eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-12-14
112
124
10.4230/LIPIcs.FSTTCS.2015.112
article
Efficient Algorithms for Morphisms over Omega-Regular Languages
Fleischer, Lukas
Kufleitner, Manfred
Morphisms to finite semigroups can be used for recognizing omega-regular languages. The so-called strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic morphism) and a trivial complementation procedure. We give a quadratic-time algorithm for computing the syntactic morphism from any given strongly recognizing morphism, thereby showing that minimization is easy as well. In addition, we give algorithms for efficiently solving various decision problems for weakly recognizing morphisms. Weakly recognizing morphism are often smaller than their strongly recognizing counterparts. Finally, we describe the language operations needed for converting formulas in monadic second-order logic (MSO) into strongly recognizing morphisms, and we give some experimental results.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol045-fsttcs2015/LIPIcs.FSTTCS.2015.112/LIPIcs.FSTTCS.2015.112.pdf
Büchi automata
omega-regular language
syntactic semigroup
recognizing morphism
MSO