The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
A decision procedure for combinations of propositional temporal logic and other specialized theories
Journal of Automated Reasoning
Automata-Theoretic techniques for modal logics of programs
Journal of Computer and System Sciences
An axiomatization of Lamport's temporal logic of actions
CONCUR '90 Proceedings on Theories of concurrency : unification and extension: unification and extension
Handbook of theoretical computer science (vol. B)
Interval logics for temporal specification and verification
Interval logics for temporal specification and verification
Automata For Modeling Real-Time Systems
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
On the Relation of Programs and Computations to Models of Temporal Logic
Temporal Logic in Specification
Using a Theorem Prover for Reasoning about Concurrent Algorithms
CAV '92 Proceedings of the Fourth International Workshop on Computer Aided Verification
Mechanical Verification of Concurrent Systems with TLA
CAV '92 Proceedings of the Fourth International Workshop on Computer Aided Verification
An Old-Fashioned Recipe for Real Time
Proceedings of the Real-Time: Theory in Practice, REX Workshop
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
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The Temporal Logic of Actions (TLA) devised by Lamport is a logic for proving the correctness of concurrent systems. A distinctive feature of the logic is the use of “action formulae” to encode the “before-after” behaviour of transitions, a feature that is especially suitable for Lamport's transition-axiom method. Abadi has given a complete axiomatization for the propositional fragment of this logic, and conjectured that its validity problem may be in PSPACE. In this paper we confirm that conjecture. In fact we show that the validity problem for TLA is PSPACE-complete. For this we give a space-optimal automata-theoretic decision procedure for TLA. Our result is obtained with respect to a logic which is a conservative extension of Lamport's TLA. Thus our decision procedure applies to the more restricted logic. We show how the automata-theoretic framework handles abstraction, as used in TLA, a feature considered useful for hierarchical and compositional reasoning.