578b&#xff0c;\u7531\u963f\u5170\u00b7\u56fe\u7075&#xff08;Alan Turing&#xff09;\u4e8e1936\u5e74\u63d0\u51fa\u3002\u5b83\u5b9a\u4e49\u4e86\u201c\u53ef\u8ba1\u7b97\u6027\u201d\u7684\u6570\u5b66\u8fb9\u754c&#xff0c;\u5e76\u6210\u4e3a\u73b0\u4ee3\u8ba1\u7b97\u673a\u7684\u7406\u8bba\u57fa\u7840\u3002<\/p>\n<h3>4.1. \u56fe\u7075\u673a\u7684\u5b9a\u4e49<\/h3>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u56fe\u7075\u673a\u662f\u4e00\u4e2a\u62bd\u8c61\u7684\u6570\u5b66\u8ba1\u7b97\u8bbe\u5907&#xff0c;\u7531\u4ee5\u4e0b\u7ec4\u4ef6\u6784\u6210&#xff1a;<\/p>\n<p><span style=\"color:#4da8ee\">\u65e0\u9650\u957f\u7684\u7eb8\u5e26&#xff08;Tape&#xff09;<\/span>&#xff1a;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u88ab\u5212\u5206\u4e3a\u79bb\u6563\u7684\u683c\u5b50&#xff0c;\u6bcf\u4e2a\u683c\u5b50\u53ef\u5b58\u50a8\u4e00\u4e2a\u7b26\u53f7&#xff08;\u6765\u81ea\u6709\u9650\u5b57\u6bcd\u8868 <img decoding=\"async\" alt=\"\\\\Sigma\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100647-6889eeb76c77e.png\" \/>&#xff0c;\u5982 <img decoding=\"async\" alt=\"\\\\{0, 1, \\\\text{blank}\\\\}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100647-6889eeb7c146a.png\" \/>&#xff09;\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u8bfb\u5199\u5934&#xff08;Head&#xff09;<\/span>&#xff1a;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u53ef\u4ee5\u8bfb\u53d6\u5f53\u524d\u683c\u5b50\u7684\u7b26\u53f7&#xff0c;\u5e76\u6839\u636e\u89c4\u5219\u5199\u5165\u65b0\u7b26\u53f7\u3001\u5de6\u79fb&#xff08;L&#xff09;\u6216\u53f3\u79fb&#xff08;R&#xff09;\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u72b6\u6001\u5bc4\u5b58\u5668&#xff08;State Register&#xff09;<\/span>&#xff1a;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u4fdd\u5b58\u5f53\u524d\u72b6\u6001 <img decoding=\"async\" alt=\"q \\\\in Q\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100648-6889eeb8289c6.png\" \/>&#xff08;<img decoding=\"async\" alt=\"Q\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100648-6889eeb86bcc3.png\" \/>\u00a0\u4e3a\u6709\u9650\u72b6\u6001\u96c6&#xff09;&#xff0c;\u5305\u62ec\u4e00\u4e2a\u7279\u6b8a\u7684\u8d77\u59cb\u72b6\u6001 <img decoding=\"async\" alt=\"q_0\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100648-6889eeb8c6aaf.png\" \/>\u00a0 \u548c\u82e5\u5e72\u7ec8\u6b62\u72b6\u6001&#xff08;\u5982\u63a5\u53d7\u72b6\u6001 <img decoding=\"async\" alt=\"q_{\\\\text{accept}}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100649-6889eeb91994e.png\" \/>\u00a0 \u548c\u62d2\u7edd\u72b6\u6001 <img