Download Complexity of Constraints: An Overview of Current Research by Nadia Creignou, Phokion G. Kolaitis, Heribert Vollmer PDF

By Nadia Creignou, Phokion G. Kolaitis, Heribert Vollmer

Nowadays constraint delight difficulties (CSPs) are ubiquitous in lots of assorted components of computing device technology, from man made intelligence and database structures to circuit layout, community optimization, and conception of programming languages. for that reason, you will need to study and pinpoint the computational complexity of yes algorithmic projects relating to constraint pride. The complexity-theoretic result of those initiatives could have an instantaneous influence on, for example, the layout and processing of database question languages, or innovations in data-mining, or the layout and implementation of planners.

This state of the art survey includes the papers that have been invited by way of the organizers after end of a global Dagstuhl-Seminar on Complexity of Constraints, held in Dagstuhl fortress, Germany, in October 2006. a few audio system have been solicited to put in writing surveys featuring the cutting-edge of their forte. those contributions have been peer-reviewed via specialists within the box and revised ahead of they have been collated to the nine papers of this quantity. furthermore, the amount encompasses a reprint of a survey via Kolaitis and Vardi at the logical method of constraint pride that first seemed in 'Finite version idea and its Applications', released by way of Springer in 2007.

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If Γ ⊆ Γ and Γ can express equality, then Lex-Min-Sat(Γ ) ≤pmet Lex-Min-Sat(Γ ). Proof. Let φ be a Γ -formula with Var(φ) = {x1 , . . , x1 < · · · < xn . We construct a formula by replacing in φ every constraint from Γ by its defining existentially quantified Γ ∪ {=} -formula. Any occurring equality constraint can be removed in using the Γ -implementation of the equality relation, which exists due to the prerequisites. Finally we delete all the existential quantifiers. The Γ -formula φ so obtained is over a set of variables {x1 , .

Otherwise, #Csp(Γ ) is #·P-complete under Turing reductions. Boolean Constraint Satisfaction Problems: When Does Post’s Lattice Help? 25 Related to the counting problem is the unique satisfiability problem. Thus, Unique-Sat(Γ ) is the problem of deciding whether a given Γ -formula has a unique model. This problem is in the complexity class DP, the class of languages equal to an intersection of two languages, one from NP and the other from coNP. Unless the polynomial hierarchy collapses, DP is a strict superclass of NP and coNP.

23. [Maximum ones satisfiability] – If Γ is 1-valid or dual Horn or affine with width 2, then Max-Ones(Γ ) is in PO. – Else if Γ is affine, then Max-Ones(Γ ) is APX-complete. – Else if Γ is Horn or bijunctive, then Max-Ones(Γ ) is poly-APX-complete. – Else if Γ is 0-valid, then finding a feasible solution to Max-Ones(Γ ) is in P but finding a solution of positive value is NP-hard. – Else the task of finding any feasible solution to Max-Ones(Γ ) is NP-hard. Now let us examine the problem Max-Sat in which a given Γ -formula φ has as feasible solutions space the set of all truth assignments.

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