O. Grumberg and R.P. Kurshan. How linear can branching-time be. In Proceedings of the First International Conference on Temporal Logic, volume 827 of Lecture Notes in Artificial Intelligence, pages 180-- 194, Bonn, July 1994. Springer-Verlag.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of next points, then we can defer the branching at this point by identifying these next points. If such a situation does not occur in a model (we shall later call such a model closed) then a homomorphism with this model as its domain can only be injective (in the branching time logic CTL (see [GK94]) a structure with this property is called deterministic) Let f : M M be a homomorphism. a) The following conditions are satisfied: i) For all t in T and s in T with s f(t) there exists an s in T with s t and f(s) s . ii) For every s in T with s f(t) there exists an s in T with ....

....elements are mapped to minimal elements. The first part is equivalent to branch surjectivity. So our notion of branch surjective homomorphism is equivalent to the notion of p morphism (between forests) in [Be83] Similar notions (between structures) can also be defined for CTL (see for instance [GK94]) Loosely, a homomorphism from M to M in our sense corresponds to a simulation relation from M to M ( GK94] They have a similar result as Theorem 3.5 for the CTL fragment containing only , respectively . We intend to use homomorphisms in a number of algebraic constructions on models, ....

[Article contains additional citation context not shown here]

O. Grumberg, R.P. Kurshan, How Linear Can Branching-time Be?, in: D.M. Gabbay, H.J. Ohlbach (eds.), Temporal Logic, Proceedings of the First International Conference on Temporal Logic, ICTL'94, Springer-Verlag, 1994, pp. 180-194.

....the same as in the modal case. In particular, a rst order formula = t) in the language with binary (temporal precedence) and unary predicates P; Q; one for each proposition letter p; q; is P; F de nable i it is invariant for two sided bisimulation. The purely modal proof of [12] goes through in toto. This observation can be used e.g. for quick proofs of non TL de nability by concrete counterexamples. To be sure, there are some minor technical di erences here and there. For instance, the standard modal technique of tree unraveling has to be modi ed to allow for ....

....To appear in the Journal of Symbolic Logic. 10] J. Barwise and L. Moss. Vicious Circles. On the mathematics of non wellfounded phenomena. CSLI Publications, Stanford, 1996. 11] R. B auerle, C. Schwarze and A. von Stechow, eds. Semantics from Di erent Points of View. Springer, Berlin, 1979. [12] J. van Benthem. Modal Correspondence Theory. Dissertation, Mathematisch Instituut, University of Amsterdam, 148 pp. 1976. 13] J. van Benthem. The Logic of Time. Reidel, Dordrecht (second edition 1991) 1983. 14] J. van Benthem. The Ubiquity of Logic in Natural Language . In The Tasks of ....

[Article contains additional citation context not shown here]

Orna Grumberg and Robert P. Kurshan. How linear can branching-time be? In International Conference on Temporal Logic, number 827 in Lecture Notes in Articial Intelligence, Bonn, Germany, 1994.

....equivalences. These equivalences are then compared to each other and to those induced by the non at versions of the logics. Section 4 concludes. Some proofs in this article have been moved into the appendices. Comparative expressivity of CTL like temporal logics is studied in, among others, [9, 12, 10]. Behavioural equivalences ( 6] induced by temporal logics are the subject of [13, 2, 19, 15, 7, 1, 11, 20, 5] 2 Flat Linear time Temporal Logic: Expressivity Throughout this article, we assume given a nonempty set Prop of propositions. De nition 2.1 The logic LTL is the set of formulae de ....

Orna Grumberg and Robert P. Kurshan. How linear can branching-time be? In International Conference on Temporal Logic, number 827 in Lecture Notes in Articial Intelligence, Bonn, Germany, 1994.

....Since often we want to specify that all the computations of the program satisfy some property, the interest in derived languages is clear. Branching temporal logic formulas that describe derived languages constitute a strict fragment of CTL . In fact, this fragment, called strongly linear in [GK94], is a strict fragment of the universal fragment 8CTL of CTL . A necessary and sufficient condition for CTL formulas to be strongly linear is given in [CD88] a CTL formula is strongly linear iff omitting all its path quantifiers results in an LTL formula such that and A are ....

