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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 30 | Number 1 | Year 2016 | Article Id. IJMTT-V30P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V30P508

Properties of semigroups in (semi-)automata


D.D. Padma Priya, G. Shobhalatha, R. Bhuvana Vijaya
Abstract

There is a close relationship between automata and semigroups. Automata includes calculating machines, computers, telephone switch boards, elevators and so on. Algebraic automata theory make extensive use of semigroups. The aim of this paper is to summarize the results of semigroup theory which will be described through (semi- )automata. For different types of (semi-)automata, we identified different structures of semigroups and their properties.

Keywords
semigroup, automata, (semi-)automata, monoid, regular, band.
References

[1] Lidl, Rudolf, and Günter Pilz. Applied abstract algebra. Springer Science & Business Media, 2012.
[2] Taira, Kazuaki. "Theory of Semigroups." Semigroups, Boundary Value Problems and Markov Processes. Springer Berlin Heidelberg, 2014. 143-198
[3] Skolicki, Zbigniew. "Semigroups and Automata." Schedae Informaticae 11 (2002): 11-20.
[4] Kambites, Mark. "Automatic semigroups and categories." Theoretical computer science 353.1 (2006): 272-290.
[5] Ginzburg, Abraham. Algebraic theory of automata. Academic Press, 2014.
[6] Cain, Alan J. "Automaton semigroups." Theoretical Computer Science410.47 (2009): 5022-5038.
[7] Trotter, Peter G. "Completely regular semigroups." Semigroup Forum. Vol. 64. No. 2. Springer New York, 2002.
[8] Brzozowski, Janusz, and Nicolae Santean. "Predictable semiautomata."Theoretical Computer Science 410.35 (2009): 3236-3249.

Citation :

D.D. Padma Priya, G. Shobhalatha, R. Bhuvana Vijaya, "Properties of semigroups in (semi-)automata," International Journal of Mathematics Trends and Technology (IJMTT), vol. 30, no. 1, pp. 43-47, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V30P508

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