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Electronic Colloquium on Computational Complexity

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TR11-073 | 3rd May 2011
Andrew Drucker

Efficient Probabilistically Checkable Debates

Probabilistically checkable debate systems (PCDSs) are debates between two competing provers, in which a polynomial-time verifier inspects a constant number of bits of the debate. It was shown by Condon, Feigenbaum, Lund, and Shor that every language in PSPACE has a PCDS in which the debate length is polynomially bounded. ... more >>>


TR11-072 | 1st May 2011
Danny Hermelin, Xi Wu

Weak Compositions and Their Applications to Polynomial Lower-Bounds for Kernelization

Revisions: 1

We introduce a new form of composition called \emph{weak composition} that allows us to obtain polynomial kernelization lower-bounds for several natural parameterized problems. Let $d \ge 2$ be some constant and let $L_1, L_2 \subseteq \{0,1\}^* \times \N$ be two parameterized problems where the unparameterized version of $L_1$ is \NP-hard. ... more >>>


TR11-071 | 27th April 2011
Serge Gaspers, Stefan Szeider

The Parameterized Complexity of Local Consistency

Revisions: 1

We investigate the parameterized complexity of deciding whether a constraint network is $k$-consistent. We show that, parameterized by $k$, the problem is complete for the complexity class co-W[2]. As secondary parameters we consider the maximum domain size $d$ and the maximum number $\ell$ of constraints in which a variable occurs. ... more >>>



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