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By Ryszard Janicki
Concurrent structures abound in human event yet their totally sufficient conceptualization as but eludes our so much capable thinkers. The comfortable (ConcurrentSystem) notation and conception was once built within the final decade as one in all a couple of mathematical ways for conceptualizing and interpreting concurrent and reactive structures. The snug method extends theconventional notions of grammar and automaton from formal language and automata conception to collections of "synchronized" grammars and automata, allowing method specification and research of "true" concurrency with no aid to non-determinism. snug thought is constructed to an outstanding point of element and constitutes the 1st uniform and self-contained presentationof all effects approximately snug released some time past, in addition to together with many new effects. comfortable concept is used to research a enough variety of commonplace difficulties regarding concurrency, synchronization and scheduling, to permit the reader to use the ideas offered tosimilar difficulties. The comfortable version is usually with regards to many various types of concurrency, quite Petri Nets, speaking Sequential tactics and the Calculus of speaking Systems.
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Extra info for Specification and Analysis of Concurrent Systems: The COSY Approach
Example text
We shall discuss this approach in Sect. 3. 2. 1 23 VFS Semantics of COSY Simple Properties of Vector Sequences Let n ;:::: 1 be an integer, and let EVh ... , EVn be non-empty finite sets of elements which we shall call events. Define Ev = EVI U ... U Evn • Intuitively each EVi represents a set of events that must occur one at a time. Ev is the set of all events of the system. Consider a Cartesian product Evr X ••• X Ev~. If vectors (:el, ... , :en) and (Yl, ... , Yn) belong to this set, their concatenation is defined as: (:el, ...
2, so in particular, we have the relation ind ~ TxT defined as (tl, t 2 ) E ind {:} (Vi)tl Xn )) = Xi. Note that for every 21. ) = hi(x). Let ind ~ Ev x Ev be the following relation: (Va, bE Ev)(a, b) E ind:{:} ((Vi = 1, ... ,n)a 'f. EVi V b 'f. EVi). The relation ind is called the independency, and intuitively, only independent events can be executed concurrently. For every a E Ev, let i(a) = {jla E EVj}. 1 Let a,b E Ev. The following are equivalent: (a) (a,b) E ind (b) ab = ba and a =F b (c) (Vi = 1, ... 1, i(a) = {1}, i(b) relation is depicted in Fig. 3. Let Ind ~ 2Ev \ = {2}, i(c) = {1,2} o and the independency 0 be the following family of sets of events: A E Ind:{:} ((Va, bE A)a = b V (a, b) E ind).