A coalgebraic perspective on linear weighted automata

  • Authors:

  • Filippo Bonchi;Marcello Bonsangue;Michele Boreale;Jan Rutten;Alexandra Silva

  • Affiliations:

  • ENS Lyon, Université de Lyon, LIP (UMR 5668 CNRS ENS Lyon UCBL INRIA), 46 Allée dItalie, 69364 Lyon, France;Leiden Institute of Advanced Computer Science, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands and Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands;Dipartimento di Sistemi e Informatica, Universití di Firenze, Viale Morgagni 65, I-50134 Firenze, Italy;Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands and Radboud Universiteit Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands;Radboud Universiteit Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands and Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands and HASLab/INESC TEC, ...

  • Venue:
  • Information and Computation
  • Year:
  • 2012

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Abstract

Weighted automata are a generalisation of non-deterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for non-deterministic automata, their behaviours can be expressed in terms of either (weighted) bisimilarity or (weighted) language equivalence. Coalgebras provide a categorical framework for the uniform study of state-based systems and their behaviours. In this work, we show that coalgebras can suitably model weighted automata in two different ways: coalgebras on Set (the category of sets and functions) characterise weighted bisimilarity, while coalgebras on Vect (the category of vector spaces and linear maps) characterise weighted language equivalence. Relying on the second characterisation, we show three different procedures for computing weighted language equivalence. The first one consists in a generalisation of the usual partition refinement algorithm for ordinary automata. The second one is the backward version of the first one. The third procedure relies on a syntactic representation of rational weighted languages.