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From Timed Automata to Logic  and Back
 MFCS’95, LNCS 969
, 1995
"... One of the most successful techniques for automatic verification is that of model checking. For finite automata there exist since long extremely efficient modelchecking algorithms, and in the last few years these algorithms have been made applicable to the verification of realtime automata usi ..."
Abstract

Cited by 52 (7 self)
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One of the most successful techniques for automatic verification is that of model checking. For finite automata there exist since long extremely efficient modelchecking algorithms, and in the last few years these algorithms have been made applicable to the verification of realtime automata using the regiontechniques of Alur and Dill. In this
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 39 (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...
Modal Logic: A Semantic Perspective
 ETHICS
, 1988
"... This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimul ..."
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Cited by 13 (1 self)
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This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimulations) which underly it. We introduce the syntax and semantics of basic modal logic, discuss its expressivity at the level of models, examine its computational properties, and then consider what it can say at the level of frames. We then move beyond the basic modal language, examine the kinds of expressivity offered by a number of richer modal logics, and try to pin down what it is that makes them all ‘modal’. We conclude by discussing an example which brings many of the ideas we discuss into play: games.
A Complete Deductive System for the µCalculus
, 1995
"... The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper ..."
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Cited by 13 (0 self)
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The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper
Formal Design of Reliable Real Time Systems
, 1995
"... This thesis presents formal techniques to be used when describing and developing reliable real time systems. Three different probabilistic real time logics, used to specify about reliable real time processes in terms of timed probabilistic graphs, are presented. Algorithms for verifying implementati ..."
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Cited by 5 (0 self)
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This thesis presents formal techniques to be used when describing and developing reliable real time systems. Three different probabilistic real time logics, used to specify about reliable real time processes in terms of timed probabilistic graphs, are presented. Algorithms for verifying implementations with respect to specifications in the developed logics are presented. An algorithm to construct timed probabilistic graphs from specifications in one of the logics is presented. An algorithm
AND
"... 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, ..."
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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. 0 1989 Academic Press, Inc. 1.
A Temporal Logic for Planning under Uncertainty
, 2013
"... Dealing with uncertainty in the context of planning has been an active research subject in AI. Addressing the case when uncertainty evolves over time can be difficult. In this work, we provide a solution to this problem by proposing a temporal logic to reason about quantities and probability. For th ..."
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Dealing with uncertainty in the context of planning has been an active research subject in AI. Addressing the case when uncertainty evolves over time can be difficult. In this work, we provide a solution to this problem by proposing a temporal logic to reason about quantities and probability. For this logic, we provide a PSPACE SAT algorithm together with a complete calculus. The algorithm enables us to perform planning under uncertainty via SAT, extending a technique used for classic planning. We can show that any obtained plan will have certain properties (desired or undesired). The calculus can also be used to derive the impossibility of a plan, given a set of specifications. 1
Exogenous Logics for Reasoning about Probabilistic Systems
"... Abstract. We define exogenous logics for reasoning about probabilistic systems: a probabilistic state logic EPPL, and its fixpoint extension MEPL, which is enriched with operators from the modal µcalculus. System states correspond to probability distributions over classical states and the system ev ..."
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Abstract. We define exogenous logics for reasoning about probabilistic systems: a probabilistic state logic EPPL, and its fixpoint extension MEPL, which is enriched with operators from the modal µcalculus. System states correspond to probability distributions over classical states and the system evolution is modeled by parametrized Kripke structures that capture both stochastic and non–deterministic transitions. We introduce two approaches to the verification of properties expressed in these logics, one syntactic (a weakly complete Hilbert calculus) and the other semantic (a model–checking algorithm). The completeness proof of MEPL builds on the decidability of the existential theory of the real numbers and on a polynomialspace sat algorithm for EPPL. The model checking problem for MEPL is also analysed and the logic is related to previous work. The semantics of EPPL and MEPL are defined in terms of probability distributions over sets of propositional symbols, whereas the usual approaches are designed for reasoning about distributions over paths of possible behaviour. The intended application of our logics is as a specification formalism for properties of probabilistic systems. We illustrate the use of the logics for specifying system properties with some simple examples. 1.
Fixpoint Logics for Reasoning about Probabilistic Systems
, 2010
"... Abstract. We consider exogenous logics for reasoning about probabilistic systems: a variant of probabilistic state logic EPPL[24], and its fixpoint extension MEPL, which is enriched with operators from the modal µcalculus. System states correspond to probability distributions over classical states ..."
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Abstract. We consider exogenous logics for reasoning about probabilistic systems: a variant of probabilistic state logic EPPL[24], and its fixpoint extension MEPL, which is enriched with operators from the modal µcalculus. System states correspond to probability distributions over classical states and the system evolution is modeled by parametrized Kripke structures that capture both stochastic and non–deterministic transitions. We introduce two approaches to the verification of properties expressed in these logics, one syntactic (a weakly complete Hilbert calculus) and the other semantic (a model– checking algorithm). The completeness proof of MEPL builds on the decidability of the existential theory of the real numbers and on a polynomialspace sat algorithm for EPPL. The model checking problem for MEPL is also analysed and the logic is related to previous work. The semantics of EPPL and MEPL are defined in terms of probability distributions over sets of propositional symbols, whereas the usual approaches are designed for reasoning about distributions over paths of possible behaviour. The intended application of our logics is as a specification formalism for properties of probabilistic systems. We illustrate the use of the logics for specifying system properties with some simple examples. 1