M. Hennessy and R. Milner, Algebraic laws of indeterminism and concurrency, Journal of the ACM, vol. 32 (1985), pp. 137-162.  Home/Search   Document Not in Database   Summary   ACM   TOC   Related Articles   Check

....In as far as possible behaviours are concerned, one is interested in transition systems not up to isomorphism but up to bisimulation equivalence. In fact bisimulation equivalence was, apparently independently, isolated as an adequate notion of equivalence both in the context process analysis [11, 19] (where the term bisimulation was coined) and in the Ehrenfeucht Fra ss e analysis of Kripke structures for propositional modal logics [22, 23] under the name of zig zag equivalence) The common domain of modal model theory is that of transition systems (or Kripke structures) up to bisimulation ....

M. Hennessy and R. Milner, Algebraic laws of indeterminism and concurrency, Journal of the ACM, vol. 32 (1985), pp. 137-162.

....and the implication 3 ) 4 may be proved by an argument similar to the one in Theorem 5.8. To complete the proof we need to show that 1 implies 3. It suffices to observe that on models of depth n, every basic modal formula is equivalent to a formula of rank n. a Example 5. 4 (Hennessy and Milner [12]) The converse of the inclusion in Proposition 5.1 does not hold: as is well known from the general literature on bisimulations, there are BML equivalent models that are not bisimilar. Let be a vocabulary with just a single binary relation symbol R. Define models A and B as in Figure 1 below, ....

....else, the obvious next question is: for which modal language L does coincide with Theorem 5.8 The relations and j BML1 ( coincide. Proof. The inclusion BML1 ( is immediate by an inductive argument. For the converse, we adopt an argument due to Hennessy and Milner [12]. We show that the relation Z defined by Zab whenever a and b satisfy the same BML1 ( formulas is a bisimulation. Assume it is not. If a 0 and b 0 disagree on some proposition letter, then they can t have the same BML1 ( theory. Hence, for some R and a 1 , a n we have Ra 0 a 1 : a ....

M. Hennessy and R. Milner. Algebraic laws for indeterminism and concurrency. Journal of the ACM, 32:137--162, 1985.

....is the weakest one that allows for a direct development of the model theory of Since and Until without a detour through richer languages. Modal Bisimulations We start with bisimulations for standard modal languages, often called strong bisimulations in the computational literature (see [12]) These are defined by clause 1 of Definition 3.1 together with clause 2 with the last conjunct ( and x 1 y 1 Z 1 x 2 y 2 ) left out. Strong bisimulations are much weaker than our bisimulations: they don t take the past of nodes into account. An obvious way of taking the past into account is ....

M. Hennessy and R. Milner. Algebraic laws for indeterminism and concurrency. Journal of the Association for Computing Machinery, 32:137--162, 1985.

....logic over traces. Consequently, we consider their LTL version. In the first section of this chapter, we introduce LTL t by means of its syntax and its semantics. We also define a simple fragment of LTL t which we call Hennessy Milner logic since it is in the spirit of the logic defined in [HM85] see also [Sti01] The second section provides one of the main contributions of this thesis: We give a decision procedure for LTL t formulas using alternating Buchi automata. To simplify our presentation, we show our method first for the Hennessy Milner fragment and extend our approach later ....

M. Hennessy and R. Milner. Algebraic laws for indeterminism and concurrency. Journal of the ACM, 32:137--162, 1985.

....coincides with equivalence in a simple propositional polymodal language. As a consequence bisimulations can be used as a tool in the model theory of polymodal languages. In fact, bisimulations of one form or another have proved to be an important tool in understanding their expressive power (cf. [8, 3, 1, 16, 13]) As we will see below, to develop the model theory of languages without boolean negation along similar lines, we need to consider relations between transition systems that are not equivalence relations, but only a special kind of pre orders, called directed simulations. In the computational ....

....similar lines, we need to consider relations between transition systems that are not equivalence relations, but only a special kind of pre orders, called directed simulations. In the computational literature similar (non equivalence) relations between transition systems have been considered in [8, 19], mainly as ways of formalizing the idea of one process approximating another. 3 Definitions Negation free 3, 2 formulas are built up using (countably many) propositional variables p, q, the constants and , boolean conjunction and disjunction , and unary modal operators 3 (diamond) ....

M. Hennessy and R. Milner. Algebraic Laws for Indeterminism and Concurrency. Journal of the ACM, 32:137--162, 1985.

....be given below. The technical de nition can be traced back to graph theory [6] and to automata theory [14] late 60 s) Around the same time (late 70 s, early 80 s) the notion of regular equivalence arose independently in social network analysis [13, 17] modal logic [1] and in computer science [9, 5]. In modal logic, the relation used to be called zig zag relation, in computer science it is called bisimulation, and that name stuck. Networks occur under the name of Kripke models in philosophical logic and as labeled transition systems (LTS) in the computer science literature. LTS s are used ....

....to modal logic see [2] This also contains full proofs of the three key results. We urge the reader to try to prove the rst key result. The proof is by an induction on the complexity of position terms. The two other key results are much harder to prove. The second is due to Hennessy and Milner [5], the third to van Benthem [1] Modal logic was traditionally concerned with questions regarding necessity, knowledge, belief and temporal aspects of language. Nowadays modal logic is seen as a very versatile knowledge representation language. The present paper is another example of its ....

M. Hennessy and R. Milner. Algebraic laws for indeterminism and concurrency. Journal of the ACM, 32:137-162, 1985.

....negation free modal languages. Recently, these have attracted considerable attention, both at an applied and at a theoretical level; cf. 8, 11, 14] For modal languages with a full Boolean repertoire, bisimulations have proved to be an important tool in understanding their expressive power (cf. [9, 4, 1, 18, 15]) In this paper we develop analogous tools for negation free modal languages. We introduce a kind of non symmetric simulations called directed simulations between transition systems that allow us to study the expressive power and develop the model theory of negation free languages. As far as we ....

M. Hennessy and R. Milner. Algebraic laws for indeterminism and concurrency. Journal of the ACM, 32, 137--162, 1985.

....of modal and temporal logics. Modal logics have their origin in philosophy which makes it di#cult to date their births back to a certain moment. However, in computer science where program verification plays a crucial role, modal logics have become interesting in the shape of Hennessy Milner logic [HM85], the modal calculus [Koz83] or even the dynamic logic PDL [FL79] Temporal logics, a subclass of modal logics, have been identified explicitly as LTL [Pnu77] CTL [CE81] CTL # [EH86] and various other fragments of the latter one. There are several methodologies which have been developed to ....

M. Hennessy and R. Milner. Algebraic laws for indeterminism and concurrency. Journal of the ACM, 32:137--162, 1985.

.... were rst introduced (under a di erent name) by van Benthem [4, 5] The notion was independently introduced in computer science, as an equivalence relation on process graphs; the rst reference seems to be Park [47] whereas the classic computer science paper on the subject is Hennessy Milner [28]; the latter paper also discusses the nitary approximations to bisimulations. The notion of unravelling a modal model stems from Dummett Lemon [16] Proposition 2 is analogous to similar characterizaions of logical equivalence for rst order logic, due to Ehrenfeucht and Fra ss e (cf. 31] ....

M. Hennessy and R. Milner. Algebraic laws for indeterminism and concurrency. Journal of the ACM, 32:137-162, 1985. 56

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