E. Allen Emerson. Handbook of Theoretical Computer Science, chapter 16. Elsevier, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....address can be on one side specific of the given architecture, and on the other specific of the system to be modeled, that is part of its requirements. As a case study we use the software architecture description of a Sender Receiver System. For expressing the properties we use the CTL logic [5, 4] and to prove them we use a model checking approach based on the ability of deriving a Kripke structure out of a CHAM specification, as described in Section 2. To define the properties, we first reason at the CHAM level, in order to understand in terms of the system behavior what is the property ....

....S and a set of reaction rules R, R(S) is the Kripke structure (DR (S) fSg; MR (S) L; R ; S) where for every 2 DR (S) fSg, L(S ) is the set of molecules in S and R is the relation defined by R. 2. 3 The CTL We shortly introduce the branching temporal logic CTL defined in [5, 4]. CTL is suitable to express properties of reactive systems defined by means of transition systems or Kripke structure. In this paper, we concentrate on some structural and functional properties that our architectures have to possess. Although our main focus in the analysis will be centered ....

E.A. Emerson: Temporal and Modal Logic. Handbook of Theoretical Computer Science, volume B, chapter 16. Elsevier Science Publishers B.V., 1990.

....a KD45 modality, K i is an S5 modality, and the interaction axiom K i p B i p expresses the intended interplay between the two informational operators. A considerable number of these formal studies are available in the literature and temporal extensions of these (i.e. modal combinations of CTL [5] or LTL [21] with the modalities for the mental attitudes) have appeared recently. The typical technical contribution of this line of work is to explore the metalogical properties of these logics, e.g. completeness, decidability, and computational complexity. While these investigations are ....

....for B: 0; 0; 0) wait; 0; 0; 1) attacking; 0; 1; 0) go; 0; 1; 1) win; 1; 0; 0) defeat. The modelling of the environment E requires only two bits: 0; 0) 0; 1) deliver B ; 1; 0) deliver A . In view of this a global state is modelled by a byte: g = s[1] s[2] s[3] s[4] s[5]; s[6] s[7] s[8] For instance the initial state = plan; wait; is represented as a tuple of eight 0 s. If we are to represent it in terms of propositional atoms, we shall have to insist on the atoms coding the state to be in the state of false. In other words, we would encode the initial ....

E. A. Emerson. Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter Temporal and Modal Logic, pages 995--1067. Elsevier, 1990.

....a KD45 modality, K i is an S5 modality, and the interaction axiom K i p B i p expresses the intended interplay between the two informational operators. A considerable number of these formal studies are available in the literature and temporal extensions of these (i.e. modal combinations of CTL [5] or LTL [19] with the modalities for the mental attitudes) have appeared recently. The typical technical contribution of this line of work is to explore the metalogical properties of these logics, e.g. completeness, decidability, and computational complexity. While these investigations are ....

....for B: 0, 0, 0) wait, 0, 0, 1) attacking, 0, 1, 0) go, 0, 1, 1) win, 1, 0, 0) defeat. The modelling of the environment E requires only two bits: 0, 0) #, 0, 1) deliverB , 1, 0) deliverA . In view of this a global state is modelled by a byte: g = s[1] s[2] s[3] s[4] s[5], s[6] s[7] s[8] For instance the initial state # = plan, wait, #) is represented as a tuple of eight 0 s. If we are to represent it in terms of propositional atoms, we shall have to insist on the atoms coding the state to be in the state of false. In other words, we would encode the initial ....

E. A. Emerson. Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter Temporal and Modal Logic, pages 995--1067. Elsevier, 1990.

....the translation from P to MP and on the temporal logic to which the formula belongs to. Recently, the interest in automated veri cation is moving towards concurrent real time systems. The properties to be veri ed are usually expressed in either a standard temporal logic like LTL [CGP99] and CTL [Eme90,EC82] or in their timed versions like MITL [AFH96] and TCTL [ACD93] The practical applicability of model checking is strongly restricted by the state explosion problem. Therefore, many di erent reduction techniques have been introduced in order to alleviate the state explosion. The major ....

E. A. Emerson. Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter Temporal and Modal Logic, pages 995-1067. Elsevier, 1990.

