blocks|key|1929995|text|嗯，基本上，对于CDCL的情况|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1929996|(CDCL+SAT求解器实现DPLL，但可以学习新的子句并按非时间顺序回溯。具有冲突分析的子句学习不会影响可靠性或完整性。冲突分析使用解决操作识别新的子句。因此，每个学习的子句可以通过一系列的解决步骤从原始的子句和其他学习的子句中推断出来。如果cN是新学习的子句，则ϕ是可满足的当且仅当ϕ∪{cN}也是可满足的。此外，修改后的回溯步骤也不会影响可靠性或完整性，因为回溯信息是从每个新学习的子句中获得的。)。(来源：Wikipedia)|offset|length|style|BOLD|1929997|它的工作原理如下：|1929998|首先选择一个分支变量x1。黄色圆圈意味着一个武断的决定。|1929999|​|1930000|📷|atomic|1930001|1930002|现在应用单元传播，其结果是x4必须为1(即True)。灰色圆圈表示单位传播期间的强制变量赋值。生成的图称为蕴涵图。|1930003|1930004|1930005|1930006|任意选择另一个分支变量x3。|1930007|1930008|1930009|1930010|应用单位传播并找到新的隐含图。|1930011|1930012|1930013|1930014|在这里，变量x8和x12分别被强制为0和1。|1930015|1930016|1930017|1930018|选择另一个分支变量x2。|1930019|1930020|1930021|1930022|找到隐含图。|1930023|1930024|1930025|1930026|选择另一个分支变量x7。|1930027|1930028|1930029|1930030|1930031|1930032|1930033|1930034|发现冲突！|1930035|1930036|1930037|1930038|找到导致这场冲突的切入点。从cut中，找到一个冲突的条件。|1930039|1930040|1930041|1930042|接受这个条件的否定，并将其作为一个子句。|1930043|1930044|1930045|1930046|将冲突子句添加到问题中。|1930047|1930048|1930049|1930050|不按时间顺序向后跳到适当的决策层。|1930051|1930052|1930053|1930054|向后跳转并相应地设置变量值。|1930055|1930056|1930057|(答案完全来自Wikipedia:+Conflict-Driven_Clause_Learning#Example)|1930058|以下是使用CDCL算法的解算器的列表(肯定不是完整的)，您应该查看它们：|1930059|1930060|MiniSAT.|unordered-list-item|1930061|Zchaff+SAT.|1930062|Z3.|1930063|ManySAT.|1930064|1930065|entityMap|0|LINK|mutability|MUTABLE|url|https://en.wikipedia.org/wiki/Conflict-Driven_Clause_Learning#Example|1|IMAGE|IMMUTABLE|imageUrl|https://ask.qcloudimg.com/http-save/yehe-900000/c5d95af092c661a976fdcc2dc773ff49.png|imageAlt|2|https://ask.qcloudimg.com/http-save/yehe-900000/47af00f0d09f3f5022d45e618a2217e9.png|3|https://ask.qcloudimg.com/http-save/yehe-900000/5c3c5da50d2abf84909fc6adfb58abbc.png|4|https://ask.qcloudimg.com/http-save/yehe-900000/058355851e5c469c1363592ad6c3a04f.png|5|https://ask.qcloudimg.com/http-save/yehe-900000/bef188e027431ad7decf7f54d915571c.png|6|https://ask.qcloudimg.com/http-save/yehe-900000/c615689e384b649ec613873951a05b0a.png|7|https://ask.qcloudimg.com/http-save/yehe-900000/04f7a88ae0d3e786e2f66f69dd6e884d.png|8|https://ask.qcloudimg.com/http-save/yehe-900000/7ec1eabff767e68b8c8ed8a11cb00ce6.png|9|https://ask.qcloudimg.com/http-save/yehe-900000/4e5abc09b58f67d