L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th ACM Symp. on Principles of Programming Languages, pages 174--185, January 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that might be taken from each state in a system. The standard formulations of linear time logic (LTL [16,37] and branchingtime logic (CTL [6,16] are often presented as incomparable, because of theoretical results that assert that the two logics are incomparable in terms of expressivity [3,17,27]. Indeed, in a landmark paper, Lamport presented lineartime logic and branching time logic as competing semantical interpretations of the same temporal logic notation [27] Although these insights are valuable, they have suggested that the linear time and branching time approaches are ....

.... as incomparable, because of theoretical results that assert that the two logics are incomparable in terms of expressivity [3,17,27] Indeed, in a landmark paper, Lamport presented lineartime logic and branching time logic as competing semantical interpretations of the same temporal logic notation [27]. Although these insights are valuable, they have suggested that the linear time and branching time approaches are competitors, locked in a dual where one must vanquish the other [18,50] A significant paper by Cousot and Cousot shows that this scenario need not be the case [12] By employing ....

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L. Lamport. Sometimes is sometimes "not never"--on the temporal logic of programs. In Proc. 7th ACM Symp. Principles of Prog. Lang., pages 174--185. ACM Press, 1980.

....monadic second order theory of two successors with set quantification restricted to infinite paths over infinite binary trees. Much more results have been established for comparisons among branching temporal logics and a precise hierarchy, having at the top CTL and at bottom CTL, is proved in [EC81, EH86, Lam80]. The class of logics considered in this hierarchy is defined by a general framework having as basic modalities the formulae of type VT or 3T, where T is an LTL formula, and formulae are built up by using boolean connectives and nesting on these basic modalities. Then, the differences among the ....

....universal quantification over all the computations. Then, given a linear time temporal logic L, the corresponding branching time logic is BL(L) VTI T is in L. Not surprisingly, the main limitation of the linear time logics is the inability to express the existential path quantification [EH86, Lam80]. 3.3 atisfiability In this section we analyze the satisfiability problem, that is, given a formula we want to establish if it is satisfiable. This problem has a clear meaning in practice: given a specification, is there an implementation fulfilling it The traditional approach to solve this ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proceedings of the 7th A CM Symposium on Principles of Programming Languages, pages 174-185, 1980. 129

....technique that was recently proposed in the field of plant production and multimedia scheduling [Prad 00, Prad 99, GiPrV97] This technique associates Petri nets with Girard s Linear Logic. Except for its name, Girard s Linear Logic has no connections with the Linear Temporal Logic (LTL) Lam80] commonly used in Model Checking [Merz00] One of its main benefits lies in its ability to handle unsynchronized and distributed local partial states, which appears to be a crucial point to limit the state explosion. This technique furthermore produces symbolic variable expressions, which can ....

L. Lamport, Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. of the 7th A CM Symposium on Principles of Programming Languages, pp. 175-185, Jan. 1980.

....of functional programs. Expressions of the term language, Core Clean, can be embedded in propositions, including logical variables bound by universal or existential quantifiers. The Sparkle logic has a notation to express an undefined value but does not provide modalities. Temporal logics [Pnu77, Lam80] for programs were developed to provide a formalism in which to express properties of programmed processes. Linear temporal logic (LTL) supports property assertions quantified over the temporal traces of a process, where by a trace, we mean a sequence of states entered in a process trajectory as ....

Leslie Lamport. Sometimes is sometimes "not never"--on the temporal logic of programs. In Conference Record of the Seventh Annual ACM Symposium on Principles of Programming Languages, pages 174--185. ACM Press, 1980.

....problem we can reduce, as we later shall see, the validity problem for LTL to the emptiness problem (c.f. 63] ut 4 LINEAR TEMPORAL LOGIC Temporal logic [50] is a popular way of specifying properties of reactive systems. There are two basic variants of temporal logic, linear and branching [37]. In linear temporal logic (LTL) introduced to the veri cation setting by Pnueli [50] any given point in time has only one future, while branching time logics [37] allows several possible futures. The perhaps most known branching time logic is computation tree logic (CTL) introduced in ....