.... ( 11] 58] and [13] In undecidable cases one can partially solve the problem by using symbolic verification (see [9] and [18] Another method is to have verification rules for proving safety properties and response properties (see [55] 72] and [71] To extend Temporal and Modal logics ([34]) so that control and test on time and variable values are ensured, many logics have been proposed ( 59] 16] 14] and [17] These Logics extend the classical temporal operators, such as until or next , with control on time that can be expressed simply with an interval on the temporal ....

Emerson, E. A.: Temporal and Modal Logic. Handbook of Theoretical Computer Science, Elsevier Science Publishers, Amsterdam, 1990, 996--1072.

....for P and checking that MP j= is automated. The complexity of model checking methods strongly depends on the translation from P to MP and on the type of the temporal logic that the formula belongs to. In this paper we consider model checking algorithms for Computation Tree Logic (CTL ) Eme90] We are not concerned with the problem of getting a model MP from a program P and just assume that such a model is provided. Two valued models and logics, like CTL , are sufficient for proving properties of standard concurrent systems. However, there is a number of problems for which we need ....

E. A. Emerson, Handbook of Theoretical Computer Science, vol. B: Formal Methods and Semantics, ch. Temporal and Modal Logic, pp. 995--1067, Elsevier, 1990, pp. 995--1067.

.... that assigns to each state s 2 S a subset of . Then associates with each trajectory = s 1 e 1 s 2 e 2 : of H an word ( s 1 ) s 2 ) over the alphabet 2 . We assume that the reader is familiar with the linear time temporal logic LTL (interpreted over words) see [11]. The LTL model checking problem for hybrid systems is de ned as follows: Input: An interpreted hybrid system (H; and an LTL formula . Problem: Decide if for every trajectory of H the word ( satis es . Let M be an o minimal structure over the reals. A hybrid system H = S; S 0 ; S ....

E. A. Emerson. Temporal and modal logic. Chapter 16 of Volume B of Handbook of Theoretical Computer Science, Elsevier, 1990. 37

....Corollary 1. Let T 1 = Q 1 , L 1 , 2 a bisimulation relation between T 1 and T 2 . Then, they are language equivalent, that is, the following equality holds: L(T 1 ) L(T 2 ) Language equivalence is important as it ensures that properties expressible in LTL are preserved: Theorem 2 ([28, 10]) Let T 1 and T 2 be two language equivalent transition systems. Then, any LTL formula interpreted over observable sequences is satisfied by T 1 i# it is satisfied by T 2 . Combining Corollary 1 with Theorem 2 we conclude that bisimilarity preserves properties expressible in LTL, however ....

E. A. Emerson. Handbook of Theoretical Computer Science, volume B, chapter Temporal and modal logic, pages 995--1072. Elsevier Science, 1990.

....execution path by a Logout. This property is crucial when considering web based applications in order to avoid side effects on the next test case: all resources that are requested during a test case must be freed after execution. This kind of properties is adequately specified in temporal logics [2], e.g. Login # F Logout specifies the described property. TB 2 TB 3 Login . Logout Logout Logout Figure 6: Illustration of a consistency property (Every Login must be followed by a Logout) Whereas temporal logic specifications are not adequate for application experts and test ....

E. Emerson: Temporal and Modal Logic, Handbook of theoretical computer science, Elsevier, 1990.

....with the stack content that makes a cycle possible. This is done similarly to the construction of Section 4, but incorporating the constraints, which is possible since they are given by finite automata. 6 Branching temporal properties : CTL As shown in [EL85] branching time model checking [Eme90] can be reduced to linear time model checking. The idea is to start with the innermost path formulas, verify them with a linear time model checking procedure and then label the structure with the result. This being done, one can move to the next level of path formulas and repeat the procedure. In ....

E.A. Emerson. Temporal and modal logic. Handbook of theoretical computer science, pages 997--1072, 1990.

....is called model checking. Model checking is an automatic procedure to verify if a given system satisfies a given temporal property [4] For dense real time systems, a system is often described using Timed Automata (TA) 7] and a property is often specified in Timed Computation Tree Logic (TCTL) [14,15]. For hybrid systems, Linear HybrM Automata (LHA) 5,6] is a theoretically proven model for verification purposes. LHA was also recently used as a formal model for timing coverification of hardware software systems by the author [16] Here, we assume that all processors in our target system are ....

