2026-07-21T23:20:00Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7702 2024-03-06T10:40:44Z ddc:004 open_access

Query Learning of Derived Omega-Tree Languages in Polynomial Time Angluin, Dana Antonopoulos, Timos Fisman, Dana Learning queries infinite trees derived tree languages reactive systems We present the first polynomial time algorithm to learn nontrivial classes of languages of infinite trees. Specifically, our algorithm uses membership and equivalence queries to learn classes of omega-tree languages derived from weak regular omega-word languages in polynomial time. The method is a general polynomial time reduction of learning a class of derived omega-tree languages to learning the underlying class of omega-word languages, for any class of omega-word languages recognized by a deterministic Büchi acceptor. Our reduction, combined with the polynomial time learning algorithm of Maler and Pnueli [Maler and Pneuli, Inform. Comput., 1995] for the class of weak regular omega-word languages yields the main result. We also show that subset queries that return counterexamples can be implemented in polynomial time using subset queries that return no counterexamples for deterministic or non-deterministic finite word acceptors, and deterministic or non-deterministic Büchi omega-word acceptors. A previous claim of an algorithm to learn regular omega-trees due to Jayasrirani, Begam and Thomas [Jayasrirani et al., ICGI, 2008] is unfortunately incorrect, as shown in [Angluin, YALEU/DCS/TR-1528, 2016]. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Dana Angluin and Timos Antonopoulos and Dana Fisman 2017 Is Part Of LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2017.10 urn:nbn:de:0030-drops-77022 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.10 eng https://creativecommons.org/licenses/by/3.0/legalcode