A. E. Emerson and A. P. Sistla, Deciding full branching time logics, Information and Control, vol. 61 (1984), no. 3, pp. 175--201.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....formula. Considering that, for this problem, the lower bound of deterministic double exponential time was established in [VS85] by a reduction from alternating exponential space Turing machines, there is a double exponential blow up to save in the above procedure to match the lower bound. In [ES84] Emerson and Sistla showed that, due to the particular structure of the Biichi string automaton involved in this construction, it can be determinized with only a single exponential blow up. In a successive paper [Saf88] Safra extended this result to all nondeterministic Biichi string automata. ....

E.A. Emerson and A.P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175 - 201, 1984.

.... out of the current state, satisfies 3 ; that is, occurs somewhere along the trace . The logic with the linear temporal operators augmented with the trace quantifiers A and E is known as CTL; see [Emerson, 1990; Emerson and Halpern, 1986; Emerson and Halpern, 1985; Emerson and Lei, 1987; Emerson and Sistla, 1984] Complexity and Deductive Completeness A useful axiomatization of linear time TL without the until operator is given by the axioms 2( 2 2 ) 2( 2 2 3 3 ( 2 8x (x) t) t is free for x in ) 8x 2 28x ....

.... of temporal logic (see Section 14.2) and other seemingly stronger forms of the calculus ( Vardi and Wolper, 1986b] In the following presentation we focus on this version, since it has gained fairly widespread acceptance; see [Kozen, 1984; Kozen and Parikh, 1983; Streett, 1985b; Streett and Emerson, 1984; Vardi and Wolper, 1986b; Walukiewicz, 1993; Walukiewicz, 1995; Walukiewicz, 2000; Stirling, 1992; Mader, 1997; Kaivola, 1997] The language of the propositional calculus, also called the modal calculus, is syntactically simpler than PDL. It consists of the usual propositional constructs ....

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E. A. Emerson and P. A. Sistla. Deciding full branching-time logic. Infor. and Control, 61:175--201, 1984.

....CTL # k and PCTL # k are as expressive as MPL[ # i ) i=0 ] when interpreted over infinite k ary trees. Furthermore, a decision procedure for CTL # k can be obtained by means of the following non trivial adaptation of the decision procedure for CTL # originally developed by Emerson and Sistla [10] and later refined by Emerson and Jutla [8] Let us assume k = 2 (the generalization to an arbitrary k is straightforward) As a preliminary step, we provide an embedding of PTL 2 into PTL. To this end, we define a translation # of formulas and models of PTL 2 , over an alphabet #, to formulas and ....

....a model for # if and only if #(M) is a model for #(#) As a second preliminary step, we transform CTL # k formulas in a normal form suitable for subsequent manipulation. Such a normal form is a straightforward generalization of the normal form for CTL # formulas proposed by Emerson and Sistla [10]. This result is formally stated by the following lemma, whose proof is similar to the one for CTL # and thus omitted. Lemma 5.5 For any given CTL # k formula # 0 , there exists a corresponding formula # 1 in a normal form composed of conjunctions and disjunctions of subformulas of the form Ap, ....

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E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, 1984.

....logics. Theorem 2.4.7 (Expressiveness of CTL # k and PCTL # k CTL # k and PCTL # k are expressively equivalent to MPLP [ pre , # i ) i=0 ] when interpreted over finite (resp. infinite) k ary trees. Moreover, both QCTL # k and EQCTL # k gain the full second order power of MSOP [ pre ] [35]: Theorem 2.4.8 (Expressiveness of QCTL # k and EQCTL # k ) QCTL # k and EQCTL # k are expressively equivalent to MSOP [ pre , # i ) i=0 ] when interpreted over finite (resp. infinite) k ary trees. Emerson and Jutla proved that the satisfiability problem for CTL # is 2EXPTIMEcomplete [34] ....

....k ary trees. Emerson and Jutla proved that the satisfiability problem for CTL # is 2EXPTIMEcomplete [34] Furthermore, a decision procedure for CTL # k can be obtained by means of the following non trivial adaptation of the decision procedure for CTL # originally developed by Emerson and Sistla [35] and later refined by Emerson and Jutla [34] We start by defining an auxiliary linear time logic, called Directed k ary PLTL (PLTL k ) whose language is the smallest set of path formulas generated by the rules (P0) P2 P5) in Definition 2.4.1. PLTL k is interpreted over full paths belonging ....

