Propositional dynamic logic of regular programs
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A formal syntax and semantics for the propositional dynamic logic of regular programs is defined and principal conclusions are that deciding satisfiability of length n formulas requires time d n /log n for some d > 1, and that satisfiability can be decided in nondeterministic time cn for some c.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1979-04-01 and is currently open access. It has received 1298 citations till now. The article focuses on the topics: Propositional variable & Well-formed formula.read more
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Journal ArticleDOI
A theory of timed automata
Rajeev Alur,David L. Dill +1 more
TL;DR: Alur et al. as discussed by the authors proposed timed automata to model the behavior of real-time systems over time, and showed that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the non-deterministic case and PSPACE-complete in deterministic case.
Book ChapterDOI
Temporal and modal logic
TL;DR: In this article, a multiaxis classification of temporal and modal logic is presented, and the formal syntax and semantics for two representative systems of propositional branching-time temporal logics are described.
Journal ArticleDOI
Results on the propositional μ-calculus
TL;DR: A propositional μ-calculus L μ is defined and study, which consists essentially of propositional modal logic with a least fixpoint operator that is syntactically simpler yet strictly more expressive than Propositional Dynamic Logic (PDL).
Book
Dynamic Logic
TL;DR: This book provides the first comprehensive introduction to Dynamic Logic, a system of remarkable unity that is theoretically rich as well as of practical value.
References
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Guarded commands, nondeterminacy and formal derivation of programs
TL;DR: So-called “guarded commands” are introduced as a building block for alternative and repetitive constructs that allow nondeterministic program components for which at least the activity evoked, but possibly even the final state, is not necessarily uniquely determined by the initial state.
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Semantical analysis of modal logic i. normal propositional calculi
TL;DR: In this article, a semantical analysis of modal logic ii and non-normal modal propositional calculi is presented, and the tableaux that leads to a decision procedure for the propositional calculus is considered.
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Semantical considerations on floyd-hoare logic
TL;DR: An appropriate axiom system is given which is complete for loop-free programs and also puts conventional predicate calculus in a different light by lumping quantifiers with non-logical assignments rather than treating them as logical concepts.
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The Computational Complexity of Provability in Systems of Modal Propositional Logic
TL;DR: The computational complexity of the provability problem in systems of modal propositional logic is investigated and it is found that every problem computable in polynomial space is reducible to the provable problem in any modal system between K and S4.