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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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Cited by 1300 (17 self)
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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...
A zeroone law for logic with a fixedpoint operator
 Inform. and Control
"... The logic obtained by adding the leastfixedpoint operator to firstorder logic was proposed as a query language by Aho and Ullman (in "Proc. 6th ACM Sympos. on Principles of Programming Languages, " 1979, pp. 110120) and has been studied, particularly in connection with finite models, b ..."
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Cited by 20 (7 self)
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The logic obtained by adding the leastfixedpoint operator to firstorder logic was proposed as a query language by Aho and Ullman (in "Proc. 6th ACM Sympos. on Principles of Programming Languages, " 1979, pp. 110120) and has been studied, particularly in connection with finite models, by numerous authors. We extend to this logic, and to the logic containing the more powerful iterativefixedpoint operator, the zeroone law proved for firstorder logic in (Glebskii, Kogan, Liogonki, and Talanov (1969), Kibernetika 2, 3142; Fagin (1976), J. Symbolic Logic 41, 5058). For any sentence q ~ of the extended logic, the proportion of models of q ~ among all structures with universe {1, 2,..., n} approaches 0 or 1 as n tends to infinity. We also show that the problem of deciding, for any cp, whether this proportion approaches 1 is complete for exponential time, if we consider only q)'s with a fixed finite vocabulary (or vocabularies of bounded arity) and complete for doubleexponential time if ~0 is unrestricted. In addition, we establish some related results. © 1985 Academic Press, Inc.
The propositional mucalculus is elementary
 of Lecture
"... ABSTRACT: The propositional mucalculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the Propositional Dynamic Logic of Fischer and Ladner, the infinite looping construct of Streett, and the Game Logic of Parikh. We give an elementary time decision p ..."
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Cited by 15 (0 self)
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ABSTRACT: The propositional mucalculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the Propositional Dynamic Logic of Fischer and Ladner, the infinite looping construct of Streett, and the Game Logic of Parikh. We give an elementary time decision procedure, using a reduction to the emptiness problem for automata on infinite trees. A small model theorem is obtained as a corollary. 1.
RALL: Machinesupported Proofs for Relation Algebra
 PROCEEDINGS OF CADE14, LECTURE NOTES IN COMPUTER SCIENCE 1249
, 1997
"... We present a theorem proving system for abstract relation algebra called RALL (= RelationAlgebraic Language and Logic), based on the generic theorem prover Isabelle. On the one hand, the system is an advanced case study for Isabelle/HOL, and on the other hand, a quite mature proof assistant for ..."
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Cited by 7 (0 self)
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We present a theorem proving system for abstract relation algebra called RALL (= RelationAlgebraic Language and Logic), based on the generic theorem prover Isabelle. On the one hand, the system is an advanced case study for Isabelle/HOL, and on the other hand, a quite mature proof assistant for research on the relational calculus. RALL is able to deal with the full language of heterogeneous relation algebra including higherorder operators and domain constructions, and checks the typecorrectness of all formulas involved. It offers both an interactive proof facility, with special support for substitutions and estimations, and an experimental automatic prover. The automatic proof method exploits an isomorphism between relationalgebraic and predicatelogical formulas, relying on the classical universalalgebraic concepts of atom structures and complex algebras.
Algebraic Foundations of the Unifying Theories of Programming
, 2007
"... Hoare and He’s Unifying Theories of Programming take a relational view on semantics. The meaning of a nondeterministic, imperative program is described by ‘designs’ composed of two relations. They represent terminating states and relate the initial and final values of the observable variables, resp ..."
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Hoare and He’s Unifying Theories of Programming take a relational view on semantics. The meaning of a nondeterministic, imperative program is described by ‘designs’ composed of two relations. They represent terminating states and relate the initial and final values of the observable variables, respectively. Several ‘healthiness conditions’ are imposed by the theory to obtain properties found in practice. This work determines the structure of designs and modifies the theory to support nonstrict computations. It achieves these goals by identifying healthiness conditions and related axioms that involve unnecessary restrictions and subsequently removing them. The outcome provides a clear account of the algebraic foundations of the Unifying Theories of Programming. One of the results is a generalisation of designs by constructing them on semirings with ideals, structures having fewer axioms than relations. This clarifies the essential algebraic structure of designs, allows the reuse of existing mathematical theory and connects to further semantical approaches. The framework is extended by algebraic formulations of finite and infinite iteration, domain, preimage, determinacy, invariants and convergence. Calculations
Acknowledgments
, 2000
"... this report were made possible mainly with the financial support of the Ford Foundation. Additional contributions were received from Cosmetics Oriflame Romania and the Open Society Institute. We owe much to John Robbins, who conceived and developed the idea of this project. We thank the following ..."
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this report were made possible mainly with the financial support of the Ford Foundation. Additional contributions were received from Cosmetics Oriflame Romania and the Open Society Institute. We owe much to John Robbins, who conceived and developed the idea of this project. We thank the following for their contributions, support and assistance: The main implementers of the project: Renate Weber, Nicole Watson, Roxana Tesiu, Gulhan Borubaeva, Aurelija Kuzmaite, Tanya Lokshina, Genoveva Tisheva, and all the local rapporteurs and host NGOs; IHF staff who provided editorial and administrative assistance: Brigitte Dufour, Paula TscherneLempi inen, Ursula Lindenberg, Joachim Frank, Maria Kolb, Natalia Lazareva, Rainer Tannenberger, Judith Vitt and David Theil; Friends in the diplomatic, foundation, and civil society community and others who helped: Irena Gross, Sylvia Hordosch, Evelyn Watson, Milos UvericKostic, Agnes Horvthov, Liz Bonkow
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...