J-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... la wa re di#erent (b a d re independent versus bca409z80fi4OOza c or vice versa [36] It is possible to extend so ca led partialorder semantics for processa lgebra with stocha stic informa tion to obta in suita ble non interlea ving sema ntica models for stochaO ic processa lgebra5 We refer to [8,32] for further rea ing. 5.3 Synchronisation Proba ly the most intriguing question in the design of stocha stic processa lgebra is rela ted to the synchronisa tion of stocha stica ctions of two concurrent system components. If botha ctionsa re subject to stocha sticdela ys, wha t should be the ....

J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures.Ph th esis, Centre for Telematics and Information Tech nology, Ensch ede, 1996.

....used to describe such systems, e.g. Petri nets [13] generalised semi Markov processes [8] and stochastic process algebras etc. In this paper we will consider stochastic process algebras, for which a number of formalisms, techniques and tools are available, e.g. PEPA [10] TIPP [9] EMPA [3] PA GS [11] and SPADES [7] Stochastic process algebras offer a number of advantages over other techniques such as Petri nets. In particular, stochastic process algebras are compositional and allow a specification to be built Irish Workshop on Formal Methods, 1999 1 as a number of smaller components composed ....

Joost-Pieter Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, Centre for Telematics and Information Technology, P.O. Box 217, 7500 AE Enschede The Netherlands, April 1996.

....behaviour model that we use, the prime event structure (Figure 3) Prime event structure Event structures [NPW81] can be classified as behaviour noninterleaving branching time models. Different event structure models have been defined in the literature. An overview can be found in [Kat96] Definition 2 A (labelled) prime event structure (PES) is a quadruple (E; #; l) where ffl E is a countable set of events, ffl E Theta E is a partial order, the causality relation, ffl # E Theta E is the (irreflexive and symmetric) conflict relation, ffl l : E A is the ....

J.-P. Katoen. Quantitative and qualitative extensions of event structures. PhD thesis, University of Twente, 1996.

....of events and identify the preceding succeeding events of every event, we can derive a protocol specification which contains only the message exchanges necessary to guarantee the partial order of events. In this paper, we propose a method to obtain a finite representation of event structures[10, 13, 16] from contextfree process specifications. And then, we propose a protocol synthesis method using the finite representation of event structures. Here, an event is an occurrence of an action in the execution sequence of a process. For example, in the execution sequence abac , the first ....

....latter one in order to identify the dynamic occurrence of each event. The main idea of an event ID is that if the above two notions of occurrence are combined, we can completely identify any event executed by the possibly recursive process. The notion of an event ID is inspired by both [1] and [10] Definition 3 For each process definition P : B of a context free process specification, let T (B) be the syntactical tree of the behaviour expression B. Then we represent a path from the root node of T (B) to any other node by (P : op 1d1 ; op 2d2 ; opn 1 dn 1 ; opn ) where for ....

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J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. CTIT Ph.D-thesis series No.96-09, Centre for Telematics and Information Technology, Enshede, The Netherlands, Sept. 1996.

....the time for which another has been enabled can be statistically dismissed the distribution is memoryless. This means that for PEPA, a resume semantics is equivalent to a restart semantics. Non interleaving semantics have been developed for stochastic process algebras. For example, Katoen [51] develops a quantitative extension of event structures, which provides a partial order of process terms expressing only the necessary causality between activities, and not arbitrary interleavings. These semantics have the advantage that models grow linearly as the number of cooperating components ....

J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, Proefschrift Universiteit Twente, Enschede, Netherlands, 1996.

....downward compatible in the sense that by ignoring the probabilistic distributions one recovers the classical early interleaving semantics of calculus. We now briefly recall some work similar to ours. A stochastic extension of bundle event structures with phase type distributions is presented in [9, 24]. The authors also present a process algebra whose semantics is defined in terms of the stochastic event structures. There is also a stochastic extension to LOTOS where distributions are not limited to exponential ones [3] even if the restriction of knowing at the top level all the ....

....to calculate. However symbolic manipulators such as Mathematica can be adopted. Further study is needed to devise a subset of probabilistic distributions that allows an easy manipulation of the data. As far as the comparison with similar approaches is concerned, we mention the work by [3] and [24] that can deal with mobility only indirectly, although ty have multi way synchronization. We claim that a formalism suitable to describe mobile agent paradigms can be of help when dealing with distributed systems because of the widespread dissemination of applications based on mobility like Java ....

J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, Center for Telematics and Information Technology, University of Twente, 1996. Available as CTIT No. 96-09.

....that forces recalculation of distributions is totally independent from those distributions. The need for recalculation stems from the interleaving view on independent actions. Therefore, resorting to a non interleaving semantics clearly eases the definition of a formal semantics. Katoen et al. [9, 46, 48] define an event structure semantics for a language with distributions that are closed under maximum, e.g. phase type distributions, a quite general class of distributions. 47] describes how to perform discrete event simulation for such specifications. 35] develops a denotational semantics for a ....

