E.A. Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that can be unwound in an actual model of the formula. A refinement of the quotient construction that exploits the above property is the tableau construction. In subsection 3.3.1, we will describe this technique for C L. Tableau based decision procedures for various logics are given in [BAHP83, EC82, EH85, HS84, LN, LN98, Pra79, Wo183, Wo185]. In subsection 3.3.2 we give the complexity results on C L, L L and some meaningful fragments of L L. A decision procedure for the satisfiability of formulae in C L involves an elaborate reduction to the emptiness problem for finite state automata on infinite trees. This will be discussed in ....

E.A. Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1-24, 1985.

....path is NP complete [EL87] TCTL [Koy90] or Timed CTL , allows adding timing subscripts to the usual modalities. In Timed KSs (i.e. Kripke structures where edges carry a discrete duration weight) the existence of a path of a given accumulated duration is NP complete [LMS02a] CTL [EH85] allows arbitrary Boolean combinations (not nesting) of the U and X modalities under a path quantifier. Thus CTL is the branching time extension of L (U, X) the fragment of linear time logic with modal depth one, for which the existence of a path is NP complete [DS02] B # (F) and B # ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1--24, 1985.

....we would write which says, For all traces 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) ....

.... ) 2 8x (x) t) t is free for x in ) 8x 2 28x and rules 2 : Compare the axioms of PDL (Axioms 17) The propositional fragment of this deductive system is complete for linear time propositional TL, as shown in [Gabbay et al. 1980] Sistla and Clarke, 1982] and [Emerson and Halpern, 1985] have shown that the validity problem for most versions of propositional TL is PSPACE complete for linear structures and EXPTIME complete for branching structures. Embedding TL in DL TL is subsumed by DL. To embed propositional TL into PDL, take an atomic program a to mean one step of program ....

[Article contains additional citation context not shown here]

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. J. Comput. Syst. Sci., 30(1):1--24, 1985.

....think of the future as being a branching structure, then the meaning of must be clarified so that we know whether j means that j must be true on some path in the future, or on all paths in the future. Thus there is a great variety of such logics, including dense logics [BKP86] branching logics [EH82] and past time logics [LPZ85] many of which can be placed in a single framework [Fis89] In this report we will only consider a model of time that is linear and discrete, and allows statements about the present and future. The model structure for such a logic can be given as M = hS, N , pi ....

E. A. Emerson and J. Y. Halpern. Decision Procedures and Expressiveness in the Temporal Logic of Branching Time. In Proceedings of the Fourteenth ACM Symposium on the Theory of Computing, pages 169--180, 1982.

....[ES89, Eme90] Below we consider: an extension of CTL, introduced in [EH86] and where Boolean combinations (not nesting) of temporal modalities are allowed under the scope of a path quanti er. e.g. CTL allows formulae like A(aUb cUd) There exists a translation from CTL to CTL [EH85] hence the two logics have the same expressive power) but such a translation must produce exponential size formulae [Wil99b, AI01] is B(U, X, in the notation of [EH86] but we prefer to see it as B(L (U, X) ECTL: an extension of CTL, introduced in [EH86] where the E F and A ....

....the classical temporal modality, instead of Until and Next. The name BT # is from [CES86] 4.2.2 Model checking fragments of CTL # As far as model checking is concerned, ECTL behaves like CTL: The situation is more interesting for the satis ability problem. It is EXPTIME complete for CTL [EH85] and this leaves much room for fragments that could be less intractable, see [ESS92] for example. The choice of what are the CTL modalities is mostly a historical accident (see Remark 2.4) and it is possible to de ne more expressive logics for which essentially the same model checking ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):124, 1985.

....moment in time. The syntax of BTL extends the syntax of first order logic with two formation rules: ffl if A is a formula then so is first A, and ffl if A is a formula then so is next i A. BTL is a relatively simple branching time logic. For more on branching time logics one can refer to [11, 24, 25]. 4.1 Semantics of BTL formulas The semantics of temporal formulas of BTL are given using the notion of branching temporal interpretation. Branching temporal interpretations extend the temporal interpretations of the linear time logic of Chronolog [3] Definition 4.1. A branching temporal ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1--24, February 1985.