6dbf35df0beaeb2af.png|10|https://ask.qcloudimg.com/http-save/yehe-900000/d88a6670d4b92776978ac3437838eb67.png|11|https://ask.qcloudimg.com/http-save/yehe-900000/c3e00b38d69955f1f9d7a858d55e9e1e.png|12|https://ask.qcloudimg.com/http-save/yehe-900000/5b1583a9f70d7edd13737097ef227a02.png|13|https://ask.qcloudimg.com/http-save/yehe-900000/63451e76984ef9e001d8afa4d636d069.png|14|https://ask.qcloudimg.com/http-save/yehe-900000/62d33ad48be594aa64cb77b9cfef920f.png|15|https://ask.qcloudimg.com/http-save/yehe-900000/f048907772f90d42fd8495618dde6147.png|16|17|http://minisat.se/|18|http://www.princeton.edu/~chaff/zchaff.html|19|https://z3.codeplex.com/|20|http://www.cril.univ-artois.fr/~jabbour/manysat.htm^0|0|1|H|5R|9|0|0|0|0|0|0|1|1|0|0|0|0|0|1|2|0|0|0|0|0|1|3|0|0|0|0|0|1|4|0|0|0|0|0|1|5|0|0|0|0|0|1|6|0|0|0|0|0|1|7|0|0|0|0|0|1|8|0|0|0|0|0|1|9|0|0|0|0|0|1|A|0|0|0|0|0|1|B|0|0|0|0|0|1|C|0|0|0|0|0|1|D|0|0|0|0|0|1|E|0|0|0|0|0|1|F|0|7|1E|G|0|0|0|0|7|H|0|0|A|I|0|0|2|J|0|0|7|K|0|0^^$0|@$1|2|3|4|5|6|7|4H|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|4I|8|@$D|4J|E|4K|F|G]]|9|@$D|4L|E|4M|1|4N]]|A|$]]|$1|H|3|I|5|6|7|4O|8|@]|9|@]|A|$]]|$1|J|3|K|5|6|7|4P|8|@]|9|@]|A|$]]|$1|L|3|M|5|6|7|4Q|8|@]|9|@]|A|$]]|$1|N|3|O|5|P|7|4R|8|@]|9|@$D|4S|E|4T|1|4U]]|A|$]]|$1|Q|3|M|5|6|7|4V|8|@]|9|@]|A|$]]|$1|R|3|S|5|6|7|4W|8|@]|9|@]|A|$]]|$1|T|3|M|5|6|7|4X|8|@]|9|@]|A|$]]|$1|U|3|O|5|P|7|4Y|8|@]|9|@$D|4Z|E|50|1|51]]|A|$]]|$1|V|3|M|5|6|7|52|8|@]|9|@]|A|$]]|$1|W|3|X|5|6|7|53|8|@]|9|@]|A|$]]|$1|Y|3|M|5|6|7|54|8|@]|9|@]|A|$]]|$1|Z|3|O|5|P|7|55|8|@]|9|@$D|56|E|57|1|58]]|A|$]]|$1|10|3|M|5|6|7|59|8|@]|9|@]|A|$]]|$1|11|3|12|5|6|7|5A|8|@]|9|@]|A|$]]|$1|13|3|M|5|6|7|5B|8|@]|9|@]|A|$]]|$1|14|3|O|5|P|7|5C|8|@]|9|@$D|5D|E|5E|1|5F]]|A|$]]|$1|15|3|M|5|6|7|5G|8|@]|9|@]|A|$]]|$1|16|3|17|5|6|7|5H|8|@]|9|@]|A|$]]|$1|18|3|M|5|6|7|5I|8|@]|9|@]|A|$]]|$1|19|3|O|5|P|7|5J|8|@]|9|@$D|5K|E|5L|1|5M]]|A|$]]|$1|1A|3|M|5|6|7|5N|8|@]|9|@]|A|$]]|$1|1B|3|1C|5|6|7|5O|8|@]|9|@]|A|$]]|$1|1D|3|M|5|6|7|5P|8|@]|9|@]|A|$]]|$1|1E|3|O|5|P|7|5Q|8|@]|9|@$D|5R|E|5S|1|5T]]|A|$]]|$1|1F|3|M|5|6|7|5U|8|@]|9|@]|A|$]]|$1|1G|3|1H|5|6|7|5V|8|@]|9|@]|A|$]]|$1|1I|3|M|5|6|7|5W|8|@]|9|@]|A|$]]|$1|1J|3|O|5|P|7|5X|8|@]|9|@$D|5Y|E|5Z|1|60]]|A|$]]|$1|1K|3|M|5|6|7|61|8|@]|9|@]|A|$]]|$1|1L|3|1M|5|6|7|62|8|@]