....model checking framework [4,15] as introduced in Section 1. Model checking verifies if a given system satisfies a given property. In our framework, a real time system is described using TA [7] see Definition 2) and a temporal property is specified using Timed Computation Tree Logic (TCTL) [14,15] (see Definition 6) In our framework, recall from Section 4.2, a system 5 = is composed of the following components: a set of n processes, P, P, modeled by n timed automata d= d, d, re spectively, where di= M,m,C,D,z, E,z,pi) l i n, and a set of m processors, ....

E. Emerson, Temporal and modal logic, Handbook of Theoretical Computer Science, 1990.

....types and logical properties, we are primarily interested in maximal models. 6 Specifying objects The modal mu calculus is very powerful when used a temporal logic of labelled transition systems. It is well known that the temporal modalities of the propositional branching time temporal logic CTL [Eme94] are expressible 10 within the mu calculus (in fact, it can be shown that all of CTL [Eme94] can be expressed within the mu calculus) In this short section we shall describe how properties of calculus can be described this way. We let the set Act denote the set of possible observations; we ....

....The modal mu calculus is very powerful when used a temporal logic of labelled transition systems. It is well known that the temporal modalities of the propositional branching time temporal logic CTL [Eme94] are expressible 10 within the mu calculus (in fact, it can be shown that all of CTL [Eme94] can be expressed within the mu calculus) In this short section we shall describe how properties of calculus can be described this way. We let the set Act denote the set of possible observations; we write [Act]F as an abbreviation of V ff2Act [ff]F and similarly, we write hActiF as an ....

E.A. Emerson. Handbook of Theoretical Computer Science, chapter Temporal and Modal Logic, pages 995--1072. Elsevier, 1994. 19

....between a state based and a logic based approach to coverage, and we distinguish between a system and its environment. Our de nitions are independent of the temporal logic being used. The algorithms we are going to present are for the branching time logic CTL, de ned in Section 2. 1 (see also [Eme90]) We distinguish between two types of systems: closed and open [HP85] A closed system is a system whose behavior is completely determined by the state of the system. An open system is a system that interacts with its environment and whose behavior depends on external choices made by the ....

E.A. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, pages 997-1072, 1990.

.... temporal logics, in branching temporal logics one can specify possibility requirements such as every input sequence can be extended so that the output signal v eventually becomes true ( DTV99] This is achieved via existential and universal quanti cation provided in branching temporal logics [Lam80,Eme90]. In this paper, we concentrate on branching temporal logics. The realizability problem for a branching temporal logic is to determine, given a branching time speci cation , whether there exists a program f : 2 I ) 2 O whose computation tree satis es [ALW89,PR89] Realizing boils ....

E.A. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, pages 997-1072, 1990.

....2M (in the same settings as above) 1 CTL and C vs. Second Order Logics The propositional Calculus of D. Kozen (C ) 10, 11] is a powerful propositional program logic with fixpoints. In particular, a very popular with model checking community state based temporal Computation Tree Logic (CTL) [7, 4, 5] is interpretable in C . It is almost a folklore that CTL is less expressive than C . Nevertheless, expressibility problem rises every time when a particular property is concerned: whether this property can be expressed in CTL, in C , or both logics are inadequate. For example, paper [1] reports ....

Emerson E.A. Temporal and Modal Logic. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, 995-1072.

....easy And why do we give non mathematical names for them The answers are quite simple. Program logics are modal logics used in softand hardware verification and specification for reasoning about programs. In 1980 ies program logics comprised ffl dynamic logics [14, 16] ffl temporal logics [15, 17], and their extensions by means of fixpoints. A more recent addition to the family of program logics is logic of knowledge [18] The utility of this logic for this application is that it provides a language that formalizes constructs capturing notions that are used informally in reasoning about ....

....more important as soon as model checking is applied to huge models with, say, 10 100 states, since large sets representation problem arises. 46 6. 3 Concluding remarks We would like to recommend some further reading on mathematical theory of program logics 26 : first [18] 14] 15] 16] [17] z in any order. For those who are interested in applications of program logics some reading is recommended below also. Temporal logic have been shown to provide a convenient framework for specifying and reasoning about properties of a broad class of systems which can be presented or ....

