2026-08-25T22:08:57Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27347 2026-08-24T14:08:30Z ddc:004 open_access

Decomposition of Automata Recognizing Ideals Berry, Mathias Héam, Pierre-Cyrille Jecker, Ismaël Finite state automata decomposition Shuffle ideals Minimizing the size of finite automata is a fundamental problem in theoretical computer science. Beyond standard minimization, further reductions can be achieved by decomposing an automaton into smaller components whose languages combine via intersection or union to recover the original language. However, in general, no polynomial-time algorithm is known for computing such decompositions. In this paper, we focus on automata that recognize ideals, that is, languages at level 1/2 in the Straubing–Thérien hierarchy. Equivalently, these languages are expressible as a finite union of languages of the form Σ^*a₁Σ^*… Σ^*a_nΣ^* where Σ is an alphabet and a_i are letters of Σ. We show that the two problems of deciding whether an automata recognizing an ideal can be decomposed into an intersection or a union of smaller automata are decidable in NL. Moreover, we provide a polynomial-time algorithm that computes a decomposition into an intersection, if one exists, while ensuring that the resulting components also recognize ideal languages. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mathias Berry and Pierre-Cyrille Héam and Ismaël Jecker 2026 Is Part Of LIPIcs, Volume 391, 37th International Conference on Concurrency Theory (CONCUR 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2026.16 urn:nbn:de:0030-drops-273473 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2026.16 eng https://creativecommons.org/licenses/by/4.0/legalcode