....a popular way of specifying properties of reactive systems. There are two basic variants of temporal logic, linear and branching [37] In linear temporal logic (LTL) introduced to the veri cation setting by Pnueli [50] any given point in time has only one future, while branching time logics [37] allows several possible futures. The perhaps most known branching time logic is computation tree logic (CTL) introduced in [15] There has been a two decade long debate, albeit currently not so intense, among researchers in the concurrency community which paradigm, the branching or the linear, ....

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L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proceedings of the 7th ACM Symposium on Principles of Programming Languages, pages 174-185, January 1980.

....formalism leads to an undecidable model checking problem even for finite state systems. The branching time paradigm is more general than the linear time paradigm, in the sense that we can view a (universally quantified) linear time specification as a branching time specification specification [Lam80,Pnu85] This does not contradict the fact that model checking of pushdown specification is decidable in the branching time paradigm. Indeed, a translation of a nondeterministic pushdown word automaton that recognizes a language L into a nondeterministic pushdown tree automata that recognizes the ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In 7th POPL, pp. 174--185, 1980.

....prefix of length k only (We call such formalisms bounded formalisms. What would be the blow up of such a translation Also, sometime we want to verify branching temporal properties (that is, properties that describe the whole computation tree of a system, and not its individual computations) Lam80,EH86] Can we extend the results from the linear framework to the branching one So, the enhanced goal of this research has become the study of clopen regular linear and branching properties. We start with the linear framework. We first show that The definition of safety we consider here is ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th POPL, pp. 174--185, 1980.

....to users, would result in a dialog on the subject of property specification logic between the research community, language developers, and language users. 2 Expressiveness and Usability 2. 1 The Nature of Time Two possible views regarding the nature of time induce two types of temporal logics [Lam80,Pnu85a] In linear temporal logics, time is treated as if each moment in time has a unique possible future. Thus, linear temporal formulae are interpreted over linear sequences, and we regard them as describing the behavior of a single computation of a system. In branching temporal logics, each ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th ACM Symp. on Principles of Programming Languages, pages 174--185, January 1980.

.... been convincing calls see (e.g. LPZ85] for bringing the glory of the past into LPTL, by adding the past operators, For axiomatization, semantic tableau, and examples of use of LPTL extended with the past operators previously and since see the recent [LP00] For more on fairness: see [GPSS80] Lam80] LPS81] For more on properties specified by temporal logic, see [Sis94] and for a detailed study of their hierarchy see [MP90] 3.3 Axiomatic system for LPTL Axiom schemata: The following axiomatic system is a streamlined version of the future part of the Since Until logic over #N, # . ....

....on model checking, attend that course, or see e.g. EL86] SW91] Zuc93b] KVW94] Zuc93a] Var98] 7.2 Branching time vs linear time logics The debate on the pros and contras of using linear vs branching time temporal logics has been alive and unabating since the begining of the 80 s. See [Lam80] and [EH86] for the beginning of it. Of course, the linear and branching time approaches have somewaht di#erent spheres of application, viz. linear time approach is the more natural when the properties to be checked are about single program executions, while the branching time approach is more ....

L. Lamport. Sometimes is sometimes "not never"- on the temporal logic of programs. In Proc. of the 7th Annual ACM Symp. on Principles of Programming Languages, pages 174--185, 1980.

....other primary interface is the modeling language, which is typically the hardware description language used by the designers) One of the major aspects of all temporal languages is their underlying model of time. Two possible views regarding the nature of time induce two types of temporal logics [65]. In linear temporal logics, time is treated as if each moment in time has a unique possible future. Thus, linear temporal logic formulas are interpreted over linear sequences and we regard them as describing a behavior of a single computation of a program. In branching temporal logics, each ....

....the branching temporal logic 8CTL is a fragment of CTL in which only universal path quantification is allowed. Note that LTL has implicit universal path quantifiers in front of its formulas. The discussion of the relative merits of linear versus branching temporal logics goes back to 1980 [80,65,31,8,82,35,33,18,100,101]. As analyzed in [82] linear and branching time logics correspond to two distinct views of time. It is not surprising therefore that LTL and CTL are expressively incomparable [65,33,18] The LTL formula FGp is not expressible in CTL, while the CTL formula AFAGp is not expressible in LTL. On the ....

