Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Theoretical Computer Science
The Complexity of Tree Automata and Logics of Programs
SIAM Journal on Computing
Completeness of Kozen's axiomatisation of the propositional &mgr;-calculus
Information and Computation
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
Modal and temporal properties of processes
Modal and temporal properties of processes
On the Expressivity of the Modal Mu-Calculus
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
The Complexity of the Graded µ-Calculus
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Modular Games for Coalgebraic Fixed Point Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
A Coalgebraic Perspective on Monotone Modal Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Automata and fixed point logic: A coalgebraic perspective
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
A finite model construction for coalgebraic modal logic
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
A Solver for Modal Fixpoint Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
Automata for coalgebras: an approach using predicate liftings
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Flat coalgebraic fixed point logics
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Optimal tableau algorithms for coalgebraic logics
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Global caching for coalgebraic description logics
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Coinductive Predicates and Final Sequences in a Fibration
Electronic Notes in Theoretical Computer Science (ENTCS)
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The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this paper, we introduce the coalgebraic µ-calculus, an extension of the general (coalgebraic) framework with fixpoint operators. Our main results are completeness of the associated tableau calculus and EXPTIME decidability. Technically, this is achieved by reducing satisfiability to the existence of non-wellfounded tableaux, which is in turn equivalent to the existence of winning strategies in parity games. Our results are parametric in the underlying class of models and yield, as concrete applications, previously unknown complexity bounds for the probabilistic µ-calculus and for an extension of coalition logic with fixpoints.