.... of fixpoints is bounded [3, 1] One of lacking elements in this picture was finitary complete axiomatisation of the logic (infinitary axiomatisation was given in [13] There exist finitary axiomatisations for many weaker propositional logics of programs like PDL [8, 19, 14, 11, 16] CTL [5] or Process Logic [9] Completeness proofs for these logics use the so called Henkin method which consists of constructing a model for a non refutable formula. The use of this method depends on the ability of syntactic model construction which is provided by collapsed model theorem or a result of ....

E.Allen Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1--24, 1985.

.... built from maximal consistent sets [15, 8] or tableaux which explicitly build models from consistent sets, as illustrated by the delicate proofs of completeness for CTL # [14] and modal calculus [18] and even the proofs of completeness for LTL [7, 13] future linear time logic) and CTL [5] (computation tree logic) In this paper we introduce a simple game theoretic approach to satisfiability checking of temporal logic, for LTL and CTL, which has the same complexity as using automata. The mechanism involved, the use of a focus , is both explicit and transparent, and underpins a ....

...., #n , # j is not B consistent, and so B # # 1 # . # #n # # j . So by AXGen and axioms 9,8 and 6 B # AX# 1 # . # AX#n # EX# j (and using 7 instead of 6 one deals with the case when l = 0) Finally the ARel and ERel rules are used to capture # s winning strategy. # In [5] soundness and completeness of the following axiom system for CTL is proved using tableaux. Ax1. any tautology instance Ax2. EF# # E(ttU#) Ax3. AF# # A(ttU#) Ax4. EX(# # #) # EX# # EX# Ax5. AX# # EX# Ax6. E(#U#) # # # (# # EXE(#U#) Axioms 1. any tautology instance 2. ....

Emerson, E., and Halpern, J. (1985). Decision procedures and expressiveness in the temporal logic of branching time. Journal of Comput. System Sci., 30, 1-24.

....logic RTPL. That is: Given a logical property is it possible to automatically synthesize a satisfying finite TPG (provided any such exists) This problem is also known as the problem of model construction. The satisfiability problems for CTL and the modal calculus have been proven decidable [EC82, EH85, Wol85, KP83] whereas for TCTL and T the same problems are undecidable [ACD90] In [LLW95] a bounded satisfiability problem is proven decidable for the logic L , and as our logic RTPL has adopted the same concept of formula clocks and delay modalities as presented in L , we can also only prove the same kind ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. J. Comput. System Sci., pages 30(1):1--24, 1985.

....such reasoning is the same as that of model checking. Note, however, that full support of assume guarantee reasoning is not guaranteed by the mere inclusion of regular events. Sugar adds regular events to CTL, resulting in a mixed linear branching semantics [BBDE 01] in the style of CTL [EH85] which makes it rather difficult to fully support assume guarantee reasoning [Var01] In Temporal e, the main focus is on describing finite sequences using regular expressions. It is not clear whether the language has full regularity [Mor99] which is required for full support of ....

E.A. Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1-- 24, 1985.

.... nesting of fixpoints is bounded [3, 1] One of lacking elements in this picture was finitary complete axiomatisation of the logic (infinitary axiomatisation was given in [13] There exist finitary axiomatisations for many weaker propositional logics of programs like PDL [8, 19, 14, 11, 16] CTL [5] or Process Logic [9] Completeness proofs for these logics use the so called Henkin method which consists of constructing a model for a non refutable formula. The use of this method depends on the ability of syntactic model construction which is provided by collapsed model theorem or a result of ....

E.Allen Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1--24, 1985.