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E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, June 1984.

....Logic and QCTL # k be Quantified Directed Computation Tree Logic [8] Quantified versions of propositional temporal logics add to the language quantified formulas of the form #Q#, where Q is a proposition letter and # is a formula. It is known that Buchi # QLTL [1] and Rabin k # QCTL # k [7]. By applying Theorem 11, we have that Buchi(Rabin k ) QLTL(QCTL # k ) It follows that QLTL(QCTL # k ) is expressively equivalent to MSO# [ 1 , 2 , succ i ) i=0 , 1] Since QLTL and QCTL # k are nonelementarily decidable [1, 33] by Corollary 12, we have that QLTL(QCTL # k ) is ....

E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, June 1984.

....model checking of a formula j over a finite state machine FSM is as follows. A state machine FSM satisfies a linear temporal formula j if, and only if, for all linear models, M, in FSM, starting from s 0 , hM, s 0 i = j. Note that if we were using a branching time temporal logic such as CTL [ES84], we would check the satisfiability of the formula Aj, meaning that for all paths, j must be satisfied, over the whole state machine. Thus, our main aim is to develop an effective procedure for model checking linear temporal formulae over finite state machines. 3 Standard Model Checking ....

E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61:175--201, 1984.

....have already seen that deterministic Buchi automata are strictly weaker than their nondeterministic counterpart. Nevertheless determinisation is a very important and useful property. It is used in decision procedures for various program logics such as 1. the modal calculus [53, 58] 2. CTL [18]. and not least the monadic 2nd order theory of the binary tree which we will return to later. So it is of interest to find alternative notions of automata for which determinisation is in fact possible. Three well known such notions exist, called Muller, Rabin, and Streett automata. In the ....

E. A. Emerson and A.P. Sistla. Deciding full branching time logic. Information and Control, 61:175--201, 1984.

....shows there is no difference in absolute expressive power between the restricted syntax and full propositional temporal logic in terms of METATEM programs. Suppose that OE is a formula from PTL using the propositions from P . Using the algorithms of Vardi and Wolper [VW86] or Emerson and Sistla [ES84] we can build a nondeterministic finite state Buchi 2 P automaton A = S; T ; S 0 ; F ) which recognizes a P structure if, and only if, it is a model of OE. We could determinize A using results of McNaughton [McN66] or Safra [SV89] and then translate the deterministic (Rabin) automaton into ....

E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61:175--201, 1984.

....very recent draft [Rey00] he announced that such a rule can be omitted if the past operators are added to the language. Theorem: The satisfiability problem for CTL # is EXPEXPTIME complete. Emerson and Sistla produced a double exponential time algorithm for deciding satisfiability for CTL # in [ES84] by an elaborated reduction to non emptiness of automata on infinite trees. A matching lower bound can be obtained by reduction from alternating exponential space bounded Turing machines. References: For more on variations of branching time logics and a comprehensive comparison of their ....

E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, June 1984.

....interpreted often are finite they represent infinite behaviour like runs of programs. Therefore the automata being used typically are automata over infinite objects with Buchi, Muller, or Street acceptance conditions. For branching time logics automata accepting trees instead of words are helpful [KG96, BVW94, ES84]. In some cases handling negation is not easy since complementing Buchi automata for example involves a fair amount of work [Buc62, Tho99] No automata theoretic method has been identified so far that can be 3 used in order to prove completeness of an axiom systems, i.e. to show that a consistent ....

....since this is a matter of axioms and rules rather than of the syntactical structure of a formula. Therefore it is hard to relate these two issues on the automata theoretic level. Nevertheless, it is claimed that no tableau like method works for checking satisfiability of a CTL # formula [ES84] because it requires determinisation which is not a problem when using automatatheoretic techniques. This explains why the completeness of CTL # has been an open problem for a long time [Rey00] 4 Games Similar to the idea of Ehrenfeucht Frasse games [Tho93] two abstract players are given ....

E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, June 1984.

