Decision Problems for Subclasses of Rational Relations over Finite and Infinite Words

We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the case of finite words, where the problem is decidable. Further...

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Bibliographic Details
Published in:Discrete Mathematics and Theoretical Computer Science Vol. 21; no. 3; pp. 1 - 32
Main Authors: Loding, Christof, Spinrath, Christopher
Format: Journal Article
Language:English
Published: Nancy DMTCS 01.07.2019
Subjects:
Algorithms
Decision theory
Machine theory
Mathematical research
Polynomials
Germany
ISSN:1462-7264, 1365-8050
Online Access:Get full text
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Summary:We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the case of finite words, where the problem is decidable. Furthermore, we show that it is decidable in doubly exponential time for an automatic relation over infinite words whether it is a recognizable relation. We also revisit this problem in the context of finite words and improve the complexity of the decision procedure to single exponential time. The procedure is based on a polynomial time regularity test for deterministic visibly pushdown automata, which is a result of independent interest. Keywords: rational relations, automatic relations, omega-automata, finite transducers, visibly pushdown automata
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ISSN:1462-7264
1365-8050