decoding=\"async\" alt=\"q_{\\\\text{reject}}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100649-6889eeb9573d9.png\" \/>\u00a0&#xff09;\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u8f6c\u79fb\u51fd\u6570&#xff08;Transition Function&#xff09;<\/span>&#xff1a;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u51b3\u5b9a\u673a\u5668\u7684\u884c\u4e3a&#xff0c;\u5f62\u5f0f\u4e3a&#xff1a;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<img decoding=\"async\" alt=\"\\\\delta: Q \\\\times \\\\Sigma \\\\rightarrow Q \\\\times \\\\Sigma \\\\times \\\\{L, R\\\\}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100649-6889eeb98eac6.png\" \/><br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u542b\u4e49&#xff1a;\u82e5\u5f53\u524d\u72b6\u6001\u4e3a <img decoding=\"async\" alt=\"q\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100650-6889eeba09360.png\" \/>&#xff0c;\u8bfb\u5230\u7684\u7b26\u53f7\u4e3a <img decoding=\"async\" alt=\"a\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100650-6889eeba50bcb.png\" \/>&#xff0c;\u5219\u8f6c\u79fb\u5230\u72b6\u6001 <img decoding=\"async\" alt=\"q&#039;\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100650-6889eebaa578a.png\" \/>&#xff0c;\u5199\u5165\u7b26\u53f7 <img decoding=\"async\" alt=\"a&#039;\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100650-6889eebadb36d.png\" \/>\u00a0&#xff0c;\u5e76\u79fb\u52a8\u8bfb\u5199\u5934\u3002<\/p>\n<h3>4.2. \u56fe\u7075\u673a\u7684\u5de5\u4f5c\u6d41\u7a0b<\/h3>\n<p><span style=\"color:#4da8ee\">\u521d\u59cb\u5316<\/span>&#xff1a;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u7eb8\u5e26\u8f93\u5165\u5b57\u7b26\u4e32&#xff08;\u5982 101&#xff09;&#xff0c;\u5176\u4f59\u683c\u5b50\u4e3a\u7a7a\u767d\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u8bfb\u5199\u5934\u6307\u5411\u6700\u5de6\u7aef\u7b26\u53f7&#xff0c;\u72b6\u6001\u8bbe\u4e3a <img decoding=\"async\" alt=\"q_0\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100648-6889eeb8c6aaf.png\" \/>\u00a0\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u9010\u6b65\u6267\u884c<\/span>&#xff1a;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u6839\u636e\u5f53\u524d\u72b6\u6001\u548c\u8bfb\u5230\u7684\u7b26\u53f7&#xff0c;\u67e5\u627e\u8f6c\u79fb\u51fd\u6570 <img decoding=\"async\" alt=\"\\\\delta\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100651-6889eebb2577d.png\" \/>\u00a0\u5e76\u6267\u884c\u5bf9\u5e94\u64cd\u4f5c\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u91cd\u590d\u76f4\u5230\u8fdb\u5165\u7ec8\u6b62\u72b6\u6001\u3002<\/p>\n<p><span