|9|@]|A|$]]|$1|1N|3|M|5|6|7|63|8|@]|9|@]|A|$]]|$1|1O|3|O|5|P|7|64|8|@]|9|@$D|65|E|66|1|67]]|A|$]]|$1|1P|3|M|5|6|7|68|8|@]|9|@]|A|$]]|$1|1Q|3|1H|5|6|7|69|8|@]|9|@]|A|$]]|$1|1R|3|M|5|6|7|6A|8|@]|9|@]|A|$]]|$1|1S|3|O|5|P|7|6B|8|@]|9|@$D|6C|E|6D|1|6E]]|A|$]]|$1|1T|3|M|5|6|7|6F|8|@]|9|@]|A|$]]|$1|1U|3|1V|5|6|7|6G|8|@]|9|@]|A|$]]|$1|1W|3|M|5|6|7|6H|8|@]|9|@]|A|$]]|$1|1X|3|O|5|P|7|6I|8|@]|9|@$D|6J|E|6K|1|6L]]|A|$]]|$1|1Y|3|M|5|6|7|6M|8|@]|9|@]|A|$]]|$1|1Z|3|20|5|6|7|6N|8|@]|9|@]|A|$]]|$1|21|3|M|5|6|7|6O|8|@]|9|@]|A|$]]|$1|22|3|O|5|P|7|6P|8|@]|9|@$D|6Q|E|6R|1|6S]]|A|$]]|$1|23|3|M|5|6|7|6T|8|@]|9|@]|A|$]]|$1|24|3|25|5|6|7|6U|8|@]|9|@]|A|$]]|$1|26|3|M|5|6|7|6V|8|@]|9|@]|A|$]]|$1|27|3|O|5|P|7|6W|8|@]|9|@$D|6X|E|6Y|1|6Z]]|A|$]]|$1|28|3|M|5|6|7|70|8|@]|9|@]|A|$]]|$1|29|3|2A|5|6|7|71|8|@]|9|@]|A|$]]|$1|2B|3|M|5|6|7|72|8|@]|9|@]|A|$]]|$1|2C|3|O|5|P|7|73|8|@]|9|@$D|74|E|75|1|76]]|A|$]]|$1|2D|3|M|5|6|7|77|8|@]|9|@]|A|$]]|$1|2E|3|2F|5|6|7|78|8|@]|9|@]|A|$]]|$1|2G|3|M|5|6|7|79|8|@]|9|@]|A|$]]|$1|2H|3|O|5|P|7|7A|8|@]|9|@$D|7B|E|7C|1|7D]]|A|$]]|$1|2I|3|M|5|6|7|7E|8|@]|9|@]|A|$]]|$1|2J|3|2K|5|6|7|7F|8|@]|9|@]|A|$]]|$1|2L|3|M|5|6|7|7G|8|@]|9|@]|A|$]]|$1|2M|3|O|5|P|7|7H|8|@]|9|@$D|7I|E|7J|1|7K]]|A|$]]|$1|2N|3|2O|5|6|7|7L|8|@]|9|@$D|7M|E|7N|1|7O]]|A|$]]|$1|2P|3|2Q|5|6|7|7P|8|@]|9|@]|A|$]]|$1|2R|3|-4|5|6|7|7Q|8|@]|9|@]|A|$]]|$1|2S|3|2T|5|2U|7|7R|8|@]|9|@$D|7S|E|7T|1|7U]]|A|$]]|$1|2V|3|2W|5|2U|7|7V|8|@]|9|@$D|7W|E|7X|1|7Y]]|A|$]]|$1|2X|3|2Y|5|2U|7|7Z|8|@]|9|@$D|80|E|81|1|82]]|A|$]]|$1|2Z|3|30|5|2U|7|83|8|@]|9|@$D|84|E|85|1|86]]|A|$]]|$1|31|3|-4|5|6|7|87|8|@]|9|@]|A|$]]|$1|32|3|-4|5|6|7|88|8|@]|9|@]|A|$]]]|33|$34|$5|35|36|37|A|$38|39]]|3A|$5|3B|36|3C|A|$3D|3E|3F|-4]]|3G|$5|3B|36|3C|A|$3D|3H|3F|-4]]|3I|$5|3B|36|3C|A|$3D|3J|3F|-4]]|3K|$5|3B|36|3C|A|$3D|3L|3F|-4]]|3M|$5|3B|36|3C|A|$3D|3N|3F|-4]]|3O|$5|3B|36|3C|A|$3D|3P|3F|-4]]|3Q|$5|3B|36|3C|A|$3D|3R|3F|-4]]|3S|$5|3B|36|3C|A|$3D|3T|3F|-4]]|3U|$5|3B|36|3C|A|$3D|3V|3F|-4]]|3W|$5|3B|36|3C|A|$3D|3X|3F|-4]]|3Y|$5|3B|36|3C|A|$3D|3Z|3F|-4]]|40|$5|3B|36|3C|A|$3D|41|3F|-4]]|42|$5|3B|36|3C|A|$3D|43|3F|-4]]|44|$5|3B|36|3C|A|$3D|45|3F|-4]]|46|$5|3B|36|3C|A|$3D|47|3F|-4]]|48|$5|35|36|37|A|$38|39]]|49|$5|35|36|37|A|$38|4A]]|4B|$5|35|36|37|A|$38|4C]]|4D|$5|35|36|37|A|$38|4E]]|4F|$5|35|36|37|A|$38|4G]]]]

