为SAT4J解算器输入CNF

Question

我是一个全新的sat4j求解器..

它说一些cnf文件应该作为输入

是否有任何可能的方法将规则作为输入并获得它是否可满足？

我的规则将是那种:

Problem = ( 

     ( staff_1         <=>          staff_2 ) AND 
     ( doctor_1        <=>      physician_2 ) 

) AND ( 

     ( staff_1         AND         doctor_1 )

)  AND (

    NOT( ward_2             AND physician_2 ) AND 
    NOT( clinic_2           AND physician_2 ) AND 
    NOT( admission_record_2 AND physician_2 ) 

) AND (

   NOT( hospital_2          AND physician_2 ) AND 
   NOT( department_2        AND physician_2 ) AND 
   NOT( staff_2             AND physician_2 )
)

有人可以帮我解决这个问题,使用sat4j求解器吗？

Answer 1

如果您想使用SAT4J,您需要转换您的问题CNF格式.

首先需要将这些文本变量转换为整数.

1 = staff_1
2 = staff_2
3 = doctor_1
4 = physician_2
5 = ward_2 
6 = clinic_2
7 = admission_record_2 
8 = hospital_2
9 = department_2 

然后,以下是将问题转换为CNF格式时需要了解的规则和语法.

Syntax: 
    OR           = a space 
    AND          = a newline
    NOT          = -

Rules from De Morgan's laws: 
    A <=> B      = (A => B) AND (B => A)
    A  => B      = NOT(A) OR  B
    NOT(A AND B) = NOT(A) OR  NOT(B) 
    NOT(A OR  B) = NOT(A) AND NOT(B) 

这是你的示例问题,格式化应该由SAT4J读取.

(请参阅DIMACS以了解有关此格式的更多信息).

 c you can put comment here. 
 c Formatted by StackOverFlow.
 p cnf 9 12
 -1 2 0
 -2 1 0 
 -3 4 0 
 -4 3 0 
  1 0 
  3 0 
 -5 -4 0 
 -6 -4 0 
 -7 -4 0 
 -8 -4 0 
 -9 -4 0 
 -2 -4 0

我让你在这个小例子上运行SAT4J,

它会给你解决方案SATISFIABLExor UNSATISFIABLE.

你要做什么来使用SAT4J的总结很少:

 * Transform your `text_n` into a number.
 * Use the rule that I gave you to transform your problem into CNF.
 * Write the definition of your problem `p cnf nbVariables nbClauses`
 * Write everything in a FILE and run SAT4J on this file.

我希望这个循序渐进的例子能帮助很少的人.

Answer 2

您查看过他们网站上的SAT4J Howto吗？它包含一个指向Postscript 文档的链接，该文档详细介绍了 CNF 格式的语义。该格式似乎支持您在示例中使用的所有运算符（“<->”除外），但这可能是这个特定“非官方”文档中的遗漏。