J.P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, Centre for Telematics and Information Technology, Enschede, 1996.

.... (at least in their straightforward extensions) In [19] we have found the idea of distinction between nondeterministic and probabilistic nodes, that is typical for the work reported here (see also [12] In [6] taking the point of view of performance modeling and quantitative analysis (cf. e.g. [13, 7, 17]) the parallel operator is studied. The induced nondeterminism, however, is resolved in favour of probability. In the recent work of Andova [1] in the alternating approach and incorporating the basic idea underlying [6] a probabilistic process algebra featuring both nondeterministic and ....

J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, 1996. CTIT PhD-thesis series No. 96--09.

....can be defined in the usual way. We summarize the following results, 14 Proceedings of the Third AMAST Workshop on Real Time Systems where for B 2 TPA the set U(B) denotes the set of urgent actions in B. U(B) can easily be defined by induction on B. The proofs are omitted and can be found in [19]. Theorem 9. For all B; B 0 2 TPA, t; t 0 2 T and a 2 Act [ f g we have 1. hB; t 0 i (e;a;t) Gamma ) t t 0 d min (a; B) 2. 8 b 2 U(B) hB; t 0 i (e;b;t) Gamma ) t = t 0 d min (b; B) 3. d min (a; B) 1 ) 9 B 0 : hB; ti (e;a;t 0 ) Gamma B 0 ) 4. hB; ....

....0 i (e;a) Gamma Gamma . 3. Time additivity 2 : hB; ti ; hB 0 ; t (t 0 t 00 )i iff (9 B 00 : hB; ti ; hB 00 ; t t 0 i ; hB 0 ; t (t 0 t 00 )i. The proofs of all theorems are by induction on the structure of B. These proofs are rather straightforward and omitted here; see [19]. Since the transition system under Gamma is deterministic, this transition system can be represented by its set of timed event traces T [ B ] This set can be characterized in a denotational way, and subsequently proven to coincide with the set of timed event traces of the corresponding ....

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J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente (1996, forthcoming)

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J-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, 1996.

....paper. Section 6 presents the operational interleaving semantics and investigates its consistency with the metric semantics. Concluding remarks are provided in Section 7. A preliminary short version of this paper has been published as [5] some other 7 parts were contained in the dissertation [22]. 2 A real time process algebra We assume a given set of observable actions Obs and an invisible action ; 62 Obs. The action p indicates the successful termination action of a process; p 62 Obs and p 6= Let IR denote the set of non negative reals. In addition, let Act = Obs [ f ; p ....

....than timed event traces, and is similar to the treatment of traces by Mazurkiewicz [31] 4 Operators for timed event structures In this section we present some operators on timed event structures that are needed to define a compositional semantics for PA. They are basically adopted from [22,23]. We start with some basic notions. Let Events be a set such that for any event e 2 Events, e; e) 2 Events, and if e; e 0 2 Events then (e; e 0 ) 2 Events. Let TES denote the set of tes s E with E Events. Let init(E) be the set of initial events of E and exit(E) its set of ....

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J-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, 1996.

....interleaving semantics. The motivation for true concurrency models carries over to the real time setting. In fact it has been argued that the incorporation of real time properties fits naturally with both the move to true concurrency models and with the focus on lower levels of system development [6, 14, 18]. In order to realise the benefits of the true concurrency approach in the timed LOTOS setting this paper presents a true concurrency semantics for ET LOTOS. A well accepted branching time true concurrency model is event structures . These were initially developed by Nielsen, Plotkin Winskel ....

....x ] can be defined as the least upper bound (lub) of the chain (under ) FQ ( FQ (FQ ( It is beyond the scope of this report to present the fixed point theory in its full details. However, the required semantic constructions are very closely related to those presented in Katoen [18] and have similarities to those given in Bowman [5] We only consider direct recursion with a single process variable; that is, process definitions of the form: x : x : x : Such an approach can be easily generalised to multiple process definitions and mutual recursion as shown by, amongst ....

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J-P. Katoen. Quantitative and Qualitative Extensions of Event Strcutures. PhD thesis, University of Twente, 1996.

....strong timed (event) bisimulation equivalent) and thus can be used in a coherent way. This also facilitates the comparison of our timed partial order model and the wealth of existing timed interleaving models. 3 3 For space reasons the proofs are omitted from this paper; they can be found in [14]. 2 The language This paper is based on the process algebraic language PA, in fact LOTOS with a somewhat more concise syntax, generated by the following grammar: B : 0 j p j a ; B j B B j B jj G B j B[H] j B n G j B B j B [ B j P: We assume a given set of observable ....

