cl-sat

2022-04-01

Common Lisp API to Boolean SAT Solvers

Upstream URL

github.com/cl-model-languages/cl-sat

Author

Masataro Asai

License

LLGPL
README

1CL-SAT - Common Lisp API to Boolean SAT Solvers

https://travis-ci.org/cl-model-languages/cl-sat.svg?branch=master

This library provides a simple S-exp -> CNF translator and an API to Boolean SAT solvers. It does not provide actual implementation to each solver instance by itself. Currently there are two implementations. Consult the following:

  • https://github.com/guicho271828/cl-sat.minisat
  • https://github.com/guicho271828/cl-sat.glucose

NEWS

2018/12/24
Implemented Tseytin's transformation for the input logic formula.The input S-exp can be an arbitrary logical formula that is not necessarily a CNF.
2019/1/8
Implemented a :COMPETITION keyword for the generic functionSOLVE, which accepts :year, :track, :name argumentspecifying the solver that particupated in SAT Competition 2016,2017,2018.For example, you can run(solve :competition <form> :name "Lingeling" :track "main_and_glucose_hack" :year 2018)to obtain the Lingeling that participated in SAT Competition 2018.The list of available solvers are:
  • 2016: https://baldur.iti.kit.edu/sat-competition-2016/solvers/
  • 2017: https://baldur.iti.kit.edu/sat-competition-2017/solvers/
  • 2017: http://sat2018.forsyte.tuwien.ac.at/solvers/
  • Here is the list of solvers that worked.
2019/1/25
the input formula can now contain (IMPLY lhs rhs) and (IFF lhs rhs).
2019/3/6
the input formula can contain more operations. See description below

1.1Usage

In order to load and run minisat2, run follows:
(ql:quickload :cl-sat.minisat)

(cl-sat:solve '(and (or a b) (or a !b c)) :minisat)
->
(C B)
T
T

(ql:quickload :cl-sat.glucose)

(cl-sat:solve '(and (or a b) (or a !b c)) :glucose)
->
(C B)
T
T

(cl-sat:solve '(and (or a b) (or a !b c)) :competition :year 2018 :track "main_and_glucose_hack" :name "Lingeling")
->
(C B A)
T
T

1.2Solver API

Generic function =(solve pathname (eql :solvername) &rest options)=

Each solver implementation should provide a method (solve pathname (eql :solvername) &rest options). Additional arguments are passed to the underlying solvers (unless explicitly specified).

It should return a list of true variables as the first value, a boolean indicating SAT when true, and a boolean indicating whether the result is determined. For example,

  • NIL,NIL,NIL means the solver failed due to the timelimit etc. so the result was indeterminable.
  • NIL,T,T means that the problem is SAT by assigning all variables to false.
  • NIL,NIL,T means that the problem is UNSAT.
  • On some occasions, depending on the solver, it also returns the fourth value,which is a list of variables that don't matter: it can be either trueor false.

1.3Input format

Users will most often use the method specialized to the S-exp interface (solve list (eql :solvername) &rest options).

list is a cons tree of symbols as an arbitrary propositional formula. The following logical operators are supported:

  • or
  • and
  • not
  • imply => when (synonyms)
  • iff
  • eq equal <=> (synonyms, variations of IFF that take multiple statements)
  • xor

Each term can be specified by a symbol or a number, but do not mix two styles (it may contain bugs). Symbols with ! prefix and negative numbers are interpreted as the negated atoms: !A is same as (not A).

These are internally converted into a NNF via De Morgan's law and then to a CNF via Tseytin transformation.

Examples:

a ;; -> equivalent to (and (or a))

(or a b) ;; -> equivalent to (and (or a b))

(and a b c) ;; -> equivalent to (and (or a) (or b) (or c))

(and 1 !b c) ;; -> undefined

(and a (or !b c)) ;; equivalent to (and (or a) (or (not b) c))

(or (and a b) (and b c)) ; -> (and (or aux1 aux2) (or (not aux1) a) (or aux1 (not a) (not b)) ...)

1.4S-exp converters

Users might also be interested in the functions used for processing the logical formula.

(symbolicate-form form)
This function is the first step of converting the input into a normal form.It normalizes the input tree containing numbers and !-negated vars into a tree of symbols.Note that it does not guarantee to return any type of normal forms (e.g. NNF,CNF,DNF,ANF).It accepts any types of compound forms, not limited to AND/OR/NOT.
(expand-extensions form)
Translates extended logical operations into AND, OR, NOT. It support the following operations:
  • IMPLY, =>, WHEN (synonyms),
  • IFF,
  • EQ, EQUAL, <=> (synonyms, a variation of IFF that takes multiple statements),
  • XOR.
(simplify-nnf form)
Remove some obvious constants / conflicts in the NNF. The result does not contain:
  • Single compound forms:
    • (and X), (or X)
  • Compound forms containing true/false constants:
    • (and ... (or) ... ) -> (or)
    • (or ... (and) ... ) -> (and)
    • (or ... X ... (not X) ... ) -> (and)
    • (and ... X ... (not X) ... ) -> (or)
  • Duplicated forms:
    • (and ... X ... X ... ) -> (and ... X ... ...)
    • (or ... X ... X ... ) -> (or ... X ... ...)
(to-nnf form)
Applying De-Morgan's law, the resulting tree contains negationsonly at the leaf nodes. Calls expand-extensions and simplify-nnf internally.
(to-cnf form &optional converter)
Translates the results to a CNF.Calls symbolicate-form and to-nnf internally.converter argument specifies which algorithm to use for the conversion, defaulting to #'to-cnf-tseytin.

1.5Helper functions

(var suffix &optional (prefix "V"))

This function interns SUFFIX (usually a number, but can be any printable object) to a symbol with the optional PREFIX. The new symbol is interned in a package CL-SAT.VARIABLES .

This function is particularly useful for implementing some SAT encoding of other problems, such as knapsack or bin-packing problem.

1.6Dependencies

Required libraries depends on the solver instance. See the corresponding documentation.

This library is at least tested on implementation listed below:

  • SBCL 1.3.5 on X86-64 Linux 3.19.0-59-generic (author's environment)

Also, it depends on the following libraries:

trivia by Masataro Asai
NON-optimized pattern matcher compatible with OPTIMA, with extensible optimizer interface and clean codebase
alexandria by
Alexandria is a collection of portable public domain utilities.
iterate by
Jonathan Amsterdam's iterator/gatherer/accumulator facility

1.7Author

  • Masataro Asai (guicho2.71828@gmail.com)

2Copyright

Copyright (c) 2016 Masataro Asai (guicho2.71828@gmail.com)

3License

Licensed under the LLGPL License.

Dependencies (5)

  • alexandria
  • fiveam
  • iterate
  • trivia
  • trivial-features
  • GitHub
  • Quicklisp