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L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th ACM Symp. on Principles of Programming Languages, pages 174--185, January 1980.

....formal definition of MG and involves some technical complications required in order to make sure that the environment disables only transitions from OR states. ut 6 Discussion The discussion of the relative merits of linear versus branching temporal logics is almost as early as these paradigms [Lam80] One of the beliefs dominating this discussion has been while specifying is easier in LTL, model checking is easier for CTL . Indeed, the restricted syntax of CTL limits its expressive power and many important behaviors (e.g. strong fairness) can not be specified in CTL. On the other hand, ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proceedings of the 7th ACM Symposium on Principles of Programming Languages, pages 174-- 185, January 1980.

....is that time has a branching, tree like nature: at each moment, time may split into alternate sequences representing different possible futures. Both approaches have been applied to 35 program reasoning, and it is a matter of debate as to say whether branching or linear time is preferable [EH86, Lam80, Pnu85] Kozen s (propositional) modal calculus (K) Koz83] has expressive power subsuming many modal and temporal logics such as LTL and CTL [BCM 92, CGH94, EL85] Therefore, it is a natural choice to use calculus to specify the properties. However, it can be difficult to express ....

L. Lamport. Sometimes is sometimes "not never" ! on the temporal logic of programs. In Proc. 7th Ann. ACM Symp. on Principles of Programming Languages, pages 174--185, 1980. 174

....that the model checking task can be automated when checking finite state systems. Temporal logics are often used as property description languages since they can describe event orderings without having to introduce time explicitly. There are two main kinds of temporal logics: linear and branching [16]. In linear temporal logics, each moment in time has a unique possible future, while in branching temporal logics, each moment in time has several possible futures. Efficient model checking algorithms for linear time temporal logic were developed by exploiting the close relationship of the ....

L. Lamport. Sometimes is sometimes "not never" --- on the Temporal Logic of Programs. Proceedings 7th ACM Symposium on Principles of Programming Languages, pages 174-- 185, January 1980.

....MkM 0 satisfies . If the answer is yes, we say that M robustly satisfies . The problem of robust model checking, initially posed in [GL91] is to determine, given M and , whether M robustly satisfies . Two possible views regarding the nature of time induce two types of temporal logics [Lam80]. In linear temporal logics, time is treated as if each moment in time has a unique possible future. Thus, linear temporal logic formulas are interpreted over linear sequences and we regard them as describing a behavior of a single computation of a program. In branching temporal logics, each ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th POPL, pages 174--185, 1980.

.... program with respect to a desired behavior by checking whether a labeled transition system that models the program satisfies a temporal logic formula that specifies this behavior (for a survey, see [8] Two possible views regarding the nature of time induce two types of temporal logics [34]. In linear temporal logics, time is treated as if each moment in time has a unique possible future. Thus, linear temporal logic formulas are interpreted over linear sequences and we regard them as describing a behavior of a single computation of a program. In branching temporal logics, each ....

.... , we denote by A the 8CTL formula obtained from by preceding each temporal connective by the path quantifier A. For example, if is G(req F grant) then A above is AG(req AF grant) The discussion of the relative merits of linear versus branching temporal logics goes back to 1980 [34,11,1,42,14,12,5]. As analyzied in [42] linear and branching time logics correspond to two distinct views of time. It is not surprising therefore that LTL and CTL are expressively incomparable [34,12,5] On the other hand, CTL seems to be superior to LTL when it comes to algorithmic verification, as we now ....

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L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th ACM Symposium on Principles of Programming Languages, pages 174--185, January 1980.

....(is a model of) the propositional temporal logic formula that specifies that behavior. Hence the name model checking for the verification methods derived from this viewpoint. Surveys can be found in [CG87, Wol89, CGL93] We distinguish between two types of temporal logics: linear and branching [Lam80] In linear temporal logics, each moment in time has a unique possible future, while in branching temporal logics, each moment in time may split into several possible futures. The complexity of model checking for both linear and branching temporal logics is well understood: suppose we are given a ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th ACM Symposium on Principles of Programming Languages, pages 174--185, January 1980.

