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Determinisation of Finitely-Ambiguous Copyless Cost Register Automata

Authors Théodore Lopez , Benjamin Monmege , Jean-Marc Talbot

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Author Details

Théodore Lopez
  • Aix Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France
Benjamin Monmege
  • Aix Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France
Jean-Marc Talbot
  • Aix Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France

Funding

This work has been funded by the DeLTA project (ANR-16-CE40-0007).

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Théodore Lopez, Benjamin Monmege, and Jean-Marc Talbot. Determinisation of Finitely-Ambiguous Copyless Cost Register Automata. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 75:1-75:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.MFCS.2019.75

Abstract

Cost register automata (CRA) are machines reading an input word while computing values using write-only registers: values from registers are combined using the two operations, as well as the constants, of a semiring. Particularly interesting is the subclass of copyless CRAs where the content of a register cannot be used twice for updating the registers. Originally deterministic, non-deterministic variant of CRA may also be defined: the semantics is then obtained by combining the values of all accepting runs with the additive operation of the semiring (as for weighted automata). We show that finitely-ambiguous copyless non-deterministic CRAs (i.e. the ones that admit a bounded number of accepting runs on every input word) can be effectively transformed into an equivalent copyless (deterministic) CRA, without requiring any specific property on the semiring. As a corollary, this also shows that regular look-ahead can effectively be removed from copyless CRAs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantitative automata
Keywords
  • Cost-register automata
  • Look-ahead removal
  • Unambiguity
  • Determinisation

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