....transition graph M and some state s in M we have M; s j= f , in which case M is called a model for f . The decision problem of a temporal logic formula is to test whether or not the given formula is satis able. We have following results for the decision problems of CTL and CTL. Theorem 1 ([9, 5]) Given a CTL formula f , f is satis able if and only if it is satis able in a nite state transition graph with number of nodes at most double exponential in the length of the formula f . Theorem 2 ( 6] The decision problem of CTL (resp. CTL) is complete for deterministic double (resp. ....

....the lower as well as the upper bound of the complexity of the decision problem for CTL (resp. CTL) is deterministic double (resp. single) exponential in the length of the given formula. To test the satis ability of a CTL formula f , we have the following sound and complete decision procedure [6, 9, 8]: 1. Derive a Rabin tree automaton for the CTL formula f [9] The number of states (resp. acceptance condition pairs) of the Rabin tree automaton is double (resp. single) exponential in the length of the formula f . 2. Test the emptiness of the Rabin tree automaton [8] If the Rabin tree ....

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E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Inform. and Control, vol 61, no. 3, pp 175-201, 1984.

.... no nite complete axiomatization for CTL with respect of the class of standard models has been found yet (but some completeness results for more general semantics are presented in (Stirling, 1992) The validity in CTL was proved decidable in deterministic double exponential time in (Emerson and Sistla, 1984). 3. Interpretation of CTL into the Temporal Logic with Reference Pointers 3.1. Extended Computation Trees for CTL models. In this section we transform the CTL models from T into a form suitable for the language with reference pointers. Computation Tree Logics 7 For any model T ....

Emerson, E.A., & A.P. Sistla, Deciding full Branching Time Logic, Information and Control, 61(3), 1984, 175-201.

....tool and the developer. There are various classes of interpretations which are suitable for modelling a temporal behaviour. We will deal with transition systems only. Furthermore, there also are various logics that allow the formalisation of temporal properties over transition systems. CTL # (cf. [4]) is not just one of them but probably the most appropriate one for expressing temporal properties. The linear time logic LTL (cf. 7] and the branching time logic CTL (cf. 1] for example can be found as genuine syntactic fragments of CTL # . A lot of interesting properties, like something ....

E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, June 1984.

....where every maximal sequence of pairwise connected states counts as a path. The essential di#culty in such an axiomatisation is characterising limit closure.This has become apparent e.g. with the standard computation tree logic, for which the axiomatisation problem has been open for some while [35, 25, 83]. Here limit closure is characterised by a a new inference rule, the # # # induction.Thecom pleteness proof is is based on transforming formulae to a strongly aconjunctive deterministic normal form. An intriguing aspect in this completeness proof is that the ability to transform a formula to ....

....that is complete with respect to all su#x and fusion closed models by adding the axiom # # ## # ## # #. However, the problem of completely axiomatising CTL # for R generable models, i.e. capturing limit closure by axioms, has been an open problem for some while, stated e.g. in [35, 25, 83]. The best that is known is an axiomatisation for CTL, a restricted sublogic of CTL # , where limit closure is characterised by the axiom schema ## # G(### # ##)#(### # G#) 30, 25] We present next a solution to this axiomatisation problem with respect to R generable structures for the ....

Emerson, E. A. & Sistla, A. P.: Deciding full branching time logic, in Information and Control, vol. 61, 1984, pp. 175-201

....mu calculus TL to a branching time formalism using path quantifiers # # # and # # #, for some path # and for all paths #. This way of extending a linear formalism to a branching one is familiar from various temporal logics; probably the best example is the full computation tree logic CTL # [28, 29], which extends the standard linear time temporal logic TL with path quantifiers. We call the formalism consisting of TL and path quantifiers here the extended computation tree logic # # TL. In general, due to the interaction of path quantifiers with other operators of the logic, it has turned ....

....#, for some path # and for all paths # are another way of extending TL to a formalism capable of describing branching properties. This way of extending a linear time formalism to a branching one is used in various temporal logics; probably the best example is the full computation tree logic CTL # [28, 29], which extends the standard linear time temporal logic TL with path quantifiers. We call the formalism consisting of TL andpathquantifiershere the extended computation tree logic # # TL. Expressively equivalent formulations of extended computation tree logic using linear time operators ....