....that specifies the desired behavior clearly should be neither valid nor unsatisfiable, which entails that a computer aided verification system has to have the capacity for validity checking in addition to truth checking. We distinguishbetween two types of temporal logics: linear and branching [Lam80]. In linear temporal logics, each moment in time has a unique possible future, while in branching temporal logics, each moment in time may split into several possible futures. For both types of temporal logics, a close and fruitful connection with the theory of automata on infinite structures has ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proceedingsof the 7th ACM Symposiumon Principles of ProgrammingLanguages, pages 174--185, January 1980.

....satisfies (is a model of) the propositional temporal logic formula that specifies that behavior. Hence the name model checking for the verification methods derived from this viewpoint. A survey can be found in [Wol89] We distinguish between two types of temporal logics: linear and branching [Lam80]. In linear temporal logics, each moment in time has a unique possible future, while in branching temporal logics, each moment in time may split into several possible futures. For linear temporal logics, a close and fruitful connection with the theory of automata on infinite words has been ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proceedings of the 7th ACM Symposium on Principles of Programming Languages, pages 174--185, January 1980.

.... Temporal logics, which are modal logics geared towards the description of the temporal ordering of events, have been adopted as a powerful tool for specifying and verifying open programs [MP92a, MP95] Two possible views regarding the nature of time induce two types of temporal logics [Lam80] In linear temporal logics, time is treated as if each moment Address: CS Department, Rice University, Houston TX 77005 1892, U.S.A. Email: vardi cs.rice.edu , URL: http: www.cs.rice.edu vardi. Supported in part by NSF grants CCR 9628400 and CCR 9700061, and by a grant from the Intel ....

....holds. The branching temporal logic CTL is a fragement of CTL in which every temporal operator is preceded by a path quantifier. For example, while above is a CTL formula, the CTL formula AG(req F grant) is not a CTL formula. The expressive powers of LTL and CTL are incomparable [Lam80] while CTL is more expressive than both LTL and CTL [EH86] The discussion of the relative merits of linear versus branching temporal logics is by now almost 20years old [Lam80, CE81, QS81, Pnu81, BMP83, Pnu85b, EH86, Sti87] One of the most frequent arguments in this discussion relates to ....

[Article contains additional citation context not shown here]

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th ACM Symposium on Principles of Programming Languages, pages 174--185, January 1980.

....that models c flIFIP 1996. Published by Chapman Hall 2 Relating Linear and Branching Model Checking the program satisfies a temporal logic formula that specifies this behavior (for a survey, see [CGL93] Two possible views regarding the nature of time induce two types of temporal logics [Lam80] In linear temporal logics, time is treated as if each moment in time has a unique possible future. Thus, linear temporal logic formulas are interpreted over linear sequences and we regard them as describing a behavior of a single computation of a program. In branching temporal logics, each ....

....restriction to branchable subformulas takes care of formulas like ( discussed above, and still leaves us with the bulk of LTL formulas used in practice. 5 CONCLUSIONS The discussion of the relative merits of linear versus branching temporal logics is almost as early as these paradigms [Lam80] We mainly refer here to the linear temporal logic LTL and the branching temporal logic CTL. One of the beliefs dominating this discussion has been while specifying is easier in LTL, model checking is easier for CTL . The attractive complexity of CTL model checking have compensated for its lack ....

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th POPL, pp. 174--185, 1980.

No context found.

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th ACM Symp. on Principles of Programming Languages, pages 174--185, January 1980.

No context found.

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th ACM Symp. on Principles of Programming Languages, pages 174--185, January 1980.

No context found.

L. Lamport, Sometimes is sometimes "not never"---on the temporal logic of programs, Proceedings of the 7th ACM symposium on principles of programming languages, January 1980, pp. 174--185.

No context found.

L. Lamport. Sometimes is sometimes "not never" - on the temporal logic of programs. In Proc. 7th ACM Symp. on Principles of Programming Languages, pages 174--185, January 1980.

No context found.

L. Lamport. Sometimes is sometimes "not never"- on the temporal logic of programs. In Proc. of the 7th Annual ACM Symp. on Principles of Programming Languages, pages 174--185, 1980. 80

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