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 desktop technology, from man made intelligence and database structures to circuit layout, community optimization, and idea of programming languages. for this reason, you will need to examine and pinpoint the computational complexity of sure algorithmic initiatives regarding constraint delight. The complexity-theoretic result of those projects could have a right away influence on, for example, the layout and processing of database question languages, or thoughts in data-mining, or the layout and implementation of planners.

This cutting-edge survey comprises the papers that have been invited through the organizers after end of a global Dagstuhl-Seminar on Complexity of Constraints, held in Dagstuhl citadel, Germany, in October 2006. a couple of audio system have been solicited to jot down surveys providing the cutting-edge of their forte. those contributions have been peer-reviewed via specialists within the box and revised earlier than they have been collated to the nine papers of this quantity. additionally, the quantity encompasses a reprint of a survey via Kolaitis and Vardi at the logical method of constraint delight that first seemed in 'Finite version conception and its Applications', released by way of Springer in 2007.

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Extra info for Complexity of Constraints: An Overview of Current Research Themes

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If F ⊆ OD , then F (n) := F ∩ OD denotes the set of all n-ary functions in F . An m–ary relation on D is a subset ⊆ Dm . The elements of are m–tuples a = (a1 , . . , am ) ∈ Dm . We write a(i) to denote the ith entry ai of a. The (m) set of all m–ary relations on D is RD := { | ⊆ Dm }, and the set of all (m) finitary relations on D is RD := m∈N+ RD . For a relation set Γ ⊆ RD we (m) put Γ (m) := Γ ∩ RD . We do not distinguish sharply between relations and predicates. So instead of a ∈ we also write (a).

This linear system has the good property of being Vandermonde, and therefore inversible. Thus these terms, and hence the number of solutions of φ can be computed in polynomial time from the Nl ’s (and the uj ’s). Therefore, there is a Turing reduction from #Csp(Γ ) to #Csp(Γ ) with p queries to the oracle. 15. For most of the above computational problems where the Galois connection helps a priori, the definition of the problem somehow allows to “hide” the new existentially quantified variables that are introduced by the application of the Galois connection.

It is believed that W[1]complete problems are not fixed-parameter-tractable. For more background on parameterized complexity the reader is asked to consult the monograph [FG06]. In [Mar05] Marx investigated the parameterized complexity of p-Sat(Γ ) defined as follows. Problem: Input: p-Sat(Γ ) a Γ -formula φ where each variable can occur at most once in each constraint, and an integer k Parameter: k Question: Is there a truth assignment setting exactly k variables to true that satisfies φ? He introduced a new property, weak separability, that plays a crucial role in the parameterized complexity of problems.

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