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

Jean Camille Birget, Stuart W. Margolis

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish
Pages (from-to)159-168
Number of pages10
JournalSemigroup Forum
Volume76
Issue number1
DOIs
StatePublished - Jan 2008

Bibliographical note

Funding Information:
Both authors were supported in part by NSF grant DMS-9970471. The first author was also supported in part by NSF grant CCR-0310793. The second author acknowledges the support of the Excellency Center, “Group Theoretic Methods for the Study of Algebraic Varieties” of the Israeli Science Foundation.

Keywords

  • Free groups
  • Inverse automata
  • Inverse semigroups

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