....under two grants No. 8 T11C 029 08 and No. 2 P301 007 04. 1 Program proof rules were defined for first order versions of the following logics: LTL [14] fair CTL [9] and ISTL [23] However, a complete proof system is known only for the first order LTL [25, 16] propositional versions of CTL [8], TSL, and ISTL [22] The logics TSL and TrPTL have not yet been extended to their first order versions. In the present paper we partialy fill this gap . We define a first order version of the logic TSL (FTSL, for short) interpreted over Mazurkiewicz trace systems. The modalities allow ....

E.A. Emerson, and J.Y. Halpern, Decision Procedures and Expressiveness in the Temporal Logic of Branching Time, Proc. of 14th Annual ACM Symp. on Theory of Computing, San Francisco, pp. 169-180,

....closest translation in CTL: #G#F (resource requested) # #F (resource granted) Question: Why are these di#erent Which is stronger 4.4.1 Complete axiomatic system for CTL. The first complete axiomatic system for CTL was proposed by Emerson and Halpern in [EH82] see also the journal version [EH85] Here we give a streamlined version of the axiomatic system for CTL presented in [Eme90] from which all original axioms are easily derivable. Axiom schemata: Enough classical tautologies; K X ) #X(# # #) # (#X# # #X#) D X ) #X#, REC #U ) #(#U#) # (# # (# # ....

....# #) # (#(#U#) # #) LFP #U ) #G( # # (# # #X#) # #) # (#(#U#) # #) Rules: Modus ponens (MP) NEC #G ) # # implies # #G#, Theorem: CTL is complete. The completeness can be proved by constructing a semantic tableau for any satisfiable formula. For details see [EH85] or [Eme90] Alternatively, for a modal model theoretic proof, see [Gol92] Exercise # : Goldblatt in [Gol92] has replaced the axioms (LFP #U ) and (LFP #U ) with the corresponding induction rules: # Ind) # # # (# # #X#) # # implies # #(#U#) # #, # Ind) # # # ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

....di#erent from what seems to be the closest translation in CTL: #G#F (resource requested) # #F (resource granted) Question: Why are these di#erent Which is stronger 4.4.1 Complete axiomatic system for CTL. The first complete axiomatic system for CTL was proposed by Emerson and Halpern in [EH82] see also the journal version [EH85] Here we give a streamlined version of the axiomatic system for CTL presented in [Eme90] from which all original axioms are easily derivable. Axiom schemata: Enough classical tautologies; K X ) #X(# # #) # (#X# # #X#) D X ) #X#, ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. In Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, pages 169--180, San Francisco, California, 5--7 May 1982.

....s 0 s 1 w 1 w 2 v 1 v 2 t # # # # # # # b b a a a a a # # # 1 3 2 3 1 2 1 2 # # 1 5 4 5# # # # # # # # # # # # ## # # # # # # ## # # # # # # # # ## # # ## # # ## # # ## # # # # # Fig. 7. 9 Model checking for PBTL # Similarly to the way in which CTL # extends CTL [24], our logic PBTL can be extended to a much richer logic PBTL # which allows more complex path formulas, i.e. arbitrary combinations of path formulas by the boolean connectives and the operators X and U . This logic (more precisely, the logic pCTL # which essentially coincides with PBTL # ) was ....

Emerson EA, Halpern J: Decision Procedures and Expressiveness in the Temporal Logic of Branching Time, J Comput Syst Sci 30: 1--24 (1985)

....is extracted from the filtered tableau. Another way is to use maximal consistent sets [Sti92] Tableaux have been used to solve the model checking problem, for example for the calculus [Cle90] Satisfiability checking for branching time temporal logics was also done in a tableau based way [EH85, EC82]. However, it was also shown that there exists an intimate relationship between 2 tableaux for temporal logics and automata over infinite trees [Eme85] 3 Automata The use of automata for modal and temporal logics is widely accepted in computer science where this is often identified with being ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

....Suppose inductively that #t # k , f # k# occurs at node v k (and is preceded by #t # j , f # j # for all j k) and v k is the lowest node at which #t # k , f # k# occurs. If k = n, then the lemma is proved. Suppose that k n. In this case, v k is an 3 See Emerson and Halpern [EH85] for the upper bound. open node since t # k and f # k both satisfy the same predicate symbol, p #(k) From now on, let us assume that there are no not moves, but that instead Samson may play on the left or on the right. This may slightly decrease the size of T by removing not moves, but ....

