584 research outputs found
The Complexity of Bisimulation and Simulation on Finite Systems
In this paper the computational complexity of the (bi)simulation problem over
restricted graph classes is studied. For trees given as pointer structures or
terms the (bi)simulation problem is complete for logarithmic space or NC,
respectively. This solves an open problem from Balc\'azar, Gabarr\'o, and
S\'antha. Furthermore, if only one of the input graphs is required to be a
tree, the bisimulation (simulation) problem is contained in AC (LogCFL). In
contrast, it is also shown that the simulation problem is P-complete already
for graphs of bounded path-width
09421 Abstracts Collection -- Algebraic Methods in Computational Complexity
From 11.10. to 16.10.2009, the Dagstuhl Seminar 09421 ``Algebraic Methods in Computational Complexity \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Algebraic Methods in Computational Complexity
From 11.10. to 16.10.2009, the Dagstuhl Seminar 09421 “Algebraic Methods in Computational Complexity “ was held in Schloss Dagstuhl-Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available
04421 Abstracts Collection -- Algebraic Methods in Computational Complexity
From 10.10.04 to 15.10.04, the Dagstuhl Seminar 04421
``Algebraic Methods in Computational Complexity\u27\u27
was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Canonizing Graphs of Bounded Tree Width in Logspace
Graph canonization is the problem of computing a unique representative, a
canon, from the isomorphism class of a given graph. This implies that two
graphs are isomorphic exactly if their canons are equal. We show that graphs of
bounded tree width can be canonized by logarithmic-space (logspace) algorithms.
This implies that the isomorphism problem for graphs of bounded tree width can
be decided in logspace. In the light of isomorphism for trees being hard for
the complexity class logspace, this makes the ubiquitous class of graphs of
bounded tree width one of the few classes of graphs for which the complexity of
the isomorphism problem has been exactly determined.Comment: 26 page
Algebraic and Combinatorial Methods in Computational Complexity
At its core, much of Computational Complexity is concerned with combinatorial objects and structures. But it has often proven true that the best way to prove things about these combinatorial objects is by establishing a connection (perhaps approximate) to a more well-behaved algebraic setting. Indeed, many of the deepest and most powerful results in Computational Complexity rely on algebraic proof techniques. The PCP characterization of NP and the Agrawal-Kayal-Saxena polynomial-time primality test are two prominent examples. Recently, there have been some works going in the opposite direction, giving alternative combinatorial proofs for results that were originally proved algebraically. These alternative proofs can yield important improvements because they are closer to the underlying problems and avoid the losses in passing to the algebraic setting. A prominent example is Dinur's proof of the PCP Theorem via gap amplification which yielded short PCPs with only a polylogarithmic length blowup (which had been the focus of significant research effort up to that point). We see here (and in a number of recent works) an exciting interplay between algebraic and combinatorial techniques. This seminar aims to capitalize on recent progress and bring together researchers who are using a diverse array of algebraic and combinatorial methods in a variety of settings
- …