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Emerson, E. A. & Halpern, J. Y.: Deciding full branching time logic, in Information and Control, vol. 61, 1984, pp. 175-201

....a winning strategy for one of the players. Once such a strategy is found, i.e. computed by a verification tool for example, it can be used to enable an interactive play between the tool and the developer. In this case we will deal with transition systems and the full branching time logic CTL # [2] only, although there are other models for concurrency, too. CTL # subsumes other temporal logics like LTL [5] and CTL [1] syntactically, and thus the results on the games for CTL # easily carry over to these other logics as well. On the other hand, CTL # can be translated into the modal ....

E. Allen Emerson and A. Prasad Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, June 1984.

.... my knowledge, no finite complete axiomatization for CTL with respect to the class of standard models has been published yet (but some completeness results for more general semantics are presented in [Sti 92] The validity in CTL was proved decidable in deterministic double exponential time in [EmS 84] 2 Interpretation of CTL into the Temporal Logic with Reference Pointers 2.1 Extended Computation Trees for CTL models. In this section we transform the CTL models from T into a form suitable for the language with reference pointers. For any model T = hS; R; V i from T we define an ....

Emerson, E.A., & A.P. Sistla, Deciding full Branching Time Logic, Information and Control, 61(3), 1984, 175-201. 20

.... Emerson 1981) is sufficient to express most of the properties that require branching time modeling, for example the properties of simple concurrent programs (that do not deal with fairness) There are several extensions of CTL of which CTL is commonly considered as a full branching time logic (Emerson and Sistla 1984). In particular, the core logic we concentrate on, CTL, can be extended to Extended CTL (ECTL) Emerson 1990) which incorporates simple fairness constraints. It has been shown that CTL and ECTL can be respectively extended to CTL and ECTL , where boolean combinations of 3 temporal ....

.... . Recall that it has been shown that while CTL is equivalent to its base logic CTL, ECTL is strictly more expressive than both CTL and ECTL (Emerson 1990) and that the most powerful branching time system of this class is CTL (which allows all possible combinations of modalities) (Emerson and Sistla 1984). In both cases ECTL and CTL it is unlikely that the resolution approach developed for CTL can be extended straightforwardly. All problems are due to the structures of formulae admissible in these systems, namely, due to the nested linear modalities in the case of ECTL and also due to the ....

Emerson, E. A. and Sistla, A. P. (1984) Deciding full branching time logic. Information and Control, 61(3), pages 175--201.

.... k . Theorem 7. Expressive completeness of DCTL k and PDCTL k ) DCTL k and PDCTL k are as expressive as MPL[ # i ) k 1 i=0 ] over in nite k ary trees. ut The problem of testing satis ability is PSPACE complete for PTL [12] while it is 2EXPTIME complete for CTL [3]. As for DCTL k , it is possible to prove the following theorem. Theorem 8. DCTL k is elementary decidable) The satis ability problem for DCTL k is 2EXPTIME complete. ut 7 Let us focus now on the problem of establishing the expressiveness and complexity of DCTSL k and PDCTSL ....

E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175-201, June 1984.

....observer. Such an observer can always be constructed for a linear time formula if variables range over a finite domain. The use of observers is supported by, for example, the SDL toolset AVALON [1] but the construction of 9 observers from temporal formulae as described in, for example, [7] has to be done manually yet. However, the observer for a formula of the form 1 is trivial and the observer for a formula of the form 2, i.e. AG( a] is as follows: p q r s 0 1 where transition p is labelled with : X a ) q with X a , r with X and s with . The observer ....

E.A. Emerson and A.P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, 1984.

....that are beyond the scope of this paper. For other comments on the complexity of ETL r see Section 3. 6 The automata theoretic approach described here can be viewed as a specialization of the automatatheoretic approach to decision problems of dynamic logic described in [VW86a] see also [ES84, St82]) Note, however, that while the tree automata constructed in [ES84, St82, VW86a] accept only some models of the given formulas, the automata constructed here accept all models of the given formulas. 3 automata connectives, and one may expect their introduction to push the complexity of the ....

....complexity of ETL r see Section 3. 6 The automata theoretic approach described here can be viewed as a specialization of the automatatheoretic approach to decision problems of dynamic logic described in [VW86a] see also [ES84, St82] Note, however, that while the tree automata constructed in [ES84, St82, VW86a] accept only some models of the given formulas, the automata constructed here accept all models of the given formulas. 3 automata connectives, and one may expect their introduction to push the complexity of the logic up. We investigate both ATL f and ATL l , which are the alternating analogues ....