Well, basically, for the case of CDCL 

(CDCL SAT solvers implement DPLL, but can learn new clauses and backtrack non-chronologically. Clause learning with conflict analysis does not affect soundness or completeness. Conflict analysis identifies new clauses using the resolution operation. Therefore each learnt clause can be inferred from the original clauses and other learnt clauses by a sequence of resolution steps. If cN is the new learnt clause, then ϕ is satisfiable if and only if ϕ ∪ {cN} is also satisfiable. Moreover, the modified backtracking step also does not affect soundness or completeness, since backtracking information is obtained from each new learnt clause.).(Source : <a href="https://en.wikipedia.org/wiki/Conflict-Driven_Clause_Learning#Example" rel="nofollow noreferrer">Wikipedia</a>) 

it's working as follow : 

At first pick a branching variable, x1. A yellow circle means an arbitrary decision.

<img src="https://i.stack.imgur.com/v5YLH.png" alt="enter image description here">

Now apply unit propagation, which yields that x4 must be 1 (i.e. True). A gray circle means a forced variable assignment during unit propagation. The resulting graph is called implication graph.

<img src="https://i.stack.imgur.com/w1gIR.png" alt="enter image description here">

Arbitrarily pick another branching variable, x3.

<img src="https://i.stack.imgur.com/ScBEM.png" alt="enter image description here">

Apply unit propagation and find the new implication graph.

<img src="https://i.stack.imgur.com/ybau6.png" alt="enter image description here">

Here the variable x8 and x12 are forced to be 0 and 1, respectively.

<img src="https://i.stack.imgur.com/HEAuw.png" alt="enter image description here">

Pick another branching variable, x2.

<img src="https://i.stack.imgur.com/wlyLh.png" alt="enter image description here">

Find implication graph.

<img src="https://i.stack.imgur.com/0czvv.png" alt="enter image description here">

Pick another branching variable, x7.

<img src="https://i.stack.imgur.com/KLVzI.png" alt="enter image description here">

Find implication graph.

<img src="https://i.stack.imgur.com/JO5pE.png" alt="enter image description here">

Found a conflict!

<img src="https://i.stack.imgur.com/2I5DG.png" alt="enter image description here">

Find the cut that lead to this conflict. From the cut, find a conflicting condition.

<img src="https://i.stack.imgur.com/epmtw.png" alt="enter image description here">

Take the negation of this condition and make it a clause.

<img src="https://i.stack.imgur.com/bmbti.png" alt="enter image description here">

Add the conflict clause to the problem.

<img src="https://i.stack.imgur.com/I6e8Z.png" alt="enter image description here">

Non-chronological back jump to appropriate decision level.

<img src="https://i.stack.imgur.com/3jULI.png" alt="enter image description here">

Back jump and set variable values accordingly.

