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

Jean-Camille Birget, Stuart W. Margolis
2007 Semigroup Forum  
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
more » ... tion-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.
doi:10.1007/s00233-007-9024-6 fatcat:5p4ngj75g5dvfpbhuamofir7vy