896 research outputs found
Completeness of Flat Coalgebraic Fixpoint Logics
Modal fixpoint logics traditionally play a central role in computer science,
in particular in artificial intelligence and concurrency. The mu-calculus and
its relatives are among the most expressive logics of this type. However,
popular fixpoint logics tend to trade expressivity for simplicity and
readability, and in fact often live within the single variable fragment of the
mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL,
and the logic of common knowledge. Extending this notion to the generic
semantic framework of coalgebraic logic enables covering a wide range of logics
beyond the standard mu-calculus including, e.g., flat fragments of the graded
mu-calculus and the alternating-time mu-calculus (such as alternating-time
temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We
give a generic proof of completeness of the Kozen-Park axiomatization for such
flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on
Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer
Science, Springer, 2010, pp. 524-53
Coalgebraic Automata Theory: Basic Results
We generalize some of the central results in automata theory to the
abstraction level of coalgebras and thus lay out the foundations of a universal
theory of automata operating on infinite objects.
Let F be any set functor that preserves weak pullbacks. We show that the
class of recognizable languages of F-coalgebras is closed under taking unions,
intersections, and projections. We also prove that if a nondeterministic
F-automaton accepts some coalgebra it accepts a finite one of the size of the
automaton. Our main technical result concerns an explicit construction which
transforms a given alternating F-automaton into an equivalent nondeterministic
one, whose size is exponentially bound by the size of the original automaton.Comment: 43 page
Sahlqvist's Theorem for Boolean algebras with operators with an application to cylindric algebras
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