Logical and Algebraic Characterizations of Rational Transductions

Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congrue...

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Bibliographic Details
Published in:Logical methods in computer science Vol. 15, Issue 4; no. 4
Main Authors: Filiot, Emmanuel, Gauwin, Olivier, Lhote, Nathan
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science Association 19.12.2019
Logical Methods in Computer Science e.V
Subjects:
Computer Science
computer science - formal languages and automata theory
computer science - logic in computer science
Formal Languages and Automata Theory
rational word transductions
definability problems
algebraic characterizations
first-order logic
ISSN:1860-5974, 1860-5974
Online Access:Get full text
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Summary:Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congruences, or first-order (FO) logic. In particular, their algebraic characterization by aperiodic congruences allows to decide whether a regular language is aperiodic. We lift this decidability result to rational transductions, i.e., word-to-word functions defined by finite state transducers. In this context, logical and algebraic characterizations have also been proposed. Our main result is that one can decide if a rational transduction (given as a transducer) is in a given decidable congruence class. We also establish a transfer result from logic-algebra equivalences over languages to equivalences over transductions. As a consequence, it is decidable if a rational transduction is first-order definable, and we show that this problem is PSPACE-complete.
ISSN:1860-5974
1860-5974
DOI:10.23638/LMCS-15(4:16)2019