....of the chain (under E) FB ( FB (FB ( For this paper we just define the appropriate ordering E, the corresponding l.u.b. and present the main results. Given these ingredients it is rather straightforward to define a continuous function FB . Further details can be found in [14]. Definition 13. Let Gamma i = h(E i ; i ; 7 i ; l i ) D i ; T i ; U i i for i = 1; 2. Then Gamma 1 E Gamma 2 iff E 1 E 2 , l 1 = l 2 E 1 , D 1 = D 2 E 1 , U 1 = U 2 E 1 , and 1. 1 = 2 (E 1 Theta E 1 ) 2. 7 1 = f ( X E 1 ) e) j e 2 E 1 X 7 2 e g, and 3. 8 e 2 E 1 : T 1 ....

J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, 1996.

....with events fa; b; c; dg; the intersection of these linear orders is a poset with just the identity as the ordering relation, which surely does not capture the causality information of the event structure. Bundle event structures without constraint P1 have been baptized dual event structures in [Kat96]. Providing intentional and observational partial order definitions for dual event structures is the theme of the following sections. 3 Intentional partial order definitions In this section we present several definitions of causality in possibly causally ambiguous situations. What definition is ....

J-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. CTIT Ph. D-thesis series no. 96-09, University of Twente, 1996.

....b 6 t a 7 and t c 6 t a 5, since is not forced to occur and time does not resolve the choice. 4 Operators for timed event structures In this section we present some operators on timed event structures that are needed to define a compositional semantics for PA. They are basically adopted from [9, 10]. We start with some basic notions. Let Events be a set such that for all actions a 2 Act there is an event e a 2 Events, and (i) if e 2 Events then (e; e) 2 Events, and (ii) if e; e 0 2 Events then (e; e 0 ) 2 Events. Let TES denote the set of tes s E with E Events. Let init(E) be ....

....semantics for expressions that contain circular causal dependencies, like in a : b : 0 jj f a;b g b : a : 0, or timing constraints that avoid certain actions from happening, like in a 2 : 0 1 b : 0 where a will never happen. Such events can be removed by applying the transformations exposed in [11, 9] that preserve timed event traces. A solution to this problem is to impose an equivalence relation, say, on TES, while aiming at d(E 1 ; E 2 ) 0 , E 1 E 2 : Stated in other words, where d is the equivalent of d on TES= and E i denotes the equivalence class of E i under , we aim at d(E ....

J-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, 1996.

....them (i.e. the initial events) a random variable is also associated to an event. Though it seems sufficient to only have random variables for initial events, synchronization of events makes it necessary to allow for equipping all events with random variables, including the non initial ones (see [2, 9]) We assume mappings A and R to associate a random variable to events and bundles, respectively. A bundle X 7 e with R( X;e) U is denoted by X U 7 e; its interpretation is that if an event in X has happened at a certain time t, then the time of enabling of e is determined by t U . e.g. ....

....5 Examples of composing stochastic event structures. The semantics of our process algebra is defined using stochastic event structures. A mapping [ is defined that maps each expression B onto a stochastic event structure [ B ] in a compositional way. This mapping is completely described in [2, 9]. Let us start by considering some simple examples (cf. Figure 5) According to our synchronization principle the resulting random variable of e a in Figure 5(a) equals max(U;V ) A similar reasoning applies to (b) where, for simplicity, irrelevant random variables are omitted) Finally, in (c) ....

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J-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, CTIT Ph. D-thesis series No. 96-09, 1996.

....difficulty of the design and modelling of a system whose performance is studied rapidly grows with the size and complexity of the system itself. In the last few years, this phenomenon has drawn the attention of many researchers into extending process algebras with stochastic and real time features [15, 9, 11, 3, 6, 16]. Stochastic process algebras, as they are usually called, considerably simplify the tractability of complex systems because, in this framework, systems do not need to be modelled as a whole, but as a composition of small subsystems. Another advantage is that stochastic process algebras not only ....

J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, Department of Computer Science, University of Twente, April 1996.

....difficulty of the design and modelling of a system whose performance is studied rapidly grows with the size and complexity of the system itself. In the last few years, this phenomenon has drawn the attention of many researchers into extending process algebras with stochastic and real time features [15, 9, 11, 3, 6, 16]. Stochastic process algebras, as they are usually called, considerably simplify the tractability of complex systems because, in this framework, systems do not need to be modelled as a whole, but as a composition of small subsystems. Another advantage is that stochastic process algebras not only ....

J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, Department of Computer Science, University of Twente, April 1996.

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Joost-Pieter Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, 1996.

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J.-P. Katoen (1996): Quantitative and Qualitative Extensions of Event Structures, PhD thesis, Department of Computer Science, University of Twente.

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Joost-Pieter Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, 1996.

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J.-P. Katoen (1996): Quantitative and Qualitative Extensions of Event Structures, PhD thesis, Department of Computer Science, University of Twente.

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J.-P. Katoen (1996): Quantitative and Qualitative Extensions of Event Structures, PhD thesis, Department of Computer Science, University of Twente.

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J. P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, Centre for Telematics and Information Technology, Enschede, No. 96-09, 1996.

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Joost-Pieter Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, University of Twente, 1996.

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