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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 1102 (16 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
Relations in Concurrency
"... The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the seman ..."
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Cited by 261 (33 self)
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The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higherorder processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
Modelling Concurrency with Partial Orders
, 1986
"... Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a n ..."
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Cited by 236 (18 self)
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Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a natural class of models of concurrent processes. The heart of the approach is a notion of partial string derived from the view of a string as a linearly ordered multiset by relaxing the linearity constraint, thereby permitting partially ordered multisets or pomsets. Just as sets of strings form languages, so do sets of pomsets form processes. We introduce a number of operations useful for specifying concurrent processes and demonstrate their utility on some basic examples. Although none of the operations is particularly oriented to nets it is nevertheless possible to use them to express processes constructed as a net of subprocesses, and more generally as a system consisting of components. Th...
Reasoning about The Past with TwoWay Automata
 In 25th International Colloqium on Automata, Languages and Programming, ICALP ’98
, 1998
"... Abstract. The pcalculus can be viewed as essentially the "ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the pcalculus is EXPTIMEcomplete. This upp ..."
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Cited by 128 (12 self)
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Abstract. The pcalculus can be viewed as essentially the "ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the pcalculus is EXPTIMEcomplete. This upper bound, however, is known for a version of the logic that has only forward modalities, which express weakest preconditions, but not backward modalities, which express strongest postconditions. Our main result in this paper is an exponential time upper bound for the satisfiability problem of the pcalculus with both forward and backward modalities. To get this result we develop a theory of twoway alternating automata on infinite trees. 1
ModelChecking of Causality Properties
, 1995
"... A temporal logic for causality (Tlc) is introduced. The logic is interpreted over causal structures corresponding to partial order executions of programs. For causal structures describing the behavior of a finite fixed set of processes, a Tlcformula can, equivalently, be interpreted over their line ..."
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Cited by 43 (10 self)
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A temporal logic for causality (Tlc) is introduced. The logic is interpreted over causal structures corresponding to partial order executions of programs. For causal structures describing the behavior of a finite fixed set of processes, a Tlcformula can, equivalently, be interpreted over their linearizations. The main result of the paper is a tableau construction that gives a singlyexponential translation from a Tlc formula ' to a Streett automaton that accepts the set of linearizations satisfying '. This allows both checking the validity of Tlc formulas and modelchecking of program properties. As the logic Tlc does not distinguish among different linearizations of the same partial order execution, partial order reduction techniques can be applied to alleviate the statespace explosion problem of modelchecking. 1 Introduction One of the most successful techniques for automatic verification of finitestate systems has been modelchecking . A modelchecking algorithm decides wheth...
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 38 (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...
Hyperdocuments as Automata: Verification of Tracebased Browsing Properties by Model Checking
, 1997
"... As hypertext systems proliferate and as networks become more ubiquitous, an important problem is to determine how to provide hyperdocument interoperability. Instead of taking the approach of standardizing, and implementing, a large and complex set of browsing features gleaned from some "union" of ex ..."
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Cited by 26 (3 self)
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As hypertext systems proliferate and as networks become more ubiquitous, an important problem is to determine how to provide hyperdocument interoperability. Instead of taking the approach of standardizing, and implementing, a large and complex set of browsing features gleaned from some "union" of existing systems, we present an approach that allows each document to encode its own browsing semantics in the links of the hyperdocument. Any implementation offering the "follow link" operation can then simulate the intent of the author. The method requires a mental shift in how a hyperdocument is viewed abstractly. Instead of treating the links of a document as defining a static directed graph, they are thought of as defining an abstract program, termed the linksautomaton of the document. A branching temporal logic notation, termed HTL*, is introduced for specifying properties a document should exhibit during browsing. An automated program verification technique called model checking is ...
Once and For All
, 2011
"... It has long been known that pasttime operators add no expressive power to linear temporal logics. In this paper, we consider the extension of branching temporal logics with pasttime operators. Two possible views regarding the nature of past in a branchingtime model induce two different such exten ..."
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Cited by 26 (2 self)
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It has long been known that pasttime operators add no expressive power to linear temporal logics. In this paper, we consider the extension of branching temporal logics with pasttime operators. Two possible views regarding the nature of past in a branchingtime model induce two different such extensions. In the first view, past is branching and each moment in time may have several possible futures and several possible pasts. In the second view, past is linear and each moment in time may have several possible futures and a unique past. Both views assume that past is finite. We discuss the practice of these extensions as specification languages, characterize their expressive power, and examine the complexity of their modelchecking and satisfiability problems.
Logics for Specifying Concurrent Information Systems
 LOGICS FOR DATABASES AND INFORMATION SYSTEMS
, 1998
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