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Register Automata with Permutations

Authors Mrudula Balachander , Emmanuel Filiot , Raffaella Gentilini , Nikos Tzevelekos

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LIPIcs.MFCS.2025.14.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Register automata
  • data words
  • equivalence
  • minimization
  • active learning

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Abstract

We propose Permutation Deterministic Register Automata (pDRAs), a deterministic register automaton model where we allow permutations of registers in transitions. The model enables minimal canonical representations and pDRAs can be tested for equivalence in polynomial time. The complexity of minimization is between GI (the complexity of graph isomorphism) and NP. We then introduce a subclass of pDRAs, called register automata with fixed permutation policy, where the register permutation discipline is stipulated globally. This class generalizes the model proposed by Benedikt, Ley and Puppis in 2010, and we show that it also admits minimal and canonical representations, based on a finite-index word equivalence relation. As an application, we show that for any regular data language L, the minimal register automaton with fixed permutation policy recognizing L can be actively learned in polynomial time using oracles for membership, equivalence and data-memorability queries. We show that all the oracles can be implemented in polynomial time, and so this yields a polynomial time minimization algorithm.

Cite As Get BibTex

Mrudula Balachander, Emmanuel Filiot, Raffaella Gentilini, and Nikos Tzevelekos. Register Automata with Permutations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.14

Author Details

Mrudula Balachander
  • Université libre de Bruxelles (ULB), Belgium
Emmanuel Filiot
  • Université libre de Bruxelles (ULB), Belgium
Raffaella Gentilini
  • University of Perugia, Italy
Nikos Tzevelekos
  • Queen Mary University of London, UK

Funding

  • Balachander, Mrudula: Research Fellow at F.R.S.-FNRS.
  • Filiot, Emmanuel: Research Director at F.R.S.-FNRS. This work was partially funded by the FNRS project 40020726.

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