style=\"color:#4da8ee\">\u7ec8\u6b62<\/span>&#xff1a;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u82e5\u8fdb\u5165 <img decoding=\"async\" alt=\"q_{\\\\text{accept}}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100649-6889eeb91994e.png\" \/>\u00a0&#xff0c;\u8f93\u51fa\u201c\u63a5\u53d7\u201d&#xff1b;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u82e5\u8fdb\u5165 <img decoding=\"async\" alt=\"q_{\\\\text{reject}}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100649-6889eeb9573d9.png\" \/>\u00a0 &#xff0c;\u8f93\u51fa\u201c\u62d2\u7edd\u201d&#xff1b;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u82e5\u6c38\u4e0d\u505c\u6b62&#xff08;\u5982\u65e0\u9650\u5faa\u73af&#xff09;&#xff0c;\u5219\u95ee\u9898\u201c\u4e0d\u53ef\u8ba1\u7b97\u201d\u3002<\/p>\n<p>\u00a0<\/p>\n<p>\u793a\u4f8b&#xff1a;\u5224\u65ad\u4e8c\u8fdb\u5236\u6570\u662f\u5426\u4e3a\u5076\u6570&#xff08;\u6700\u4f4e\u4f4d\u4e3a0&#xff09;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" alt=\"\\\\delta(q_0, 0) &#061; (q_{\\\\text{accept}}, 0, R)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100651-6889eebb6c01c.png\" \/><\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" alt=\"\\\\delta(q_0, 1) &#061; (q_{\\\\text{reject}}, 1, R)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100651-6889eebbc1cf1.png\" \/><\/p>\n<p>\u00a0<\/p>\n<h3>4.3. \u56fe\u7075\u673a\u7684\u5173\u952e\u6027\u8d28<\/h3>\n<h4>4.3.1.\u00a0 \u8ba1\u7b97\u901a\u7528\u6027<\/h4>\n<p>\u4e18\u5947-\u56fe\u7075\u8bba\u9898&#xff08;Church-Turing Thesis&#xff09;&#xff1a;<br \/>\n\u00a0 \u00a0 \u4efb\u4f55\u53ef\u8ba1\u7b97\u95ee\u9898\u5747\u53ef\u7531\u56fe\u7075\u673a\u89e3\u51b3\u3002\u867d\u65e0\u6cd5\u4e25\u683c\u8bc1\u660e&#xff0c;\u4f46\u88ab\u5e7f\u6cdb\u63a5\u53d7\u3002<\/p>\n<p>\u7b49\u4ef7\u6a21\u578b&#xff1a;<br \/>\n\u00a0 \u00a0 \u56fe\u7075\u673a\u4e0e\u03bb\u6f14\u7b97\u3001\u9012\u5f52\u51fd\u6570\u3001\u73b0\u4ee3\u8ba1\u7b97\u673a&#xff08;\u51af\u00b7\u8bfa\u4f9d\u66fc\u67b6\u6784&#xff09;\u5728\u8ba1\u7b97\u80fd\u529b\u4e0a\u7b49\u4ef7\u3002<\/p>\n<h4>4.3.2. \u53ef\u8ba1\u7b97\u6027\u5206\u7c7b<\/h4>\n<p>\n\u53ef\u5224\u5b9a\u95ee\u9898&#xff08;Decidable&#xff09;,\u00a0 \u5b58\u5728\u56fe\u7075\u673a\u5728\u6709\u9650\u6b65\u5185\u603b\u80fd\u7ed9\u51fa\u7b54\u6848&#xff08;\u5982\u201c\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\u201d&#xff09;\u3002<\/p>\n<p>\u4e0d\u53ef\u5224\u5b9a\u95ee\u9898&#xff08;Undecidable&#xff09;,\u00a0\u00a0\u4f8b\u5982\u505c\u673a\u95ee\u9898&#xff08;Halting