E.A. Emerson and J.Y. Halpern, "Decision Procedures and Expressiveness in the Temporal Logic of Branching Time," J. Comput. Sys. Sci. 30(1) (1985), 1-- 24.

....open problem, at least theoretically. In practice we almost never need formulae with more than two alternations, and for these we have good model checking algorithms (see [11] for a survey) Q: And satis ability A: The satis ability problems for CTL and the calculus are Exptime complete [12, 13] (compared to Pspace for ML) By the way, both logics also have the nite model property: Every satis able sentence has a nite model [24] There is by now a huge literature on the calculus and CTL. 4 3 Modal logic and rst order logic Q: Let me get back to the basic logic ML. What puzzles me ....

A. Emerson and J. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, Journal of Computer and System Sciences, 30 (1985), pp. 1-24.

.... of maximal consistent sets [10, 5] or tableaux creations which explicitly build models from consistent sets, as illustrated by the delicate proofs of completeness for CTL # [9] and modal calculus [12] and even the proofs of completeness for LTL [4, 8] future linear time logic) and CTL [2] (computation tree logic) In this paper we introduce a simple game theoretic approach to satisfiability checking of temporal logic, for LTL and CTL, which has the same complexity as automata. The mechanisms involved are both explicit and transparent, and underpin a novel approach to developing ....

Emerson, E., and Halpern, J. (1985). Decision procedures and expressiveness in the temporal logic of branching time. Journal of Comput. System Sci., 30, 1-24.

....Every rule in a CTL game can be seen as a combination of rules of a CTL # game, and the winning conditions are simply amended to these combined rules. Therefore correctness follows from Theorem 16. 5. 2 Model Checking Games for CTL Although CTL has the same expressive power as CTL only (cf. [5, 19]) example 17 shows that the model checking games cannot be optimised for CTL like they can be for CTL. In particular, sets of formulas are needed. However, since the formula of example 18 that justifies the use of the focus is not in CTL the question whether a focus is needed for CTL ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

....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 has a unique successor. The structures over which LTL is interpreted are linear sequences. In the branching time TL (BTL) BAMP81] EH85] each time instant may have several immediate successors corresponding to different futures, for example, branches corresponding to nondeterministic choices (or concurrency) The structures over which BTL expressions are interpreted can be viewed as infinite trees. Temporal logic formulas are ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

....the branchingtime logic built on these same modalities (hence the notations PLTL = L(U; X) and CTL = B(U; X) in [Eme90] CTL , introduced in [EH86] was designed to be more expressive than both PLTL and CTL. CTL and fairness properties. Several fragments of CTL are de ned and studied in [EH85,EH86,ES89,Eme90] and other papers, where their expressive powers are compared. Clearly, what CTL really lacks in practice is the ability to express fairness properties, and this is what motivates the introduction in [EH86] of ECTL 1 , or B(U; X; 1 F ) an extension of CTL with the E 1 F modality for stating ....

....The idea of allowing boolean combinations of temporal modalities has also been applied to CTL (and other logics) In CTL one can state A GC XD ) BUC , i.e. all paths with C everywhere and D in next state, satisfy BUC . A surprising result is that CTL is not more expressive than CTL [EH85] while ECTL is more expressive than ECTL [EH86] see also [RS00] However CTL can be much more succinct than CTL, a fact that was conjectured since [EH85] but has only been proved recently [Wil99] The complexity of model checking. That CTL can be exponentially more succinct than CTL ....

[Article contains additional citation context not shown here]

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1-24, 1985.

...., 2 , and . The advantage of using modular proof rules is that it enables one to apply model checking only to the underlying modules, which have much smaller state spaces. 3 Note also that while the satisfiability problem for LTL is PSPACE complete [91] the problem is EXPTIME complete for CTL [36,32] and 2EXPTIME complete for CTL [102,34] A key observation, see [77,66,50,93,81] is that in modular verification the specification should include two parts. One part describes the desired behavior of the module. The other part describes the assumed behavior of the system within which the ....

