2026-07-23T03:47:44Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12547 2024-03-06T10:50:25Z ddc:004 open_access

Hardness Results for Constant-Free Pattern Languages and Word Equations Saarela, Aleksi Combinatorics on words pattern language word equation We study constant-free versions of the inclusion problem of pattern languages and the satisfiability problem of word equations. The inclusion problem of pattern languages is known to be undecidable for both erasing and nonerasing pattern languages, but decidable for constant-free erasing pattern languages. We prove that it is undecidable for constant-free nonerasing pattern languages. The satisfiability problem of word equations is known to be in PSPACE and NP-hard. We prove that the nonperiodic satisfiability problem of constant-free word equations is NP-hard. Additionally, we prove a polynomial-time reduction from the satisfiability problem of word equations to the problem of deciding whether a given constant-free equation has a solution morphism α such that α(xy) ≠ α(yx) for given variables x and y. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Aleksi Saarela 2020 Is Part Of LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2020.140 urn:nbn:de:0030-drops-125472 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.140 eng https://creativecommons.org/licenses/by/3.0/legalcode