Problem&#xff09;&#xff1a;\u65e0\u6cd5\u8bbe\u8ba1\u4e00\u4e2a\u56fe\u7075\u673a <img decoding=\"async\" alt=\"H\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100652-6889eebc074a0.png\" \/>&#xff0c;\u5224\u65ad\u4efb\u610f\u7a0b\u5e8f <img decoding=\"async\" alt=\"P\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100652-6889eebc5dfab.png\" \/>\u00a0\u5728\u8f93\u5165 <img decoding=\"async\" alt=\"I\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100652-6889eebca6c8a.png\" \/>\u00a0\u4e0b\u662f\u5426\u4f1a\u505c\u6b62\u3002<\/p>\n<h4>4.3.3. \u590d\u6742\u5ea6\u7c7b\u522b<\/h4>\n<p>\nP\u7c7b\u95ee\u9898,\u00a0 \u56fe\u7075\u673a\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u53ef\u89e3&#xff08;\u5982\u6392\u5e8f&#xff09;\u3002<\/p>\n<p>NP\u7c7b\u95ee\u9898,\u00a0 \u56fe\u7075\u673a\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u53ef\u9a8c\u8bc1\u89e3&#xff08;\u5982\u6570\u72ec&#xff09;\u3002<\/p>\n<p>NP\u5b8c\u5168\u95ee\u9898,\u00a0 NP\u4e2d\u6700\u96be\u7684\u95ee\u9898&#xff08;\u5982\u65c5\u884c\u5546\u95ee\u9898&#xff09;&#xff0c;\u82e5\u4efb\u4e00NP\u5b8c\u5168\u95ee\u9898\u88ab\u8bc1\u660e\u5c5e\u4e8eP&#xff0c;\u5219P&#061;NP\u3002<\/p>\n<p>\u00a0<\/p>\n<h3>4.4. \u56fe\u7075\u673a\u7684\u53d8\u4f53\u4e0e\u6269\u5c55<\/h3>\n<h4>4.4.1. \u975e\u786e\u5b9a\u6027\u56fe\u7075\u673a&#xff08;NTM&#xff09;<\/h4>\n<p>\u5141\u8bb8\u8f6c\u79fb\u51fd\u6570\u6709\u591a\u4e2a\u53ef\u80fd\u52a8\u4f5c&#xff0c;\u673a\u5668\u201c\u731c\u6d4b\u201d\u6b63\u786e\u8def\u5f84\u3002<\/p>\n<p>\u4e0e\u786e\u5b9a\u6027\u56fe\u7075\u673a&#xff08;DTM&#xff09;\u7b49\u4ef7&#xff0c;\u4f46\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u540c&#xff08;NP\u95ee\u9898\u5728NTM\u4e0a\u53ef\u591a\u9879\u5f0f\u65f6\u95f4\u6c42\u89e3&#xff09;\u3002<\/p>\n<h4>4.4.2. \u591a\u5e26\u56fe\u7075\u673a<\/h4>\n<p>\u4f7f\u7528\u591a\u6761\u7eb8\u5e26&#xff0c;\u8bfb\u5199\u5934\u72ec\u7acb\u79fb\u52a8\u3002\u7b49\u4ef7\u4e8e\u5355\u5e26\u56fe\u7075\u673a&#xff0c;\u4f46\u53ef\u63d0\u5347\u65f6\u95f4\u6548\u7387&#xff08;\u5982\u65f6\u95f4 <img decoding=\"async\" alt=\"O(n)\" class=\"mathcode\" src=\"2025-07-30kxxwmgz03ei.png\" \/>\u00a0\u53d8\u4e3a <img decoding=\"async\" alt=\"O(n\/\\\\log n)\" class=\"mathcode\" src=\"2025-07-30pb1mydmxpx5.png\" \/>&#xff09;\u3002<\/p>\n<h4>4.4.3.