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E. A. Emerson and A. P. Sistla, "Deciding Full Branching Time Logic", Information and Control 61(1984), pp. 175--201.

.... that most correctness properties of concurrent programs (that do not deal with fairness) can be expressed in a branching time logic called Computation Tree Logic (CTL) first proposed in [1] There are several extensions of CTL of which CTL is commonly considered as a full branching time logic [9]. However, the core logics we concentrate on, are CTL and its extension Extended CTL (ECTL) 5] which incorporates simple fairness constraints. It has been shown that CTL and ECTL can be respectively extended to CTL and ECTL , where boolean combinations of temporal modalities are allowed. ....

....a system called ECTL . Recall that it has been shown that CTL is equivalent to its base logic CTL, ECTL is strictly more expressive than both CTL [7] and ECTL and that the most powerful branching time system of this class is CTL (which allows all possible combinations of modalities) [9]. 5.1 Extended CTL In this section, we consider ECTL and the application of our resolution procedure to this extended logic. Throughout, we will only describe the differences between the CTL procedure and the ECTL one. We begin by examining the syntactic and semantic extensions of ECTL. We ....

E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61, 1984.

....structure. There are no surprises here Branching Time FIL (B FIL) is to FIL as CTL is to PTL. We sketch a decision procedure for B FIL that reduces the decision problem to the emptiness problem for Buchi tree automata. The procedure is straightforward adaptation of the CTL decision procedure [30]. As one might expect, it turns out that B FIL is strictly more expressive than FIL and, moreover, linear time FIL corresponds to a simple syntactic fragment of B FIL in which only universal path quantifiers are allowed, a result exactly analogous to the PTL versus CTL case. Each of the above ....

....is one reason why we chose the semantics that we did for B FIL; we keep the expressive power of CTL . The next section, which sketches a decision procedure for B FIL, further underscores this point. 2.9. 4 Deciding B FIL We use a hybrid method, first used by Emerson and Sistla to decide CTL [30], which first rewrites an arbitrary formula into an equivalent normal form, and then uses automata theoretic techniques to decide a formula in the normal form. Wolper [109] uses more direct techniques (although only for CTL) and a procedure with a similar flavour can probably be obtained for ....

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Emerson E A, Sistla A P, Deciding Full Branching Time Logic, Inf. Control, 61 (3), 1984, pp 175-201.

....is feasible. In a similar fashion we can establish a fragment of TFL that is equivalent with the logic CTL [16] which is more expressive than CTL, because it handles quantification in a more liberal way. However, the model checking problem has been shown to be PSPACE complete for CTL [17, 20], so we refrain from this translation. We give a brief description of CTL. This logic too assumes a finite set of states, and a transition system induced by a binary relation R between states. It is required that for each state s there is a state t with sRt. Hence, each path in the transition ....

E.A. Emerson and A.P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, 1984.

....with the state explosion problem. For branching temporal logics, the automata theoretic counterpart are automata on infinite trees. By reducing the satisfiability to the nonemptiness problem for these automata, optimal decision procedures have been obtained for various branching temporal logics [Eme85, EJ88, ES84, SE84, VW86b]. Unfortunately, the automata theoretic approach does not seem to be applicable to branching time model checking. Indeed, model checking can be done in linear running time for CTL [CES86, QS81] and the alternationfree fragment of the calculus [CS93] and is in NP co NP for the general ....

A.E. Emerson and A.P. Sistla. Deciding full branching time logics. Information and Control, 61(3):175--201, 1984.

....is feasible. In a similar fashion we can establish a fragment of TFL that is equivalent with the logic CTL [17] which is more expressive than CTL, because it handles quantification in a more liberal way. However, the model checking problem has been shown to be PSPACE complete for CTL [18, 22], so we refrain from this translation. We give a brief description of CTL. This logic assumes a finite set of states, and a transition system induced by a binary relation R between states. It is required that for each state s there is a state t with sRt. Hence, each path in the transition system ....

E.A. Emerson and A.P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, 1984.

