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A Generic Solution to Register-Bounded Synthesis with an Application to Discrete Orders

Authors Léo Exibard, Emmanuel Filiot, Ayrat Khalimov

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Author Details

Léo Exibard
  • Reykjavik University, Iceland
Emmanuel Filiot
  • Université libre de Bruxelles, Brussels, Belgium
Ayrat Khalimov
  • Université libre de Bruxelles, Brussels, Belgium

Funding

This work was supported by the Fonds de la Recherche Scientifique - F.R.S.-FNRS under the MIS project F451019F. Emmanuel Filiot is a senior research associate at F.R.S.-FNRS. Léo Exibard was supported by the project "Mode(l)s of Verification and Monitorability (MoVeMnt)" (no. 217987-051) of the Icelandic Research Fund.

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Léo Exibard, Emmanuel Filiot, and Ayrat Khalimov. A Generic Solution to Register-Bounded Synthesis with an Application to Discrete Orders. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 122:1-122:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ICALP.2022.122

Abstract

We study synthesis of reactive systems interacting with environments using an infinite data domain. A popular formalism for specifying and modelling such systems is register automata and transducers. They extend finite-state automata by adding registers to store data values and to compare the incoming data values against stored ones. Synthesis from nondeterministic or universal register automata is undecidable in general. However, its register-bounded variant, where additionally a bound on the number of registers in a sought transducer is given, is known to be decidable for universal register automata which can compare data for equality, i.e., for data domain (ℕ, =). This paper extends the decidability border to the domain (ℕ, <) of natural numbers with linear order. Our solution is generic: we define a sufficient condition on data domains (regular approximability) for decidability of register-bounded synthesis. The condition is satisfied by natural data domains like (ℕ, <). It allows one to use simple language-theoretic arguments and avoid technical game-theoretic reasoning. Further, by defining a generic notion of reducibility between data domains, we show the decidability of synthesis in the domain (ℕ^d, <^d) of tuples of numbers equipped with the component-wise partial order and in the domain (Σ^*,≺) of finite strings with the prefix relation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Transducers
Keywords
  • Synthesis
  • Register Automata
  • Transducers
  • Ordered Data Domains

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