81 research outputs found
Random strings and tt-degrees of Turing complete C.E. sets
We investigate the truth-table degrees of (co-)c.e.\ sets, in particular,
sets of random strings. It is known that the set of random strings with respect
to any universal prefix-free machine is Turing complete, but that truth-table
completeness depends on the choice of universal machine. We show that for such
sets of random strings, any finite set of their truth-table degrees do not meet
to the degree~0, even within the c.e. truth-table degrees, but when taking the
meet over all such truth-table degrees, the infinite meet is indeed~0. The
latter result proves a conjecture of Allender, Friedman and Gasarch. We also
show that there are two Turing complete c.e. sets whose truth-table degrees
form a minimal pair.Comment: 25 page
The complexity of computable categoricity
We show that the index set complexity of the computably categorical structures is View the MathML source-complete, demonstrating that computable categoricity has no simple syntactic characterization. As a consequence of our proof, we exhibit, for every computable ordinal α , a computable structure that is computably categorical but not relatively View the MathML source-categorical
On problems without polynomial kernels (Extended abstract).
Abstract. Kernelization is a central technique used in parameterized algorithms, and in other techniques for coping with NP-hard problems. In this paper, we introduce a new method which allows us to show that many problems do not have polynomial size kernels under reasonable complexity-theoretic assumptions. These problems include kPath, k-Cycle, k-Exact Cycle, k-Short Cheap Tour, k-Graph Minor Order Test, k-Cutwidth, k-Search Number, k-Pathwidth, k-Treewidth, k-Branchwidth, and several optimization problems parameterized by treewidth or cliquewidth
Polynomial Kernels and User Reductions for the Workflow Satisfiability Problem
The Workflow Satisfiability Problem (WSP) is a problem of practical interest
that arises whenever tasks need to be performed by authorized users, subject to
constraints defined by business rules. We are required to decide whether there
exists a plan -- an assignment of tasks to authorized users -- such that all
constraints are satisfied.
The WSP is, in fact, the conservative Constraint Satisfaction Problem (i.e.,
for each variable, here called task, we have a unary authorization constraint)
and is, thus, NP-complete. It was observed by Wang and Li (2010) that the
number k of tasks is often quite small and so can be used as a parameter, and
several subsequent works have studied the parameterized complexity of WSP
regarding parameter k.
We take a more detailed look at the kernelization complexity of WSP(\Gamma)
when \Gamma\ denotes a finite or infinite set of allowed constraints. Our main
result is a dichotomy for the case that all constraints in \Gamma\ are regular:
(1) We are able to reduce the number n of users to n' <= k. This entails a
kernelization to size poly(k) for finite \Gamma, and, under mild technical
conditions, to size poly(k+m) for infinite \Gamma, where m denotes the number
of constraints. (2) Already WSP(R) for some R \in \Gamma\ allows no polynomial
kernelization in k+m unless the polynomial hierarchy collapses.Comment: An extended abstract appears in the proceedings of IPEC 201
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