....tree automata are exactly as expressive as the alternation free fragment of calculus [KV98] a translation of formulas of monadic second order logic to Rabin tree automata. Today, Rabin automata are used in order to reason about specifications of the full branching time logic CTL [ES84, VS85], as well as to model programs with fairness conditions. The nonemptiness problem for Rabin automata plays a crucial role in solving various decision problems in logic. As a result, many efforts have been put in developing simple algorithms for nonemptiness checking. In [Rab69] Rabin described a ....

A.E. Emerson and A.P. Sistla. Deciding full branching time logics. Information and Control, 61(3):175--201, 1984.

....a sound and complete axiomatisation for extended computation tree logic CTL . The axiom system contains a new inference rule reflecting the limit closure of paths, as the axiomatisation is sound and complete with respect to the class of R generable models. The computation tree logic CTL [9] arises by adding path quantifiers to the standard propositional linear time temporal logic TL, and is used widely in specification and verification of concurrent systems (for surveys, see [5, 16] The extended computation tree logic CTL is an interesting extension of CTL , using linear ....

....an axiomatisation that is complete with respect to all suffix and fusion closed models by adding the axiom 8fiOE ) fi8OE. However, the problem of completely axiomatising CTL for R generable models, i.e. capturing limit closure by axioms, has been an open problem for some while, stated e.g. in [9, 5, 16]. The best that is known is an axiomatisation for CTL, a restricted sublogic of CTL , where limit closure is characterised by the axiom schema 8G(OE ) 9fiOE) OE ) 9GOE) 7, 5] The current paper solves this axiomatisation problem with respect to R generable structures for the extended ....

Emerson, E. A. & Sistla, A. P.: Deciding full branching time logic, in Information and Control, vol. 61, pp. 175-201, 1984

....model checking of a formula j over a finite state machine FSM is as follows. A state machine FSM satisfies a linear temporal formula j if, and only if, for all linear models, M, in FSM, starting from s 0 , hM, s 0 i = j. Note that if we were using a branching time temporal logic such as CTL [ES84], we would check the satisfiability of the formula Aj, meaning that for all paths, j must be satisfied, over the whole state machine. Thus, our main aim is to develop an effective procedure for model checking linear temporal formulae over finite state machines. 3 Standard Model Checking ....

E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61:175--201, 1984.

....or courses of action, or paths of computation then branching time logics are sensible to use. The main languages here are the purely branching Computational Tree Logic CTL and the combined branching linear full Computational Tree Logic CTL . CTL computation tree logic, was first described in [ES84] and [EH86] By using a slightly unusual semantics based on paths through transition structures, CTL is able to extend, in expressiveness, both the computation tree logic, CTL, of [CE81] a simple branching logic, and the standard PLTL. The formulae of CTL are also formulae of CTL so we will ....

E. Emerson and A. Sistla. Deciding full branching time logic. Information and Control, 61:175 -- 201, 1984.

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Emerson, E. A., and Sistla, A. P., Deciding Full Branching Time Logic, Information and Control, Vol. 61, pp. 175-201, June 1984.

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A. E. Emerson and A. P. Sistla, Deciding full branching time logics, Information and Control, vol. 61 (1984), no. 3, pp. 175--201.

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E. A. Emerson, A. P. Sistla (1984): Deciding Full Branching Time Logic. Information and Control, vol. 61 (3), pp. 175-201.

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E.A. Emerson and A. Sistla. Deciding Full Branching Time Logic. Information and Control, 61:175--201, 1984.

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E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, June 1984.

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E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, June 1984.

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E. Emerson and A. Sistla. Deciding full branching time logic. Information and Control, 61:175 - 201, 1984.

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E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, 1984.

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E. A. Emerson and P. A. Sistla. Deciding full branching time logic. Information and Control, 61(3):175-201, 1984.

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E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175-201, June 1984.

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E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61(3):175--201, 1984.

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E. A. Emerson, A. P. Sistla (1984): Deciding Full Branching Time Logic. Information and Control, vol. 61 (3), pp. 175-201. References 256

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A. E. Emerson and P. A. Sistla. Deciding full branching time logic. Information and Control, 61:175--201, 1984.

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Emerson, E. A. and Sistla, A. P. (1985), "Deciding Full Branching Time Logic", TR85 -28, Department of Computer Science, University of Texas at Austin.

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A.E. Emerson and A.P. Sistla. Deciding full branching time logics. Information and Control, 61(3):175--201, 1984.

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