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Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
Automated Temporal Reasoning about Reactive Systems
, 1996
"... . There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective a ..."
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Cited by 41 (2 self)
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. There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective and reliable means of specifying and ensuring correct behavior of such systems. This paper discusses known complexity and expressiveness results for a number of such logics in common use and describes key technical tools for obtaining essentially optimal mechanical reasoning algorithms. However, the emphasis is on underlying intuitions and broad themes rather than technical intricacies. 1 Introduction There is a growing need for reliable methods of designing correct reactive systems. These systems are characterized by ongoing, typically nonterminating and highly nondeterministic behavior. Examples include operating systems, network protocols, and air traffic control systems. There is w...
Safety, Liveness and Fairness in Temporal Logic
 Formal Aspect of Computing
, 1999
"... In this paper we present syntactic characterization of temporal formulas that express various properties of interest in the verification of concurrent programs. Such a characterization helps us in choosing the right techniques for proving correctness with respect to these properties. The properties ..."
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Cited by 3 (0 self)
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In this paper we present syntactic characterization of temporal formulas that express various properties of interest in the verification of concurrent programs. Such a characterization helps us in choosing the right techniques for proving correctness with respect to these properties. The properties that we consider include safety properties, liveness properties and fairness properties. We also present algorithms for checking if a given temporal formula expresses any of these properties. Key Words: Concurrent Programs, Verification, Temporal Logic, Safety Properties, Liveness Properties, Fairness Properties, Algorithms. This work is partly supported by NSF grant CCR9212183. A preliminary version of this paper appeared in the Fourth ACM Symposium on Principles of Distributed Computing. 1 Introduction In the verification of concurrent programs two kinds of properties are of primary importance and have been extensively investigated ([La77]): safety properties and liveness properties....
Anchored LTL Separation
"... Gabbay’s separation theorem is a fundamental result for linear temporal logic (LTL). We show that separating a restricted class of LTL formulas, called anchored LTL, is elementary if and only if the translation from LTL to the linear temporal logic with only future temporal connectives is elementary ..."
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Gabbay’s separation theorem is a fundamental result for linear temporal logic (LTL). We show that separating a restricted class of LTL formulas, called anchored LTL, is elementary if and only if the translation from LTL to the linear temporal logic with only future temporal connectives is elementary. To prove this result, we define a canonical separation for LTL, and establish a correspondence between a canonical separation of anchored LTL formulas and the ωautomata that recognize these formulas. The canonical separation of anchored LTL formulas has two further applications. First, we constructively prove that the safety closure of any LTL property is an LTL property, thus proving the decomposition theorem for LTL: every LTL formula is equivalent to the conjunction of a safety LTL formula and a liveness LTL formula. Second, we characterize safety, liveness, absolute liveness, stable, and fairness properties in LTL. Our characterization is effective: We reduce the problem of deciding whether an LTL formula defines any of these properties to the validity problem for LTL. Categories and Subject Descriptors Theory of computation [Logic]: Modal and temporal logics; Theory of computation [Formal languages and automata theory]: Automata over infinite objects; Theory of computation [Formal languages and automata theory]: Regular languages