Emerson E.A. Temporal and Modal Logic. Handbook of Theoretical Computer Science, v.B, Elsilver and The MIT Press, 1990, p.995-1072.

....a nite state space. This condensed state space can be computed using a variant of the standard algorithm for state space construction, but without constructing the full state space. We showed that the quotient structure obtained can be used for model checking using discrete time temporal logics [5, 25] such as RTCTL [26] In this section the method is informally described and some experimental results are shown. For a detailed treatment we refer to [14] Timed CP nets. We rst informally introduce timed CP nets. A timed CP net is a CP net extended with a global clock, and with time stamps ....

E. A. Emerson. Temporal and Modal Logic, volume B of Handbook of Theoretical Computer Science, chapter 16, pages 995-1072. Elsevier, 1990.

....) and next time ( f ) Pnu81] The semantics of LTL is defined with respect to infinite words in (2 AP ) for the set AP of atomic propositions. For example, the formula 2p (always p) is satisfied over words in all of whose letters contain the atom p. For full syntax and semantics see [Eme90] Extended Temporal Logic As mentioned above, Vardi and Wolper suggested to increase the expressive power of LTL by using 1NBW as temporal connectives [VW94] Suppose the alphabet of an 1NBW A is the set 2 AP . The 1NBW A defines a set of sequences of truth assignments to the propositions. We ....

E.A. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, pages 997--1072, 1990.

....in S starting in q and w is its trace is a nite in nite complete execution in S : speci cations Properties of executions and or traces are expressed via a set of temporal operators on polymorphic lazy lists. More precisely, all the temporal operators we nd in the litterature (see [11] for example) are de ned as operators on languages of potentially in nite words : P is the set of words beginning with a letter satisfying P X(L) is the set of words whose tail is in L F(L) is Eventually(L) F 1 (L) is the set of words having an in nity of suxes in L, ....

E. Emerson. Handbook of Theoretical Computer Science (volume B), chapter Temporal and Modal Logic (ed. J. Van Leeuuwen), pages 995-1072. Elsevier, 1990.

....why do we give non mathematical names for them The answers are quite simple. Program logics are modal logics used in soft19 ware and hardware verification and specification for reasoning about programs. In 1980 ies program logics comprised ffl dynamic logics [15, 18, 16] ffl temporal logics [29, 9], and their extensions by means of fixpoints. EPDL is the simplest dynamic logic, C is a very expressive extension of EPDL by fixpoints and . Temporal logics are fragments of C with a single action variable next for discrete next time. A more recent addition to the family of program logics is ....

....say, 10 100 states, since large sets representation problem arises. I would like to give some recommendations on further reading on program logics. Some books and special chapter of handbooks can be recommended for those who is interested in theory of program logics 11 : first [12] then [15, 16, 29, 18, 9] (in any order) There are also several books which discuss pragmatics and applications of program logics. A comprehensive survey (from implementation perspective) on automatic model checking techniques and applications is given in [6] Temporal logic approach to specification and to manual ....

[Article contains additional citation context not shown here]

Emerson E.A. Temporal and Modal Logic. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, p.995-1072.

....of Science, Novosibirsk, Russia 1 1 SOEPDL vs. Propositional Program Logics The propositional Calculus of D. Kozen (C) 6, 7] is a powerful propositional program logic with fixpoints. In particular, a very popular with model checking community state based temporal Computation Tree Logic (CTL) [4, 2, 3] is expressible in C. We give a new proof that CTL is less expressive than C: Proposition 1 1. No CTL formula can express an existence of a winning strategy in finite games. 2. There is C formula which expresses an existence of a winning strategy in finite games. But in spite of expressive ....

Emerson E.A. Temporal and Modal Logic. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, 995-1072.

....properties. We have not yet discussed how these properties can be expressed in such a way that automated analysis becomes possible. Propositional linear temporal logic (LTL) allows us to make very concise statements about required causal relations between the events in a distributed system [P77] [E90]. Each LTL formulae, furthermore, can be converted mechanically [GPVW95] into an w automaton [T90] that can be used in the verification process. An automata theoretic verification method [VW86] proceeds follows. 1. The property to be verified is expressed as a formula f in LTL, and then negated ....

