15,254 research outputs found
The counting complexity of group-definable languages
AbstractA group family is a countable family B={Bn}n>0 of finite black-box groups, i.e., the elements of each group Bn are uniquely encoded as strings of uniform length (polynomial in n) and for each Bn the group operations are computable in time polynomial in n. In this paper we study the complexity of NP sets A which has the following property: the set of solutions for every x∈A is a subgroup (or is the right coset of a subgroup) of a group Bi(|x|) from a given group family B, where i is a polynomial. Such an NP set A is said to be defined over the group family B.Decision problems like Graph Automorphism, Graph Isomorphism, Group Intersection, Coset Intersection, and Group Factorization for permutation groups give natural examples of such NP sets defined over the group family of all permutation groups. We show that any such NP set defined over permutation groups is low for PP and C=P.As one of our main results we prove that NP sets defined over abelian black-box groups are low for PP. The proof of this result is based on the decomposition theorem for finite abelian groups. As an interesting consequence of this result we obtain new lowness results: Membership Testing, Group Intersection, Group Factorization, and some other problems for abelian black-box groups are low for PP and C=P.As regards the corresponding counting problem for NP sets over any group family of arbitrary black-box groups, we prove that exact counting of number of solutions is in FPAM. Consequently, none of these counting problems can be #P-complete unless PH collapses
Blind identification of an unknown interleaved convolutional code
We give here an efficient method to reconstruct the block interleaver and
recover the convolutional code when several noisy interleaved codewords are
given. We reconstruct the block interleaver without assumption on its
structure. By running some experimental tests we show the efficiency of this
method even with moderate noise
Graph- versus Vector-Based Analysis of a Consensus Protocol
The Paxos distributed consensus algorithm is a challenging case-study for
standard, vector-based model checking techniques. Due to asynchronous
communication, exhaustive analysis may generate very large state spaces already
for small model instances. In this paper, we show the advantages of graph
transformation as an alternative modelling technique. We model Paxos in a rich
declarative transformation language, featuring (among other things) nested
quantifiers, and we validate our model using the GROOVE model checker, a
graph-based tool that exploits isomorphism as a natural way to prune the state
space via symmetry reductions. We compare the results with those obtained by
the standard model checker Spin on the basis of a vector-based encoding of the
algorithm.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767
Cluster formation in mesoscopic systems
Graph-theoretical approach is used to study cluster formation in mesocsopic
systems. Appearance of these clusters are due to discrete resonances which are
presented in the form of a multigraph with labeled edges. This presentation
allows to construct all non-isomorphic clusters in a finite spectral domain and
generate corresponding dynamical systems automatically. Results of MATHEMATICA
implementation are given and two possible mechanisms of cluster destroying are
discussed
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