E.A. Emerson and C.-L. Lei. Modalities for model checking: Branching time logic strikes back. In Proc. 20th ACM Symp. on Principles of Programming Languages, pages 84--96, New Orleans, January 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....CCR 9970679, INT 9981558, ITR 0085949, and ITR 0086154. Preprint submitted to Elsevier Preprint 27 July 2001 [50] but also by many others, it is the most natural format for this purpose. But many testing and analysis frameworks are oriented towards another format, branching time temporal logic [4,16,18], which lets one write correctness properties in terms of the potential execution steps ( branches ) that might be taken from each state in a system. The standard formulations of linear time logic (LTL [16,37] and branchingtime logic (CTL [6,16] are often presented as incomparable, because of ....

.... logic and branching time logic as competing semantical interpretations of the same temporal logic notation [27] Although these insights are valuable, they have suggested that the linear time and branching time approaches are competitors, locked in a dual where one must vanquish the other [18,50]. A significant paper by Cousot and Cousot shows that this scenario need not be the case [12] By employing abstract interpretation, a theory of abstraction of structure [9,10,25] Cousot and Cousot show that a system s concrete operational semantics generates execution traces whose behaviors are ....

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E.A. Emerson and C.L. Lei. Modalities for model checking: Branching time logic strikes back. In Proc. 20th ACM Symp. Principles of Prog. Lang., pages 84--96. ACM Press, 1985.

....set of the pair then it intersects also the second set. The nonemptiness check for Streett automata can thus be also based on identification of the fair SCCs of the automaton graph. Other types of automata for which the nonemptiness check is based on identification of fair cycles are listed in [15]. The LTL model checking problem and the LTL model checking with strong fairness (compassion) reduce to language emptiness checking of generalised B uchi automata and Streett automata respectively [36, 26] Fair cycle detection is used to check the CTL formula EGf under the full (generalised) ....

.... checking problem and the LTL model checking with strong fairness (compassion) reduce to language emptiness checking of generalised B uchi automata and Streett automata respectively [36, 26] Fair cycle detection is used to check the CTL formula EGf under the full (generalised) fairness constraints [15]. Hence, the Supported by GA CR grant no. 201 00 1023 core procedure in many model checking algorithms is the fair cycle detection. These algorithms are in common use in explicit and symbolic LTL model checkers such as SPIN [22] and SMV [29] respectively, in fair CTL model checkers such as ....

E. A. Emerson and C.-L. Lei. Modalities for model checking: branching time logic strikes back. Science of Computer Programming, 8:275 -- 306, 1987.

....Temporal logics such as LTL and CTL are used for specification languages for automated verification. Gottlob and Koch [GK02] have that the core of XPATH can be viewed as a fragment of CTL . The following algorithm is practical. Theorem 4. 3 (Lichtenstein and Pneuli [LP85] Emerson and Lei [EL87]) The evaluation problems for LTL and CTL on the class of Kripke structures are FPT in time n) where k is the size of the query, and n is the size of the input instance. Given that the material has only been investigated by only a few authors, and the area is definitely important, it is ....

E. Emerson and C. Lei, "Modalities for Model Checking: Branching Time Logic Strikes Back," Scence of Computer Programming, 8 (1987), 275-306.

....follows by a reduction from 3 SAT. 1 For CTL the following result holds [CES86] Theorem 3.23 The model checking problem for CTL is in deterministic linear time. The following theorem allows to extend to branching time logics the results obtained for corresponding linear time logics [EL85], where the correspondence is given by the fact that the considered branching time logic can be defined using as basic modalities the formulae V9 or 39 for all formulae 9 of the linear time logic. Theorem 3.24 Given a model checking algorithm for a linear logic L, there is a model checking ....

E.A. Emerson and C.L. Lei. Modalities for model-checking: Branching time logic strikes back. In Proceedings of the 12th A CM Symposium on Principles of Programming Languages, pages 84-96, 1985.

