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Reznykov, Illya I.; Sushchansky, V.

doi:10.1016/j.jalgebra.2006.03.039

Journal of Algebra

2006

DOI: 10.1016/j.jalgebra.2006.03.039

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On the 3-state Mealy automata over an m-symbol alphabet of growth order [nlogn/2logm]

Illya I. Reznykov¹,

V. Sushchansky

Abstract: On the 3-state Mealy automata over an m-symbol alphabet of growth order [n log n/2 log m ] AbstractWe consider sequence {J m , m 2} of 3-state Mealy automata over an m-symbol alphabet such that the growth of J m is intermediate of order [n log n/2 log m ]. For each automaton J m we describe the transformation monoid S J m , defined by it, provide generating series for the growth functions, and consider some properties of S J m and J m .

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Cited by 3 publications

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Analysis of an Exhaustive Search Algorithm in Random Graphs and the $n^{c\log n}$-Asymptotics

Banderier¹,

Hwang²,

Ravelomanana³

et al. 2014

SIAM J. Discrete Math.

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We analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual G n,p -model where each possible edge appears independently with the same probability p. The expected cost turns out to be of the less common asymptotic order n c log n , which we explore from several different perspectives. Also we collect many instances where such an order appears, from algorithmics to analysis, from probability to algebra. The limiting distribution of the cost required by the algorithm under a purely idealized random model is proved to be normal. The approach we develop is of some generality and is amenable for other graph algorithms.MSC 2000 Subject Classifications: Primary 05C80, 05C85; secondary 65Q30.

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Analysis of an Exhaustive Search Algorithm in Random Graphs and the $n^{c\log n}$-Asymptotics

Banderier¹,

Hwang²,

Ravelomanana³

et al. 2014

SIAM J. Discrete Math.

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show abstract

A Mealy Machine With Polynomial Growth of Irrational Degree

Bartholdi

Reznykov

2008

Int. J. Algebra Comput.

Self Cite

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Abstract. We consider a very simple Mealy machine (two non-trivial states over a two-symbol alphabet), and derive some properties of the semigroup it generates. It is an infinite, finitely generated semigroup, and we show that the growth function of its balls behaves asymptotically like n α , for α = 1 + log 2/log; that the semigroup satisfies the identity g 6 = g 4 ; and that its lattice of two-sided ideals is a chain.

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Inverse Semigroups of Partial Automaton Permutations

Olijnyk

Sushchansky

Słupik

2010

Int. J. Algebra Comput.

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The inverse semigroup of partial automaton permutations over a finite alphabet is characterized in terms of wreath products. The permutation conjugacy relation in this semigroup and the Green's relations are described. Criteria of primary conjugacy and conjugacy are given for certain naturally defined families of partial automaton permutations. Sufficient conditions under which an inverse semigroup admits a level transitive action are presented. We give explicit examples (monogenic inverse semigroups and some commutative Clifford semigroups) of inverse semigroups generated by finite automata.

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On the 3-state Mealy automata over an m-symbol alphabet of growth order [nlogn/2logm]

Cited by 3 publications

References 12 publications

Analysis of an Exhaustive Search Algorithm in Random Graphs and the $n^{c\log n}$-Asymptotics

Analysis of an Exhaustive Search Algorithm in Random Graphs and the $n^{c\log n}$-Asymptotics

A Mealy Machine With Polynomial Growth of Irrational Degree

Inverse Semigroups of Partial Automaton Permutations

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