Elsevier

Theoretical Computer Science

Volume 609, Part 2, 4 January 2016, Pages 344-360
Theoretical Computer Science

On structure and representations of cyclic automata

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Abstract

In this paper we study structure and representations of cyclic automata. Corresponding to Green's equivalences in semigroup theory, we introduce three binary relations say L, R and H on cyclic automata. An automaton is said to be strict if L is an equivalence on the set of states. Some properties of these relations are established for giving characterizations of three subclasses of strict automata. Also, we provide representations of strict automata by representing the states as vectors and describing the state transitions in terms of matrix operations. These results generalize and extend Ito's representations of strongly connected automata.

Keywords

Endomorphisms of automata
Strict automata
Clifford monoids
Representations
Monoid-matrix type automata

Cited by (0)

1

The first author is supported by the National Natural Science Foundation of China (61402364) and the Grant of Natural Science Foundation of Shaanxi Province (2014JQ1014).

2

The second author is supported by the National Natural Science Foundation of China (11261021, 11571278) and the Grant of Natural Science Foundation of Jiangxi Province (20142BAB201002).

3

The third author is supported by China Postdoctoral Science Foundation (2011M501466).