Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Improved upper and lower bounds for modal logics of programs
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
In transition from global to modular temporal reasoning about programs
Logics and models of concurrent systems
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
A linear-time model-checking algorithm for the alternation-free modal mu-calculus
Formal Methods in System Design - Special issue on computer-aided verification: special methods II
Model checking and modular verification
ACM Transactions on Programming Languages and Systems (TOPLAS)
CTL and ECTL as fragments of the modal &mgr;-calculus
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
Fast and simple nested fixpoints
Information Processing Letters
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
Model checking
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
An automata-theoretic approach to modular model checking
ACM Transactions on Programming Languages and Systems (TOPLAS)
Symbolic Model Checking
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
Temporal Logic with Fixed Points
Temporal Logic in Specification
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
An Improved Algorithm for the Evaluation of Fixpoint Expressions
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Logical Specification and Analysis of Fault Tolerant Systems Through Partial Model Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Deciding monotone duality and identifying frequent itemsets in quadratic logspace
Proceedings of the 32nd symposium on Principles of database systems
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One source of complexity in the µ-calculus is its ability to specify an unbounded number of switches between universal (AX) and existential (EX) branching modes. We therefore study the problems of satisfiability, validity, model checking, and implication for the universal and existential fragments of the µ-calculus, in which only one branching mode is allowed. The universal fragment is rich enough to express most specifications of interest, and therefore improved algorithms are of practical importance. We show that while the satisfiability and validity problems become indeed simpler for the existential and universal fragments, this is, unfortunately, not the case for model checking and implication. We also show the corresponding results for the alternation-free fragment of the µ-calculus, where no alternations between least and greatest fixed points are allowed. Our results imply that efforts to find a polynomial-time model-checking algorithm for the µ-calculus can be replaced by efforts to find such an algorithm for the universal or existential fragment.