scholarly journals Constraint Satisfaction, Logic and Forbidden Patterns

2007 ◽  
Vol 37 (1) ◽  
pp. 132-163 ◽  
Author(s):  
Florent Madelaine ◽  
Iain A. Stewart
Keyword(s):  
Constraint Satisfaction ◽  
Forbidden Patterns

scholarly journals Variable and value elimination in binary constraint satisfaction via forbidden patterns

2015 ◽  
Vol 81 (7) ◽  
pp. 1127-1143 ◽  
Author(s):  
David A. Cohen ◽  
Martin C. Cooper ◽  
Guillaume Escamocher ◽  
Stanislav Živný
Keyword(s):  
Constraint Satisfaction ◽  
Binary Constraint ◽  
Forbidden Patterns

scholarly journals Variable Elimination in Binary CSPs

2019 ◽  
Vol 66 ◽  
pp. 589-624
Author(s):  
Martin C. Cooper ◽  
Achref El Mouelhi ◽  
Cyril Terrioux
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Benchmark Problems ◽  
Study Variable ◽  
Variable Elimination ◽  
Problem Instances ◽  
Forbidden Patterns

We investigate rules which allow variable elimination in binary CSP (constraint satisfaction problem) instances while conserving satisfiability. We study variable-elimination rules based on the language of forbidden patterns enriched with counting and quantification over variables and values. We propose new rules and compare them, both theoretically and experimentally. We give optimised algorithms to apply these rules and show that each define a novel tractable class. Using our variable-elimination rules in preprocessing allowed us to solve more benchmark problems than without.

scholarly journals Galois Connections for Patterns: An Algebra of Labelled Graphs

2021 ◽  
pp. 125-150
Author(s):  
David A. Cohen ◽  
Martin C. Cooper ◽  
Peter G. Jeavons ◽  
Stanislav Živný
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Galois Connection ◽  
Language Classes ◽  
Finite Set ◽  
Binary Constraint ◽  
Tree Width ◽  
To Come ◽  
Forbidden Patterns ◽  
Near Unanimity

AbstractA pattern is a generic instance of a binary constraint satisfaction problem (CSP) in which the compatibility of certain pairs of variable-value assignments may be unspecified. The notion of forbidden pattern has led to the discovery of several novel tractable classes for the CSP. However, for this field to come of age it is time for a theoretical study of the algebra of patterns. We present a Galois connection between lattices composed of sets of forbidden patterns and sets of generic instances, and investigate its consequences. We then extend patterns to augmented patterns and exhibit a similar Galois connection. Augmented patterns are a more powerful language than flat (i.e. non-augmented) patterns, as we demonstrate by showing that, for any $$k \ge 1$$ k ≥ 1 , instances with tree-width bounded by k cannot be specified by forbidding a finite set of flat patterns but can be specified by a finite set of augmented patterns. A single finite set of augmented patterns can also describe the class of instances such that each instance has a weak near-unanimity polymorphism of arity k (thus covering all tractable language classes).We investigate the power of forbidding augmented patterns and discuss their potential for describing new tractable classes.

scholarly journals The Tractability of CSP Classes Defined by Forbidden Patterns

2012 ◽  
Vol 45 ◽  
pp. 47-78 ◽  
Author(s):  
D. A. Cohen ◽  
M. C. Cooper ◽  
P. Creed ◽  
D. Marx ◽  
A. Z. Salamon
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
The Novel ◽  
Considerable Effort ◽  
Relational Properties ◽  
Np Complete ◽  
Novel Concept ◽  
Forbidden Patterns ◽  
Special Case ◽  
Hybrid Properties

The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses. The main two approaches consider structural properties (restrictions on the hypergraph of constraint scopes) and relational properties (restrictions on the language of constraint relations). Recently, some authors have considered hybrid properties that restrict the constraint hypergraph and the relations simultaneously. Our key contribution is the novel concept of a CSP pattern and classes of problems defined by forbidden patterns (which can be viewed as forbidding generic sub-problems). We describe the theoretical framework which can be used to reason about classes of problems defined by forbidden patterns. We show that this framework generalises certain known hybrid tractable classes. Although we are not close to obtaining a complete characterisation concerning the tractability of general forbidden patterns, we prove a dichotomy in a special case: classes of problems that arise when we can only forbid binary negative patterns (generic sub-problems in which only disallowed tuples are specified). In this case we show that all (finite sets of) forbidden patterns define either polynomial-time solvable or NP-complete classes of instances.

scholarly journals Sandwiches for promise constraint satisfaction

2021 ◽  
Vol 82 (1) ◽  
Author(s):  
Guofeng Deng ◽  
Ezzeddine El Sai ◽  
Trevor Manders ◽  
Peter Mayr ◽  
Poramate Nakkirt ◽  
...  
Keyword(s):  
Constraint Satisfaction
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