....of the pair then it intersects also the second set. The nonemptiness check for Streett automata can thus be also based on identi Thetacation of the fair SCCs of the automaton graph. Other types of automata for which the nonemptiness check is based on identi Thetacation of fair cycles are listed in [15]. The LTL model checking problem and the LTL model checking with strong fairness (compassion) reduce to language emptiness checking of generalised B # uchi automata and Streett automata respectively [36, 26] Fair cycle detection is used to check the CTL formula EGf under the full (generalised) ....

.... problem and the LTL model checking with strong fairness (compassion) reduce to language emptiness checking of generalised B # uchi automata and Streett automata respectively [36, 26] Fair cycle detection is used to check the CTL formula EGf under the full (generalised) fairness constraints [15]. Hence, the Supported by GA i CR grant no. 201 00 1023 core procedure in many model checking algorithms is the fair cycle detection. These algorithms are in common use in explicit and symbolic LTL model checkers such as SPIN [22] and SMV [29] respectively, in fair CTL model checkers such as ....

E. A. Emerson and C.-L. Lei. Modalities for model checking: branching time logic strikes back. Science of Computer Programming, 8:275 # 306, 1987.

....2.2 Branching time logics and NP hard path modalities We assume familiarity with temporal logic model checking [Eme90,CGP99,Sch03] Several branching time logics combine the path quantifiers E and A with lineartime modalities whose path existence problem is in NP. Here are five examples: FCTL [EL87], or Fair CTL , allows restricting to the fair paths of a Kripke structure, where the fair paths are defined by an arbitrary Boolean combination of F P i s. The existence of a fair path is NP complete [EL87] TCTL [Koy90] or Timed CTL , allows adding timing subscripts to the usual ....

....modalities whose path existence problem is in NP. Here are five examples: FCTL [EL87] or Fair CTL , allows restricting to the fair paths of a Kripke structure, where the fair paths are defined by an arbitrary Boolean combination of F P i s. The existence of a fair 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 ....

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E. A. Emerson and Chin-Laung Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275--306, 1987.

....good starting point for exploration of the entire state space. Symbolic guided search speeds up CTL model checking and has been shown elsewhere to benefit LTL model checking as well as w regular language containment [BRS99] Combining the two approaches yields a guided search algorithm for CTL [EL87] which we plan to implement. More work remains to be done in the integration of our approach with existing techniques for abstraction. In particular, we are interested in the combination of guided search with the iterative refinement schemes of [PH97, Jan99] ....

E. A. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8:275--306, 1987.

....single state has a self loop. The product is empty if no non trivial SCC contains a state belonging to the set of nal states. Another way is to use the nested depth rst algorithm of [10] The SCC based algorithm has been extended in many ways to take into account di erent fairness constraints [43, 16, 39, 40]. Model checking safety properties does not di er much from the procedure above. The steps are the same, but some of the procedures di er. In the rst step, instead of constructing a B uchi automaton we construct an automaton on nite words which captures the bad pre xes of the formula. The two ....

E.A. Emerson and C-L. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275-306, 1987.

....[Var95] but the algorithms implemented in popular LTL model checkers (such as Spin [Hol97] are based on standard nondeterministic automata. In principle, model checking CTL # is an easy adaptation of the model checking algorithms for LTL, as was observed by Emerson and Lei: Theorem 3. 4 [EL87, CES86] For any linear time future only logic L, there is a polynomial time Turing reduction from model checking B(L) to model checking L. Hence if L has model checking in some complexity class C, then B(L) has model checking in P C . This applies to CTL # since CTL # is B(LTL) we only need ....

....Turing reduction from model checking B(L) to model checking L. Hence if L has model checking in some complexity class C, then B(L) has model checking in P C . This applies to CTL # since CTL # is B(LTL) we only need to remember that LTL has PSPACE complete model checking. Corollary 3. 5 [EL87, CES86] The model checking problem for CTL # is in PSPACE , that is, in PSPACE. The algorithm underlying Theorem 3.4 is quite simple: one uses a dynamic programming approach la CTL and rst computes in which states the subformulae are satis ed before dealing with the superformula. For a ....