\u00a0 \u91cf\u5b50\u56fe\u7075\u673a&#xff08;QTM&#xff09;<\/h4>\n<p>\u7eb8\u5e26\u548c\u72b6\u6001\u4e3a\u91cf\u5b50\u6bd4\u7279&#xff0c;\u8f6c\u79fb\u51fd\u6570\u4e3a\u5e7a\u6b63\u7b97\u5b50\u3002\u53ef\u89e3\u51b3\u7ecf\u5178TM\u96be\u89e3\u95ee\u9898&#xff08;\u5982Shor\u7b97\u6cd5&#xff09;&#xff0c;\u8ba1\u7b97\u590d\u6742\u5ea6\u7c7b\u4e3a BQP\u3002<\/p>\n<h3>4.5. \u56fe\u7075\u673a\u7684\u529f\u80fd\u793a\u4f8b<\/h3>\n<h4>4.5.1 \u7b97\u672f\u8fd0\u7b97<\/h4>\n<p>\u52a0\u6cd5&#xff1a;\u8f93\u5165 #a#b#&#xff08;a, ba,b \u4e3a\u4e8c\u8fdb\u5236\u6570&#xff09;&#xff0c;\u901a\u8fc7\u72b6\u6001\u8f6c\u79fb\u9010\u4f4d\u8ba1\u7b97\u5e76\u5904\u7406\u8fdb\u4f4d\u3002<\/p>\n<p>\u4e58\u6cd5&#xff1a;\u9700\u66f4\u590d\u6742\u7684\u72b6\u6001\u8bbe\u8ba1&#xff0c;\u5229\u7528\u591a\u5e26\u56fe\u7075\u673a\u4f18\u5316\u3002<\/p>\n<h4>4.5.2 \u8bed\u8a00\u8bc6\u522b<\/h4>\n<p>\u5224\u5b9a\u56de\u6587&#xff08;Palindrome&#xff09;, \u68c0\u67e5\u8f93\u5165\u5b57\u7b26\u4e32\u662f\u5426\u6b63\u53cd\u76f8\u540c&#xff08;\u5982 madam&#xff09;\u3002<br \/>\n\u6b65\u9aa4&#xff1a;<\/p>\n<p>\u00a0 \u00a0 step1.\u00a0 \u590d\u5236\u8f93\u5165\u5230\u7b2c\u4e8c\u6761\u7eb8\u5e26\u3002<\/p>\n<p>\u00a0 \u00a0 step2.\u00a0 \u53cd\u8f6c\u7b2c\u4e8c\u6761\u7eb8\u5e26\u3002<\/p>\n<p>\u00a0 \u00a0 step3.\u00a0 \u9010\u5b57\u7b26\u6bd4\u8f83\u3002<\/p>\n<h4>4.5.3 \u6a21\u62df\u7b97\u6cd5<\/h4>\n<p>\u901a\u7528\u56fe\u7075\u673a&#xff08;UTM&#xff09;&#xff1a;<br \/>\n\u00a0 \u00a0 \u53ef\u6a21\u62df\u4efb\u4f55\u5176\u4ed6\u56fe\u7075\u673a&#xff0c;\u539f\u7406\u7c7b\u4f3c\u73b0\u4ee3\u8ba1\u7b97\u673a\u7684\u201c\u7a0b\u5e8f\u5b58\u50a8\u201d\u6982\u5ff5\u3002<br \/>\n\u8f93\u5165\u683c\u5f0f&#xff1a;&lt;\u7f16\u7801\u540e\u7684TM\u63cf\u8ff0&gt;#\u8f93\u5165\u5b57\u7b26\u4e32#\u3002<\/p>\n<h3>4.6. \u56fe\u7075\u673a\u7684\u5c40\u9650\u6027<\/h3>\n<p>\u7269\u7406\u9650\u5236, \u65e0\u9650\u7eb8\u5e26\u65e0\u6cd5\u771f\u5b9e\u5b9e\u73b0&#xff0c;\u4f46\u53ef\u901a\u8fc7\u201c\u5916\u5b58\u6269\u5c55\u201d\u8fd1\u4f3c&#xff08;\u5982\u786c\u76d8&#xff09;\u3002<\/p>\n<p>\u590d\u6742\u5ea6\u7206\u70b8,\u00a0\u5373\u4f7f\u53ef\u8ba1\u7b97\u7684\u95ee\u9898&#xff08;\u5982\u56fd\u9645\u8c61\u68cb&#xff09;&#xff0c;\u4e5f\u53ef\u80fd\u56e0\u65f6\u95f4\/\u7a7a\u95f4\u590d\u6742\u5ea6\u8fc7\u9ad8\u800c\u5b9e\u9645\u4e0d\u53ef\u884c\u3002<\/p>\n<h3>4.7. \u56fe\u7075\u673a\u7684\u610f\u4e49<\/h3>\n<p>\u7406\u8bba\u5c42\u9762, \u5b9a\u4e49\u4e86\u8ba1\u7b97\u7684\u6570\u5b66\u8fb9\u754c&#xff0c;\u4e3a\u53ef\u8ba1\u7b97\u6027\u7406\u8bba\u5960\u57fa\u3002<\/p>\n<p>\u5de5\u7a0b\u5c42\u9762,\u00a0\u51af\u00b7\u8bfa\u4f9d\u66fc\u67b6\u6784\u7684\u8ba1\u7b97\u673a\u662f\u56fe\u7075\u673a\u7684\u7269\u7406\u5b9e\u73b0\u3002<\/p>\n<p>\u54f2\u5b66\u5c42\u9762,\u00a0\u5f15\u53d1\u201c\u673a\u5668\u80fd\u5426\u601d\u