E.A. Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

.... w.r.t. an empty KB, is a PSPACE complete problem. These important results show that adding a point based time dimension to ALC does not alter its computational behavior. However, since for branching, discrete and unbounded time reasoning in classical tense logic is an EXPTIME hard problem [22] then the same lower complexity bound carries over ALCT . When ALC is extended with an interval based time dimension (let us call it ALC INT ) the undecidability results showed by Halpern and Shoham for the logic HS, and the one presented by Bettini, apply also to ALC INT . Interesting open ....

E.A. Emerson and J.Y. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, Journal of Computer and System Science, 30:1-24, 1985.

....U ( until ) and X ( next ) while CTL is the branchingtime logic built on these same modalities (hence the notations PLTL = L(U; X) and CTL = B(U; X) in [Eme90] CTL , introduced in [EH86] was designed to be more expressive than both PLTL and CTL. Several fragments of CTL are studied in [EH85,EH86,ES89,Eme90] and other papers. Clearly, what CTL really lacks in practice is the ability to express fairness properties, and this is what motivates the introduction in [EH86] of ECTL, or B(U; X; 1 F ) an extension of CTL with the E 1 F modality for stating fairness conditions. ECTL sits between CTL and ....

....The idea of allowing boolean combinations of temporal modalities has also been applied to CTL (and other logics) In CTL one can state A GC XD ) BUC , i.e. all paths with C everywhere and D in next state satisfy BUC . A surprising result is that CTL is not more expressive than CTL [EH85] while ECTL is more expressive than ECTL [EH86] However CTL can be much more succinct than CTL, a fact that was conjectured since [EH85] but has only been proved recently [Wil99] That CTL can be more succinct than CTL has a clear impact on the complexity of model checking for the two ....

[Article contains additional citation context not shown here]

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1-24, 1985.

....if we can only reason about one agent or processor in the language, PSPACE complete with two or more agents, and EXPTIME complete if we add common knowledge to the language. If we consider time alone, the validity problem for the language with branching time modalities is EXPTIME complete [EH1], while for the The first two sections of this paper are essentially identical to the first two sections of [HV1] we include them here for completeness. While in [HV1] we described in detail lower bound results, here we describe in deraft some upper bound and completeness results. We plan to ....

E.A. Emerson and J.Y. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, J. Computer and Systems Science, 30:1, 1985, pp. 1-24.

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E.A. EMERSON AND J. Y. HALPERN, Decision procedures and expressiveness in the temporal logic of branching time, J. Cornput. System Sci. 30, No. I (1985), 1-24.

....F = f(b; s)jb 2 F; s 2 Sg. 2.4 Temporal Logics and their Semantics We will define the syntax and semantics of the Full Branching Time Logic CTL . The other logics considered (CTL and LTL) are sublogics of CTL , and will be defined as such. read as Computation Tree Logic star ) EH 82] derives its expressive power from the freedom of combining modalities which quantify over paths and the modalities which quantify states along a particular path. These modalities are A; E; F; G; X s ; and Uw ( for all futures , for some future , sometime , always , 13 strong next time , and ....

....or refine actions to a finer grain of atomicity. In [BCG 88, dNV 90] bisimulations that take into account such stuttering are defined. It is shown in [BCG 88] that states related by a stuttering bisimulation satisfy the same formulas of the powerful branching temporal logic CTL [EH 82] that do not use the next time operator, X. Although these definitions are well 122 suited to showing the relationship with CTL , they are difficult to use in proofs of bisimulation, as they often require one to exhibit a finite, but unbounded sequence of transitions to match a single ....

Emerson, E.A., Halpern, J. Y. Decision procedures and Expressiveness in the Temporal Logic of Branching Time, Proc. 14th ACM STOC, San Francisco, 1982.

