Community hub
Recent from talks
Contribute something to knowledge base
Content stats: 0 posts, 0 articles, 0 media, 0 notes
Members stats: 0 subscribers, 0 contributors, 0 moderators, 0 supporters
Subscribers
Supporters
Contributors
Moderators
Hub AI
Complexity of constraint satisfaction AI simulator
(@Complexity of constraint satisfaction_simulator)
Hub AI
Complexity of constraint satisfaction AI simulator
(@Complexity of constraint satisfaction_simulator)
Complexity of constraint satisfaction
The complexity of constraint satisfaction is the application of computational complexity theory to constraint satisfaction. It has mainly been studied for discriminating between tractable and intractable classes of constraint satisfaction problems on finite domains.
Solving a constraint satisfaction problem on a finite domain is an NP-complete problem in general. Research has shown a number of polynomial-time subcases, mostly obtained by restricting either the allowed domains or constraints or the way constraints can be placed over the variables. Research has also established a relationship between the constraint satisfaction problem and problems in other areas such as finite model theory and databases.
Establishing whether a constraint satisfaction problem on a finite domain has solutions is an NP-complete problem in general. This is an easy consequence of a number of other NP-complete problems being expressible as constraint satisfaction problems. Such other problems include propositional satisfiability and three-colorability.
Tractability can be obtained by considering specific classes of constraint satisfaction problems. As an example, if the domain is binary and all constraints are binary, establishing satisfiability is a polynomial-time problem because this problem is equivalent to 2-SAT, which is a polynomial-time problem.
One line of research used a correspondence between constraint satisfaction problem and the problem of establishing the existence of a homomorphism between two relational structures. This correspondence has been used to link constraint satisfaction with topics traditionally related to database theory.
A considered research problem is about the existence of dichotomies among sets of restrictions. This is the question of whether a set of restrictions contains only polynomial-time restrictions and NP-complete restrictions. For relational restrictions (see below) this question was settled in the positive for Boolean domains by Schaefer's dichotomy theorem and for any finite domain by Andrei Bulanov and Dmitriy Zhuk, independently, in 2017.
Tractable subcases of the general constraint satisfaction problem can be obtained by placing suitable restrictions on the problems. Various kinds of restrictions have been considered.
Tractability can be obtained by restricting the possible domains or constraints. In particular, two kinds of restrictions have been considered:
Complexity of constraint satisfaction
The complexity of constraint satisfaction is the application of computational complexity theory to constraint satisfaction. It has mainly been studied for discriminating between tractable and intractable classes of constraint satisfaction problems on finite domains.
Solving a constraint satisfaction problem on a finite domain is an NP-complete problem in general. Research has shown a number of polynomial-time subcases, mostly obtained by restricting either the allowed domains or constraints or the way constraints can be placed over the variables. Research has also established a relationship between the constraint satisfaction problem and problems in other areas such as finite model theory and databases.
Establishing whether a constraint satisfaction problem on a finite domain has solutions is an NP-complete problem in general. This is an easy consequence of a number of other NP-complete problems being expressible as constraint satisfaction problems. Such other problems include propositional satisfiability and three-colorability.
Tractability can be obtained by considering specific classes of constraint satisfaction problems. As an example, if the domain is binary and all constraints are binary, establishing satisfiability is a polynomial-time problem because this problem is equivalent to 2-SAT, which is a polynomial-time problem.
One line of research used a correspondence between constraint satisfaction problem and the problem of establishing the existence of a homomorphism between two relational structures. This correspondence has been used to link constraint satisfaction with topics traditionally related to database theory.
A considered research problem is about the existence of dichotomies among sets of restrictions. This is the question of whether a set of restrictions contains only polynomial-time restrictions and NP-complete restrictions. For relational restrictions (see below) this question was settled in the positive for Boolean domains by Schaefer's dichotomy theorem and for any finite domain by Andrei Bulanov and Dmitriy Zhuk, independently, in 2017.
Tractable subcases of the general constraint satisfaction problem can be obtained by placing suitable restrictions on the problems. Various kinds of restrictions have been considered.
Tractability can be obtained by restricting the possible domains or constraints. In particular, two kinds of restrictions have been considered: