Two-way automata and transducers with planar behaviours are aperiodic
L\^e Th\`anh D\~ung Nguy\^en, Camille No\^us, C\'ecilia Pradic
TL;DR
This paper introduces a notion of planarity for two-way automata and transducers, linking it to star-free languages and first-order transductions, thus providing a new perspective on automata theory.
Contribution
It defines a planarity restriction inspired by Temperley-Lieb monoids and demonstrates its connection to star-free languages and first-order transductions.
Findings
Planar two-way automata recognize star-free languages.
Planar transducers correspond to first-order transductions.
Planarity imposes aperiodicity on automata and transducers.
Abstract
We consider a notion of planarity for two-way finite automata and transducers, inspired by Temperley-Lieb monoids of planar diagrams. We show that this restriction captures star-free languages and first-order transductions.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Logic, programming, and type systems