Instance Compression for the Polynomial Hierarchy and beyond

Abstract. We define instance compressibility ([1], [7], [5], [6] ) for parametric problems in P H and P SP ACE. We observe that the problem ΣiCircuitSAT of deciding satisfiability of a quantified Boolean circuit with i−1 alternations of quantifiers starting with respect to W-reductions, and that analogously the problem QBCSAT (Quantified Boolean Circuit Satisfiability) is complete for parametric problems in P SP ACE with respect to W-reductions. We show the following results about these problems: 1. CircuitSAT is non-uniformly compressible within NP implies ΣiCircuitSAT is non-uniformly compressible within NP, for any i ≥ 1. 2. If QBCSAT is non-uniformly compressible (or even if satisfiability of quantified Boolean CNF formulae is non-uniformly compressible), then P SP ACE ⊆ NP/poly and PH collapses to the third level. Next, we define Succinct IP and show that QBF ormulaSAT (Quantified Boolean Formula Satisfiability) is in Succinct IP. with an existential quantifier is complete for parametric problems in Σ p i

W-Hierarchies defined by symmetric gates

The classes of the W-hierarchy are the most important classes of intractable problems in parameterized complexity. These classes were originally defined via the weighted satisfiability problem for Boolean circuits. Here, besides the Boolean connectives we consider connectives such as majority, not-all-equal, and unique. For example, a gate labelled by the majority connective outputs true if more than half of its inputs are true. For any finite set C of connectives we construct the corresponding W( C )-hierarchy. We derive some general conditions which guarantee that the W-hierarchy and the W( C )-hierarchy coincide levelwise. If C only contains the majority connective then the first levels of the hierarchies coincide. We use this to show that a variant of the parameterized vertex cover problem, the majority vertex cover problem, is W[1]-complete

Coevolution in management fashions: The case of self-managing teams in the Netherlands

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Exact Algorithms for NP-Hard Problems

A surve