....with the silent action . 2.5 Temporal Logics and their Semantics We will define the syntax and semantics of the Full Branching Time Logic CTL . The other logics considered (CTL and LTL) are sublogics of CTL , and will be defined as such. CTL (read as Computation Tree Logic star ) EH 82] derives its expressive power from the freedom of combining modalities which quantify over paths and the modalities which quantify states along a particular path. These modalities are A; E; F; G; X s ; and Uw ( for all futures , for some future , sometime , always , strong nexttime , and ....

Emerson, E.A., Halpern, J. Y. Decision procedures and Expressiveness in the Temporal Logic of Branching Time, Proc. 14th ACM STOC, San Francisco, 1982, pp. 169-180.

....that can appear in AND nodes and OR nodes. The pruning procedure can be implemented to run in time polynomial in jT 0 j, yielding an exponential time upper bound. A matching lower bound can be established by simulating alternating polynomial space Turing machines (cf. FL79] Thus, we have (cf. [EH85], EC82] Theorem 4.2. CTL satisfiability is deterministic exponential time complete. 5 Decision Procedures II: Automata theoretic Approach There has been a resurgence of interest in finite state automata on infinite objects, due to their close connection to temporal logic. They provide an ....

....checking is P complete. Membership in P was established in [CE81] by a simple algorithm based on the Tarski Knaster theorem. This was improved to the bound O(jM jjf j) for input structure M and CTL formula f in [CES86] Satisfiability testing for CTL is complete for deterministic exponential time [EH85]. The upper bound established using the tableau method was discussed previously. The lower bound follows by a generic reduction from alternating polynomial space Tm s (cf. FL79] We next consider CTL . Its model checking problem is of the same complexity as for PLTL. It is PSPACE complete with ....

Emerson, E. A., and Halpern, J. Y., Decision Procedures and Expressiveness in the Temporal Logic of Branching Time, Journal of Computer and System Sciences, vol. 30, no. 1, pp. 1-24, Feb. 85.

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E.A. Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

No context found.

E. A. Emerson and J. Y. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, Journal of Computer and System Sciences, vol. 30 (1985), pp. 1--24.

No context found.

E.A. Emerson and J.Y. Halpern, Decision Procedures and Expressiveness in the Temporal Logic of Branching Time, Proc. of 14th Annual ACM Symp. on Theory of Computing, San Francisco, pp. 169-180, 1982.

No context found.

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

No context found.

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. In Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, pages 169--180, San Francisco, California, 5--7 May 1982.

No context found.

E. Emerson and J. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. J. Comp and Sys. Sci, 30(1):1-24, 1985.

No context found.

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1{ 24, 1985.

No context found.

E. Allen Emerson and Joseph Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. J. Comput. System Sci., 30(1):1--24, 1985.

No context found.

E. Allen Emerson and Joseph Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. In ACM, editor, Proc. of the Fourteenth Annual ACM Symposium on Theory of Computing, pages 169--181, San Francisco, California, 1982.

No context found.

Emerson, E., and Halpern, J. (1985). Decision procedures and expressiveness in the temporal logic of branching time. Journal of Comput. System Sci., 30, 1-24.

No context found.

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1-24, 1985.

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Emerson, E. and J. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, in: Proceedings of the 14th ACM Symposium on Computing, 1982, pp. 169-180.

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Emerson, E.A. and Halpern J.Y. Decision Procedures and Expressiveness in the Temporal Logic of Branching Time. Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, 1982, pp. 169-180.

No context found.

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

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A. Emerson and J. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, Journal of Computer and System Sciences, 30 (1985), pp. 1-24.

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Emerson, E. and J. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, in: Proceedings of the 14th ACM Symposium on Computing, 1982, pp. 169-180.

No context found.

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1-24, 1985. 87

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1-24, 1985.

No context found.

Emerson, E.A., Halpern, J.Y., Decision Procedures and Expressiveness in the Temporal Logic of Branching Time, Proc. of 14th Annual ACM Symp. on Theory of Computing, San Francisco, pp. 169-180,

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