The State Minimization Problem for Nondeterministic Finite Automata: The Parallel Implementation of the Truncated Branch and Bound Method

Melnikov, Boris; Tsyganov, A.

doi:10.1109/paap.2012.36

Cited by 5 publications

(2 citation statements)

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“…• the classical traveling salesman problem (however, we consider our own approach to this problem, and, most importantly, our original way of specifying the input data, different from the traditional geometric placement, see, e.g., [22]); • and the problem of state-minimization for nondeterministic finite automata, see, e.g., [23,24].…”

Section: Preliminariesmentioning

confidence: 99%

An approach to analysis of the similarity of DNA-sequences

Melnikov

Melnikova²,

Pivneva

et al. 2018

Collection of Selected Papers of the IV International Conference on Information Technology and Nanotechnology

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This paper describes algorithms, corresponding computer programs and the results of computations, supplementing results published earlier. We consider the multiple sequence alignment problem, which can be nominated by a central problem in computational biology. For it, we continue to consider some different versions of so-called "triangular norm" defined on the set of triangles formed by the different distance between genomes computed by different algorithms. Besides, one of the problems considered in biocybernetics is the problem of reconstructing the distance matrix between DNA sequences, when not all the elements of the matrix under consideration are known at the input of the algorithm. In this connection, the problem arises that the developed method of comparative evaluation of algorithms for calculating the distances between sequences should be used for another problem, i.e., for reconstructing the matrix of distances between DNA sequences. In this paper, we consider the possibility of applying the method of comparative evaluation of the algorithms for calculating the distances between a pair of DNA strings that we developed and studied earlier for the reconstruction of a partially filled distance matrix. The restoration of the matrix occurs as a result of several computational passes. Estimates of unknown matrix elements are averaged in a special way using so-called risk functions, and the result of this averaging is considered as the received value of the unknown element.

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Section: Preliminariesmentioning

confidence: 99%

An approach to analysis of the similarity of DNA-sequences

Melnikov

Melnikova²,

Pivneva

et al. 2018

Collection of Selected Papers of the IV International Conference on Information Technology and Nanotechnology

Self Cite

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“…They are well-known Kameda-Weiner algorithm [10] and Melnikov algorithm that uses the so called complete (COM) and basis (BA) automata (see, for example, [11], [12], [13], [14]. Both methods use the state correspondence matrices: RAM and the #-table respectively and try to construct minimal NFA from the (prime) grids that cover all non-empty elements of that matrices.…”

Section: Nfa Minimization Algorithmsmentioning

confidence: 99%

ReFaM: A Software Tool for Minimizing Nondeterministic Finite Automata

Tsyganov

2012

2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

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In the present paper we introduce a new software tool which can be used for minimizing finite automata. The distinguishing feature of this tool is that it's primarily aimed at nondeterministic finite automata minimization. It provides several exact and heuristic minimization methods and uses parallel techniques such as OpenMP and MPI to speed up the most time consuming parts of the implemented algorithms. The description of implemented methods and available commands as well as some experimental results are provided.

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