E.A. Emerson, Temporal and modal logic, Handbook on Theoretical Computer Science, Volume B, Elsevier Science, 1990, pp. 995-1072.

.... exclusion, we cannot specify deadlock freedom (every nite interaction can be extended so that a philosopher eventually eats) In order to express possibility properties, we should specify the system using branching temporal logic, which enables both universal and existential path quanti cation [EH86, Eme90]. Second, and more crucially, the algorithm in [PR90] is not applicable for architectures that are not hierarchical, and real life designs are rarely based on hierarchical architectures. We do not count the nonelementary complexity as a limitation, as it is accompanied by a matching lower bound ....

E.A. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, pp. 997-1072, 1990.

....) K4) #a## = # (K5) X. X ) # X. X ) K6) # X. X ) # (K7) X. X ) X. X ) The propositional calculus is an interesting logic because it is both expressive and manageable. It subsumes most propositional temporal logics and propositional modal logics of programs [2, 10, 16]. Over Kripke structures which are binary trees the logic is as expressive as S2S [12] monadic second order logic of two successors [14] On the other hand the validity A NOTE ON THE COMPLETENESS OF KOZEN S AXIOMATISATION 351 problem for calculus formulas is EXPTIME complete [3] This makes it ....

E. A. Emerson, Temporal and modal logic, Handbook of theoretical computer science (J. Leeuven, editor), vol. B, Elsevier, 1990, pp. 995--1072.

....comparing linear time and branching time temporal logics as, for example, Lam80] EL85] EH86] BCG88] and [Sti92] In this thesis, I only consider linear time temporal logics because I personally feel that they are more intuitive to use. Good introductions to temporal logics may be found in [Eme90] or in the comprehensive standard textbook for linear time temporal logics [MP91] lately expanded by a second volume [MP96] In [BA93] both first order logic and temporal logic are dealt in an introductory manner. The temporal logic presented below subsumes the first order logic defined above. ....

E. Allen Emerson. Temporal and Modal Logic, chapter 16, pages 996--1072. Handbook of Theoretical Computer Science. Elsevier Science Publishers B.V., edited by j. van leeuwen edition, 1990.

....framework [SPAM91, WCL91] but the operators supported in these languages are very limited. In fact, composite CHAPTER 3. ACTIVE AND TEMPORAL DATABASES 59 event specification in the relational and temporal database framework has not been investigated. 3. 5 Temporal Logic Temporal Logic (TL) Eme90] was introduced for reasoning about systems that change with time. Propositional Temporal Logic (PTL) is an extension of classical propositional logic geared toward the description of sequences. In the linear time temporal logic (LTL) Pnu81] time is viewed as linear, that is, each time instant ....

E. A. Emerson. Handbook of Theoretical Computer Science. Elsevier Science, 1990.

....safety property is violated; the language of the generated automaton is the set of all sequences that violate the safety property. Thus, the accepting states of the automaton indicate a violation; the machine is driven into a accepting state if and only if a safety property has been violated. See [11] for a survey of the related theory and algorithms. Our JavaTriveni implementation embeds the automaton in a JavaTriveni 34377 238 . This generated 6C o B A6A is composed in parallel with the JavaTriveni 432 B A that is being monitored, thus ensuring that the monitor itorB A and the ....

E. A. Emerson. Handbook of Theoretical Computer Science, chapter Temporal and modal logic, pages 995--1072. Elsevier/The MIT Press, 1990.

No context found.

E. A. Emerson, Temporal and Modal Logic. Handbook of Theoretical Computer Science, Volume B., J. van Leeuwen Editor, Elsevier, 995-1072 (1990).

....And why do we give non mathematical names for them 22 The answers are quite simple. Program logics are modal logics used in software and hardware veri cation and speci cation for reasoning about programs. In 1980s program logics comprised dynamic logics [15, 18, 16] temporal logics [27, 9], and their extensions by means of xpoints. EPDL is the simplest dynamic logic; C is a very expressive extension of EPDL by xpoints and . Temporal logics are fragments of C with a single action variable next for discrete nexttime. A more recent addition to the family of program logics is ....

