Automata for coalgebras: an approach using predicate liftings

  • Authors:

  • Gaëlle Fontaine;Raul Leal;Yde Venema

  • Affiliations:

  • Institute for Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, The Netherlands;Institute for Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, The Netherlands;Institute for Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, The Netherlands

  • Venue:
  • ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

Universal Coalgebra provides the notion of a coalgebra as the natural mathematical generalization of state-based evolving systems such as (infinite) words, trees, and transition systems. We lift the theory of parity automata to this level of abstraction by introducing, for a set Λ of predicate liftings associated with a set functor T, the notion of a Λ-automata operating on coalgebras of type T. In a familiar way these automata correspond to extensions of coalgebraic modal logics with least and greatest fixpoint operators. Our main technical contribution is a general bounded model property result: We provide a construction that transforms an arbitrary Λ-automaton A with nonempty language into a small pointed coalgebra (S, s) of type T that is recognized by A, and of size exponential in that of A. S is obtained in a uniform manner, on the basis of the winning strategy in our satisfiability game associated with A. On the basis of our proof we obtain a general upper bound for the complexity of the nonemptiness problem, under some mild conditions on Λ and T. Finally, relating our automata-theoretic approach to the tableaux-based one of Cîrstea et alii, we indicate how to obtain their results, based on the existence of a complete tableau calculus, in our framework.