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Two-letter group codes that preserve aperiodicity of inverse finite automata

Jean-Camille Birget·Stuart W. Margolis
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Abstract

We construct group codes over two letters (i.e., bases of subgroups of a two-generated free group) with special properties. Such group codes can be used for reducing algorithmic problems over large alphabets to algorithmic problems over a two-letter alphabet. Our group codes preserve aperiodicity of inverse finite automata. As an application we show that the following problems are PSpace-complete for two-letter alphabets (this was previously known for large enough finite alphabets): The intersection-emptiness problem for inverse finite automata, the aperiodicity problem for inverse finite automata, and the closure-under-radical problem for finitely generated subgroups of a free group. The membership problem for 3-generated inverse monoids is PSpace-complete.

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Jean-Camille Birget, Stuart W. Margolis. 2007-01-09. Two-letter group codes that preserve aperiodicity of inverse finite automata. https://arxiv.org/abs/math/0701264

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