Emmanuel Filiot ; Olivier Gauwin ; Nathan Lhote - Logical and Algebraic Characterizations of Rational Transductions

lmcs:3653 - Logical Methods in Computer Science, December 19, 2019, Volume 15, Issue 4 - https://doi.org/10.23638/LMCS-15(4:16)2019
Logical and Algebraic Characterizations of Rational Transductions

Authors: Emmanuel Filiot ; Olivier Gauwin ; Nathan Lhote

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.

Volume: Volume 15, Issue 4
Published on: December 19, 2019
Accepted on: December 19, 2019
Submitted on: May 11, 2017
Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory


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