An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata

Karsten Henckell; John Rhodes; Benjamin Steinberg

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arXiv · 0812.3499

An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata

Karsten Henckell·John Rhodes·Benjamin Steinberg

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Abstract

The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, \textit{Complexity of finite semigroups}, Annals of Mathematics (2) \textbf{88} (1968), 128--160, motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes, \textit{Algebraic theory of machines, {I}: {P}rime decomposition theorem for finite semigroups and machines}, Transactions of the American Mathematical Society \textbf{116} (1965), 450--464. Here we provide an effective lower bound for group complexity.

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BibTeX RIS

Karsten Henckell, John Rhodes, Benjamin Steinberg. 2008-12-18. An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata. https://arxiv.org/abs/0812.3499

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