<img src="https://i.stack.imgur.com/mfQpG.png" alt="enter image description here"> 

(Answer completely from <a href="https://en.wikipedia.org/wiki/Conflict-Driven_Clause_Learning#Example" rel="nofollow noreferrer">Wikipedia: Conflict-Driven_Clause_Learning#Example</a>)

Here is a list (not complete for sure) of solvers who use the CDCL algorithm, you should check them out :

<ul>
<li><a href="http://minisat.se/" rel="nofollow noreferrer">MiniSAT</a>. </li>
<li><a href="http://www.princeton.edu/~chaff/zchaff.html" rel="nofollow noreferrer">Zchaff SAT</a>. </li>
<li><a href="https://z3.codeplex.com/" rel="nofollow noreferrer">Z3</a>. </li>
<li><a href="http://www.cril.univ-artois.fr/~jabbour/manysat.htm" rel="nofollow noreferrer">ManySAT</a>.</li>
</ul>

Here is a very simple cnf instance as (x1 or x2 or x3)&amp;(x1 or x2)&amp;(x2 or x3)and the formula is definitely satisfiable, the solution is x1 = x2 = x3 = 1, that is enough. So,my question is how the solver produce the assignment using DPLL or other procedure? Thanks.

How does the SAT solver produce the model(assignment[s])?

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

文章

问答

视频

教程

学习中心

腾讯云实验室

直播

竞赛

腾讯云代码分析专区

腾讯iOA零信任安全管理系统专区

腾讯云架构师技术同盟交流圈

腾讯云数据库专区

腾讯云智能顾问专区

腾讯云原生专区

腾讯混元专区

腾讯云TCE专区

腾讯云Lighthouse专区

腾讯云HAI专区

腾讯云Edgeone专区

腾讯云存储专区

腾讯云智能专区

腾讯轻联专区 

腾讯云开发专区

TAPD专区

腾讯轻量云游戏服专区

腾讯云最具价值专家

腾讯云架构师技术同盟

腾讯云创作之星

腾讯云开发者先锋

腾讯云AI代码助手

云原生构建

TAPD 敏捷项目管理

Cloud Studio

SDK中心

API中心

命令行工具

功能1上新10个字符

功能2描述100个字符功能2描述100个字符功能2描述100个字符功能2描述100个字符功能2描述100个字符功能2描述100个字符功能2描述100个字符功能2描述100个字符功能2描述100个字符。

功能2上新100个字符功能2上新100个字符功能2上新100个字符功能2上新100个字符功能2上新100个字符功能2上新100个字符功能2上新100个字符功能2上新100个字符功能2上新100个字符。

功能5描述100个字符功能5描述100个字符功能5描述100个字符功能5描述100个字符功能5描述100个字符功能5描述100个字符

功能5上新100个字符功能5上新100个字符功能5上新100个字符功能5上新100个字符功能5上新100个字符功能5上新100个字符功能5上新100个字符功能5上新100个字符功能5上新100个字符功能5上新100个字符

功能4上新

文章&问答评论现已支持表情

全新交互，全新视觉，新增快捷键、悬浮工具栏、高亮块等功能并同时优化现有功能，全面提升创作效率和体验

社区富文本编辑器全新改版！诚邀体验～ 

精选全网热门MCP server，让你的AI更好用 🚀

💥开发者 MCP广场重磅上线！

涵盖代码开发、场景应用、自动测试全流程，助你从零构建专属AI助手

一站式MCP教程库，解锁AI应用新玩法

聚焦“写作效率、视觉美观与运行性能”三方面进行全面升级，为您提供更高效、稳定的创作环境

社区富文本&Markdown编辑器全新改版上线，欢迎大家体验!

诚挚邀请您参与本次调研，分享您的真实使用感受与建议。您的反馈至关重要，感谢您的支持与参与！

社区新版编辑器体验调研

这里有一个非常简单的cnf实例，如(x1或x2或x3)&(x1或x2)&(x2或x3 )，公式肯定是可满足的，解为x1 = x2 =x3= 1，这就足够了。因此，我的问题是求解器如何使用DPLL或其他过程生成赋值？谢谢。

问SAT求解器如何生成模型(assignment[s])？
EN

回答 1

Stack Overflow用户

社区

活动

圈层

关于

腾讯云开发者

热门产品

热门推荐

更多推荐

问SAT求解器如何生成模型(assignment[s])？EN