....10 100 states, since with large sets representation problem arises. We would like to give some recommendations on further reading on program logics. Some books and special chapter of handbooks can be recommended for those who are interested in the theory of program logics : rst [12] then [15, 16, 27, 18, 9] (in any order) There are also several books which discuss the pragmatics and applications of program logics. A comprehensive survey (from the implementation perspective) on automatic model checking techniques and applications is given in [6] The temporal logic approach to speci cation and to ....

[Article contains additional citation context not shown here]

Emerson E.A. Temporal and Modal Logic. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, p.995-1072.

....in the next section 3. This exponential reduction together with exponential decidability of validity problem in Herbrand Models for SOPDL imply double exponential upper time bound for CTL . 2 Two Program Logics: CTL and SOPDL The Full Branching Time Logic (or Full Computation Tree Logic) CTL [7, 8, 9, 12, 13, 14, 15] is a powerful propositional temporal logic for reasoning about states and sequences of states of a program. The syntax of CTL is constructed from boolean values B and a finite alphabet of propositional variables P and consist of two parts: state formulae F stt and path formulae F pth . A ....

Emerson E.A. Temporal and Modal Logic. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, p.995-1072.

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E. Allen Emerson. Handbook of Theoretical Computer Science, chapter 16. Elsevier, 1990.

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E.-A. Emerson. Handbook of Theoretical Computer Science, chapter Temporal and Modal Logic, pages 995--1073. Elsevier, 1990.

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E.-A. Emerson. Handbook of Theoretical Computer Science, chapter Temporal and Modal Logic, pages 995-- 1073. Elsevier, 1990.

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E. A. Emerson. Temporal and Modal Logic, volume B of Handbook of Theoretical Computer Science, chapter 16, pages 997--1072. Elsevier, 1990. J. Van Leeuwen, Editor.

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E. A. Emerson. Temporal and Modal Logic, volume B of Handbook of Theoretical Computer Science, chapter 16, pages 997--1072. Elsevier, 1990. J. Van Leeuwen, Editor.

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E. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, B:995--1072, 1990.

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E. A. Emerson, Temporal and modal logic, Handbook of theoretical computer science, 1990, pp. 997--1072.

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E. A. Emerson. Temporal and Modal Logic, volume B of Handbook of Theoretical Computer Science, chapter 16, pages 997--1072. Elsevier, 1990. J. Van Leeuwen, Editor.

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E. A. Emerson. Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter Temporal and Modal Logic, pages 995-1067. Elsevier, 1990.

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E. Allen Emerson. Temporal and Model Logic, volume B of Handbook of Theoretical Computer Science, chapter 16, pages 997--1072. Elsevier, 1990. J. Van Leeuwen, Editor.

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E. Emerson A. Handbook of theoretical computer science, volume B, chapter 16, Temporal and Modal Logic, pages 997--1072. MIT Press and Elsevier Science Publishers, Cambridge, Massachusetts, 1990. ISBN 0-262-72015-9, J. van Leeuwen.

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E. Emerson, A. Handbook of theoretical computer science, volume B, chapter 16, Temporal and Modal Logic, pages 997--1072. MIT Press and Elsevier Science Publishers, Cambridge, Massachusetts, 1990. ISBN 0-262-72015-9, Second Printing.

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E. A. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, B: Formal Models and Sematics:995--1072, 1990.

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E. A. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, B: Formal Models and Sematics:995--1072, 1990.

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E.A. Emerson. Temporal and modal logic, Handbook of theoretical computer science. Elsevier Sciences B.V. J. van leeuwn north holland edition, 1990.

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E. A. Emerson. Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter Temporal and Modal Logic, pp. 995-1067. Elsevier, 1990.

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E. A. Emerson. Handbook of Theoretical Computer Science, chapter Temporal and modal logic, pages 995--1072. Elsevier/The MIT Press, 1990.

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E. A. Emerson, Handbook of Theoretical Computer Science, vol. B: Formal Methods and Semantics, ch. Temporal and Modal Logic, pp. 995--1067, Elsevier, 1990, pp. 995--1067.

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E. A. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics, pages 995--1072, 1990.

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E. A. Emerson. Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter Temporal and Modal Logic, p. 995-1067. Elsevier Science Publishers, 1990.

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