....lemma implies Claim 1 too. Claim 3 follows from Lemma 4.2 and the fact that BW = RW . Finally, Claim 2 follows from Theorem 3.1. Given a CTL formula and a Buchi tree automaton U associated with , we can use the characterization in [CD88] in order to determine whether is strongly linear [GK94], in which case the language of U is derivable. When the language of U is derivable, it follows from Theorem 4.3 that the linear requirement that imposes on all computations can be specified by a deterministic Buchi word automaton and that the automaton U may be determinized as well. Our ....

O. Grumberg and R.P. Kurshan. How linear can branching-time be. In Proceedings of the First International Conference on Temporal Logic, volume 827 of Lecture Notes in Artificial Intelligence, pages 180-- 194, Bonn, July 1994. Springer-Verlag.

....i and A is done by a pair of shared boolean variables r i (request) and g i (grant) Following are statements of properties, that a designer may wish to formally specify and verify about the operation of this system. Each specification is given in both NL and our target temporal logic, ACTL 4;5 [6], a subset of Computational Tree Logic (CTL) 2] These specifications will illustrate the problems encountered in NL translation as described in Sec. 1.2. 3 This example is based on one in [14] 4 The target formalism of [4] is called ACTL too. Nevertheless, it is a different formalism. 5 ....

....7 shows that the translation method conforms to this correctness criterion. The proof of this theorem is based on the reduction of correctness to single paths. Theorem 7. Let K be an SPDRS, and f = trans(K) f is a correct translation of K into ACTL. Reduction of Correctness to Single Paths In [6] three linearity properties for branching time temporal logics are defined: strong linearity, sub linearity and equi linearity. We take advantage of the strongest of these properties, stronglinearity, by restricting the formulae generated by the translation to the subset of strong linear ....

[Article contains additional citation context not shown here]

O. Grumberg and R.P. Kurshan. How linear can branching-time be? In D. M. Gabbay and H. J. Ohlbach, editors, First International Conference on Temporal Logic (ICTL'94). Lecture Notes in Artificial Intelligence 827, pages 180--194, Bonn, Germany, 1994. Springer-Verlag.

.... same set of Kripke structures (where, in the case of FQL, the Kripke structures are interpreted as a limit prefix closed automaton [6] i.e. an automaton all of whose runs are accepting) For a general treatment of the issue of equivalence between liner time and branching time structures, see [5]. The syntax and semantics of CTL, its extension CTL and of the linear time propositional temporal logic LTL are well known [3] The automata associated with FormalCheck comprising FQL are specified by a fixed set of parameterized macros. FQL is defined as arbitrary finite conjunctions of ....

O. Grumberg and R. P. Kurshan. How linear can branching-time be? In Proc. Int'l. Conf. on Temporal Logic, (ICTL'94), Bonn, Germany, 1994.

....equivalence checking and property checking. In CCS, two processes are bisimilar exactly when they satisfy the same set of formulas of the HennessyMilner logic [81] Grumberg and Kurshan have shown a relationship between classes of CTL formulas and language equivalence or containment problems [71]. 2.3 Proof Techniques Now that we have defined what we mean by program correctness, we can examine proof techniques. We first look at why formal proof techniques are important, and then examine some of these techniques: Section 2.3.1 discusses theorem proving; Section 2.3.2 discusses automatic ....

O. Grumberg and R.P. Kurhsan. How Linear Can Branching-time Be? In Gabbay and Ohlbach [61], pages 180--194.

No context found.

O. Grumberg and R.P. Kurshan. How linear can branching-time be. In Proceedings of the First International Conference on Temporal Logic, volume 827 of Lecture Notes in Artificial Intelligence, pages 180-- 194, Bonn, July 1994. Springer-Verlag.

No context found.

O. Grumberg and R.P. Kurshan. How linear can branching-time be. In Proc. 1st International Conference on Temporal Logic, volume 827 of Lecture Notes in Arti cial Intelligence, pages 180-194, Bonn, July 1994. Springer-Verlag.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC