Tractable Set Constraints

04/06/2011
by   Manuel Bodirsky, et al.
0

Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems are frequently intractable, but there are several important set CSPs that are known to be polynomial-time tractable. We introduce a large class of set CSPs that can be solved in quadratic time. Our class, which we call EI, contains all previously known tractable set CSPs, but also some new ones that are of crucial importance for example in description logics. The class of EI set constraints has an elegant universal-algebraic characterization, which we use to show that every set constraint language that properly contains all EI set constraints already has a finite sublanguage with an NP-hard constraint satisfaction problem.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/29/2018

A polynomial-time algorithm for median-closed semilinear constraints

A subset of Q^n is called semilinear (or piecewise linear) if it is Bool...
research
01/04/2012

Complexity Classification in Infinite-Domain Constraint Satisfaction

A constraint satisfaction problem (CSP) is a computational problem where...
research
06/30/2011

A Maximal Tractable Class of Soft Constraints

Many researchers in artificial intelligence are beginning to explore the...
research
07/10/2013

Tractable Combinations of Global Constraints

We study the complexity of constraint satisfaction problems involving gl...
research
03/08/2011

The tractability of CSP classes defined by forbidden patterns

The constraint satisfaction problem (CSP) is a general problem central t...
research
06/04/2021

On Classifying Continuous Constraint Satisfaction problems

A continuous constraint satisfaction problem (CCSP) is a constraint sati...
research
05/01/2020

Strong subalgebras and the Constraint Satisfaction Problem

In 2007 it was conjectured that the Constraint Satisfaction Problem (CSP...

Please sign up or login with your details

Forgot password? Click here to reset