[Article contains additional citation context not shown here]

E. A. Emerson and Chin-Laung Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275306, 1987.

....contents the various states can be reached 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 ....

E.A. Emerson and C.-L. Lei. Modalities for model checking: Branching time logic strikes back. In Proceedings of the Twelfth ACM Symposium on Principles of Programming Languages, pages 84--96, New Orleans, January 1985.

....can be expressed in LTL for which we provide an efEcient model checking algorithm. In Section 4.3 we present and analyze a model checking algorithm for CTL . In the context of Enite state systems it is well known that model checking the more powerful logic CTL can be reduced to checking LTL [5]. This technique can be transferred to pushdown systems using model checking with regular valuations. The complexity of all of the previously developed algorithms is measured in certain parameters of the problem which are usually small, and our complexity bounds are polynomials in those ....

.... are built according to the following abstract syntax equation: where A ranges over the atomic propositions (interpreted, say, by a regular valuation represented by a nite automaton of size IState I) For nite state systems, model checking CTL can be reduced to checking LTL as follows [5]: For a CTL formula , call the path depth of the maximal nesting depth of existential path quantiers within . Subformulae of can be checked in ascending order of path depth; subformulae of the form S t where t is G free are checked with an LTL algorithm which returns the set of states S v, ....

E.A. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275-306, 1987.

....DKSs, the upper bound follows. ut 5.2 Model checking TCTL over DKSs Theorem 5.2. 1. Model checking TCTL over DKSs (and ssDKSs) is EXPSPACE complete. 2. Model checking TCTL ; over DKSs (and ssDKSs) is PSPACE complete. Proof. A direct consequence of Theorem 5. 1: the techniques from [EL87] produce an algorithm for TCTL under the form of a simple polynomial time labeling algorithm that calls an oracle for TLTL model checking. Hence model checking belongs to P EXPSPACE , that is EXPSPACE. The same reasoning applies to TCTL ; and yields a a P PSPACE , that is a PSPACE ....

E. A. Emerson and Chin-Laung Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275-306, 1987.

.... states that F holds in nitely often (expressed in Linear Temporal Logic (LTL) as GF(F ) and a co B uchi acceptance speci es that F holds from some point onwards (written in LTL as FG(F ) One may also express an acceptance condition as a disjunction of co B uchi and B uchi conditions [EL87] Informally, a safety property speci es that something bad never happens during an execution, while a liveness property states that something good eventually happens. We use N to represent the natural numbers. 2.1 Syntax An MTD, T , is speci ed over a set of variables (sometimes called ....

....cubic in the size of T , and linear in the size of M . Proof. By Theorem 1 and the procedure given above, M j= T i L(A T M) This is equivalent to searching for a rejecting run of A T on some computation of M . This can be done in time linear in the size of M and linear in the size of A T [EL87] Since A T has size at most cubic in the size of T , the result follows. ut 3 Compositional Reasoning with MTD s Large systems are often composed of many concurrent, interacting processes. This leads to a blowup in the state space of the system, commonly referred to The size of AT is the size ....

E.A. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275-306, 1987. 16

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E.A. Emerson and C.-L. Lei. Modalities for model checking: Branching time logic strikes back. In Proc. 20th ACM Symp. on Principles of Programming Languages, pages 84--96, New Orleans, January 1985.

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E.A. Emerson and C.L. Lei. Modalities for model-checking: Branching time logic strikes back. In Proceedings of the 12th ACM Symposium on Principles of Programming Languages, pages 84--96, 1985.

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E.A. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275--306, 1987.

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E. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275--306, 1986.

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E.A. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275--306, 1987.

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E. A. Emerson and C.-L. Lei. Modalities for model checking: branching time logic strikes back. Science of Computer Programming, 8:275 - 306, 1987.

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E. A. Emerson and Chin-Laung Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275-306, 1987.

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E. A. Emerson and Chin-Laung Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275-306, 1987.

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E.A. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275--306, 1987.

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E. A. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8:275-306, 1987.

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E. A. Emerson and C.-L. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275--306, 1987.

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E. A. Emerson and C.-L. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275-306, 1987.

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