8003\u201d\u7684\u8ba8\u8bba&#xff08;\u56fe\u7075\u6d4b\u8bd5&#xff09;\u3002<\/p>\n<\/p>\n<h3>4.8. \u603b\u7ed3\u8868&#xff1a;\u56fe\u7075\u673a\u6838\u5fc3\u8981\u70b9<\/h3>\n<table>\n<tr>\u7ec4\u4ef6\u63cf\u8ff0\u793a\u4f8b<\/tr>\n<tbody>\n<tr>\n<td>\u7eb8\u5e26<\/td>\n<td>\u65e0\u9650\u957f&#xff0c;\u5b58\u50a8\u7b26\u53f7<\/td>\n<td>&#8230;\u7a7a\u767d,0,1,1,\u7a7a\u767d,&#8230;<\/td>\n<\/tr>\n<tr>\n<td>\u8bfb\u5199\u5934<\/td>\n<td>\u8bfb\u53d6\/\u5199\u5165\u7b26\u53f7\u5e76\u79fb\u52a8<\/td>\n<td>\u5f53\u524d\u6307\u5411\u7b2c\u4e8c\u4e2a\u683c\u5b50&#xff08;\u7b26\u53f7\u00a01&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u72b6\u6001\u5bc4\u5b58\u5668<\/td>\n<td>\u5f53\u524d\u72b6\u6001&#xff08;\u5982\u00a0<img decoding=\"async\" alt=\"q_0, q_1\" class=\"mathcode\" src=\"2025-07-301ievd1uksfg.png\" \/>\u200b&#xff09;<\/td>\n<td>\u8d77\u59cb\u72b6\u6001\u00a0<img decoding=\"async\" alt=\"q_0\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730100648-6889eeb8c6aaf.png\" \/>\u200b<\/td>\n<\/tr>\n<tr>\n<td>\u8f6c\u79fb\u51fd\u6570<\/td>\n<td>\u89c4\u5219\u8868&#xff0c;\u51b3\u5b9a\u4e0b\u4e00\u6b65\u52a8\u4f5c<\/td>\n<td><img decoding=\"async\" alt=\"\\\\delta(q_0, 1) &#061; (q_1, 0, R)\" class=\"mathcode\" src=\"2025-07-30axac2wq04ds.png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>4.9. \u56fe\u7075\u673a\u4e0e\u8ba1\u7b97\u673a\u7684\u5bf9\u5e94\u5173\u7cfb<\/h3>\n<table>\n<tr>\u56fe\u7075\u673a\u6982\u5ff5\u8ba1\u7b97\u673a\u5b9e\u73b0<\/tr>\n<tbody>\n<tr>\n<td>\u7eb8\u5e26<\/td>\n<td>\u5185\u5b58&#xff08;RAM&#043;\u786c\u76d8&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u8bfb\u5199\u5934<\/td>\n<td>CPU\u7684\u6307\u4ee4\u6307\u9488&#xff08;IP&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u72b6\u6001\u5bc4\u5b58\u5668<\/td>\n<td>CPU\u7684\u5f53\u524d\u7a0b\u5e8f\u72b6\u6001&#xff08;\u5bc4\u5b58\u5668&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u8f6c\u79fb\u51fd\u6570<\/td>\n<td><span style=\"color:#fe2c24\">\u673a\u5668\u6307\u4ee4<\/span>\u96c6&#xff08;\u5982x86&#xff09;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u56fe\u7075\u673a\u4e0d\u4ec5\u662f\u7406\u8bba\u5de5\u5177&#xff0c;\u66f4\u662f\u7406\u89e3\u8ba1\u7b97\u672c\u8d28\u7684\u94a5\u5319\u3002<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb545\u6b21\uff0c\u70b9\u8d5e17\u6b21\uff0c\u6536\u85cf8\u6b21\u3002\u5df2\u89e3\u51b3\uff1a\u95ee\u98983\u30015\u300110\u300115\u300117\u300118\uff08\u90e8\u5206\uff09\u300121\u300122\u7b49\u3002\u90e8\u5206\u89e3\u51b3\uff1a\u95ee\u98981\u30