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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.
Model checking and the Mucalculus
 DIMACS Series in Discrete Mathematics
, 1997
"... There is a growing recognition of the need to apply formal mathematical methods in the design of "high confidence" computing systems. Such systems operate in safety critical contexts (e.g., air traffic control systems) or where errors could have major adverse economic consequences (e.g., ..."
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Cited by 47 (0 self)
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There is a growing recognition of the need to apply formal mathematical methods in the design of "high confidence" computing systems. Such systems operate in safety critical contexts (e.g., air traffic control systems) or where errors could have major adverse economic consequences (e.g., banking networks). The problem is especially acute in the design of many reactive systems which must exhibit correct ongoing behavior, yet are not amenable to thorough testing due to their inherently nondeterministic nature. One useful approach for specifying and reasoning about correctness of such systems is temporal logic model checking, which can provide an efficient and expressive tool for automatic verification that a finite state system meets a correctness specification formulated in temporal logic. We describe model checking algorithms and discuss their application. To do this, we focus attention on a particularly important type of temporal logic known as the Mucalculus.
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...
Number of Variables Is Equivalent To Space
, 1999
"... We prove that the set of properties describable by a uniform sequence of firstorder sentences using at most k + 1 distinct variables is exactly equal to the set of properties checkable by a Turing machine in DSPACE [n k ] (where n is the size of the universe). This set is also equal to the set of ..."
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We prove that the set of properties describable by a uniform sequence of firstorder sentences using at most k + 1 distinct variables is exactly equal to the set of properties checkable by a Turing machine in DSPACE [n k ] (where n is the size of the universe). This set is also equal to the set of properties describable using an iterative definition for a finite set of relations of arity k. This is a refinement of the theorem PSPACE = VAR[O[1]] [7]. We suggest some directions for exploiting this result to derive tradeoffs between the number of variables and the quantifier depth in descriptive complexity. 1 Introduction In Descriptive Complexity one analyzes the complexity of a language in terms of the complexity of describing the language. It is known that the quantifier depth and number of variables needed to express the membership property of a language is closely related to the Research supported in part by NSF grant CCR9505446. y Research supported in part by NSERC, and p...
Descriptive Complexity and Finite Models
"... This paper introduces algebraic proof systems for the propositional calculus. We present new results concerning the relative efficiency of these systems, and also survey what is currently known. Many open problems are presented. 1 Introduction A fundamental problem in logic and computer science is ..."
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This paper introduces algebraic proof systems for the propositional calculus. We present new results concerning the relative efficiency of these systems, and also survey what is currently known. Many open problems are presented. 1 Introduction A fundamental problem in logic and computer science is understanding the efficiency of propositional proof systems. It has been known for a long time that NP = coNP if and only if there exists an efficient propositional proof system, but despite 25 years of research, this problem is still not resolved. (See [46] for an excellent survey of this area.) The intention of the present article is to introduce a new algebraic approach to this problem. Our proof systems are simpler than classical proof systems, and purely algebraic. It is our hope that by studying proof complexity in this light, that new upper and lower bound techniques may emerge. The use of the Nullstellensatz for propositional refutations may have been first suggested in a paper by Lo...