Two-letter group codes that preserve aperiodicity of inverse finite automata
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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Cite
@article{arxiv.math/0701264,
title = {Two-letter group codes that preserve aperiodicity of inverse finite automata},
author = {Jean-Camille Birget and Stuart W. Margolis},
journal= {arXiv preprint arXiv:math/0701264},
year = {2007}
}
Comments
10 pages