The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
The complementation problem for Bu¨chi automata with applications to temporal logic
Theoretical Computer Science
An automata theoretic decision procedure for the propositional mu-calculus
Information and Computation
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Progress measures for complementation of &ohgr;-automata with applications to temporal logic
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Weak alternating automata and tree automata emptiness
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The size-change principle for program termination
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Weak alternating automata are not that weak
ACM Transactions on Computational Logic (TOCL)
A really abstract concurrent model and its temporal logic
POPL '86 Proceedings of the 13th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
An Effective Tableau System for the Linear Time µ-Calculus
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Alternation Elimination by Complementation (Extended Abstract)
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Electronic Notes in Theoretical Computer Science (ENTCS)
A Solver for Modal Fixpoint Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
Size-change termination and satisfiability for linear-time temporal logics
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Ramsey-Based analysis of parity automata
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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The linear time μ-calculus extends LTL with arbitrary least and greatest fixpoint operators. This gives it the power to express all ω-regular languages, i.e. strictly more than LTL. The validity problem is PSPACE-complete for both LTL and the linear time μ-calculus. In practice it is more difficult for the latter because of nestings of fixpoint operators and variables with several occurrences. We present a simple sound and complete infinitary proof system for the linear time μ-calculus and then present two decision procedures for provability in the system, hence validity of formulas. One uses nondeterministic Büchi automata, the other one a generalisation of size-change termination analysis (SCT) known from functional programming. The main novelties of this paper are the connection with SCT and the fact that both decision procedures have a better asymptotic complexity than earlier ones and have been implemented.