012\u30017\u30018\u30019\u300111\u300116\u300119\u300120\u7b49\u3002\u672a\u89e3\u51b3\uff1a\u9ece\u66fc\u731c\u60f3\uff08\u95ee\u98988\u4e4b\u4e00\uff09\u3001\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\uff08\u95ee\u98988\u4e4b\u4e8c\uff09\u3001\u5e0c\u5c14\u4f2f\u7279\u7b2c16\u95ee\u9898\u7684\u5b8c\u6574\u89e3\u7b49\u3002\u5e0c\u5c14\u4f2f\u7279\u768423\u4e2a\u95ee\u9898\u5851\u9020\u4e86\u73b0\u4ee3\u6570\u5b66\u7684\u683c\u5c40\uff0c\u63a8\u52a8\u4e86\u6570\u7406\u903b\u8f91\u3001\u8ba1\u7b97\u7406\u8bba\u3001\u4ee3\u6570\u51e0\u4f55\u3001\u62d3\u6251\u5b66\u7b49\u9886\u57df\u7684\u9769\u547d\u6027\u53d1\u5c55\u30022. \u5e0c\u5c14\u4f2f\u727923\u95ee\u9898\u4e0e\u56fe\u7075\u673a\u7684\u5173\u7cfb\u4e54\u59c6\u65af\u57fa\u7684\u5f62\u5f0f\u8bed\u8a00\u7406\u8bba\u4e0e\u81ea\u52a8\u673a\u5206\u7c7b\u5de5\u4f5c\uff0c\u5960\u5b9a\u4e86\u7f16\u8bd1\u539f\u7406\u7684\u57fa\u7840\uff08\u8bcd\u6cd5\u5206\u6790\u2192\u8bed\u6cd5\u5206\u6790\u2192\u4ee3\u7801\u751f\u6210\uff09\u3002\u8fde\u63a5\u4e86\u56fe\u7075\u673a\u3001\u81ea\u52a8\u673a\u4e0e\u7f16\u7a0b\u8bed\u8a00\uff0c\u63ed\u793a\u8ba1\u7b97\u80fd\u529b\u7684\u5c42\u6b21\u7ed3\u6784\u3002<\/p>\n","protected":false},"author":2,"featured_media":49374,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[427,4805,2958],"topic":[],"class_list":["post-49394","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-427","tag-4805","tag-2958"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - 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content=\"\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb545\u6b21\uff0c\u70b9\u8d5e17\u6b21\uff0c\u6536\u85cf8\u6b21\u3002\u5df2\u89e3\u51b3\uff1a\u95ee\u98983\u30015\u300110\u300115\u300117\u300118\uff08\u90e8\u5206\uff09\u300121\u300122\u7b49\u3002\u90e8\u5206\u89e3\u51b3\uff1a\u95ee\u98981\u30012\u30017\u30018\u30019\u300111\u300116\u300119\u300120\u7b49\u3002\u672a\u89e3\u51b3\uff1a\u9ece\u66fc\u731c\u60f3\uff08\u95ee\u98988\u4e4b\u4e00\uff09\u3001\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\uff08\u95ee\u98988\u4e4b\u4e8c\uff09\u3001\u5e0c\u5c14\u4f2f\u7279\u7b2c16\u95ee\u9898\u7684\u5b8c\u6574\u89e3\u7b49\u3002\u5e0c\u5c14\u4f2f\u7279\u768423\u4e2a\u95ee\u9898\u5851\u9020\u4e86\u73b0\u4ee3\u6570\u5b66\u7684\u683c\u5c40\uff0c\u63a8\u52a8\u4e86\u6570\u7406\u903b\u8f91\u3001\u8ba1\u7b97\u7406\u8bba\u3001\u4ee3\u6570\u51e0\u4f55\u3001\u62d3\u6251\u5b66\u7b49\u9886\u57df\u7684\u9769\u547d\u6027\u53d1\u5c55\u30022. 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