M. Nielsen, G. Rozenberg, and P. Thiagarajan. Elementary transition systems. TCS, 96:3--33, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....system = SN(S) with case graph isomorphic to S, i.e. CG(N ) S. This result was among the first two constructive solutions to the problem of synthesis of a distributed realization SN(S) of a given abstract behaviour S. The other solution was provided earlier by Zielonka, see [13] Later, see [10], this result was strengthened, and the correspondence was revealed to take the form of an adjunction between the category ETS of elementary transition systems, and a category ENS of elementary net systems. More precisely, Nielsen et al. showed that the process of synthesizing an elementary net ....

Nielsen, M., Rozenberg, G. and P.S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, 96, 1, pp.: 3--32, 1992.

....properties. It includes state assignment by solving the Complete State Coding problem [4, 5] coupled with logic minimization and speedindependent technology mapping to a target library [51, 3, 25] Related approaches can be also found in [56, 1, 30] Methods based on the theory of state regions [12, 40, 6] provide an ecient framework for the solution of the above tasks, as they allow us to treat uniformly large sets of markings. State regions are also well suited for symbolic manipulation. These methods are discussed in Section 8. 2 Basic Notions Let N = hP; T; F; m 0 i be a Petri net (PN) 37] ....

....event insertion Regions, Excitation Regions and Switching Regions. Let r be a subset of the states of an SG r S. If s 62 r and s 2 r, then we say that transition s enters r. If s 2 r and s 62 r, then transition s exits r. Otherwise, transition s does not cross r. A region [40] is a subset of states with which all transitions labeled with the same event e have exactly the same entry exit relation. This relation will become the predecessor successor relation in the Petri net. Let us consider the SG shown in Figure 32. The set of states r1 is a region, since all ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, 96:3-33, 1992.

....regions in a TS directly correspond to places in an STG with a reachability graph bisimilar to the TS. This allows us to reconstruct an STG for the TS with all CSC conflicts resolved an option much more suitable for the designer than viewing the TS. The concept of regions was presented in [26], and further applied to efficient generation of Petri nets and signal transition graphs from state based models [10] The practical implementation of our method uses symbolic BDD representation of the main objects in the insertion procedure, as described in [29] It has enabled us to solve CSC ....

....implementation aspects. Experiments (in comparison with other tools) are discussed in Section X. The conclusions are drawn in Section XI. II. STATE AND EVENT MODELS A. Transition Systems A transition system (TS) might be viewed as an abstract state graph, and is formally defined as a quadruple [26] , where is a finite nonempty set of states, is a set of events, is a transition relation, and is an initial state. The elements of are called the transitions of TS and will be often denoted by instead of . The initial state will often be omitted in the following if it is not important. The ....

[Article contains additional citation context not shown here]

M. Nielsen, G. Rozenberg, and P. S. Thiagarajan, "Elementary transition systems," Theor. Comput. Sci., vol. 96, pp. 3--33, 1992.

....level, the level of transition systems. It has been stressed in [7] that the class of Petri nets normally used for hardware synthesis is restricted to 1 safe nets. Such nets are closely related to elementary nets , whose transition systems have been studied in pioneering work of Nielsen et al. [8]. This work presented an elegant idea of a region, that is a subset of transition system states which can be associated with a place in the synthesised Petri net. Further studies of Mukund [9] Badouel et al. 11] and Bernardinello et al. 10] have developed other versions of regions to deal with ....

....resets them to False. While self loops are intuitively obvious at the syntactic level, it often happens that a behaviour of that sort is easier to capture at the transition system level [1, 2] As a result, certain transition systems do not satisfy the elementarity axioms of Nielsen et al. [8] precisely for the reasons of being associated with non pure nets. In the view of the above practical motivation, this paper is aimed at theoretical extension of the class of elementary nets to semi elementary nets . Similarly, we formulate axioms for transition systems so as to check their ....

[Article contains additional citation context not shown here]

M. Nielsen, G. Rozenberg and P.S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, Vol. 96, pp. 3 - 33, 1992.

....147, 21, 144, 19, 24, 37] culminating in the recent thesis of Cattani. We summarise some of the most important results in Sec. 2.3. 2. 1 Models for Concurrency The work reported in the chapter [146] was initiated by work of Winskel [140] followed by work of Nielsen, Rozenberg and Thiagarajan [99] and Sassone et al. 119, 118] Focus of this work was to find formal relationships between some of the many di#erent models existing in the literature, describing their common structure. One of the aims declared in [146] is to set the scene for a formal classification of models for concurrency, ....

Mogens Nielsen, G. Rozenberg, and P. S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, 96:3--33, 1992.

.... Net Systems (see [Rozenberg Thiagarajan 1986, Rozenberg 1987, Thiagarajan 1987] whose elements are simple and highly readable models, and on the other it is based on some nice mathematical properties of that class, allowing us to generate a large class of behaviours from those models (see [Nielsen et al. 1992]) Moreover we will show that some interesting features proposed in the literature [Ellis Keddara 1993] to enhance the usability of Workflow Management Systems can be easily embedded within it. This paper is devoted to introducing the basic features of the Workflow Model of MWMS. In the next ....

....and on Elementary Transition (ET) Systems. Our theoretical framework makes reference to the work initiated by G. Rozenberg and P. S. Thiagarajan on EN Systems, to the further developments the same authors, together with M. Nielsen, dedicated to the co reflection between EN Systems and ET Systems [Nielsen et al. 1992], on the basis of the theory of Partial 2Structures developed by A. Ehrenfeucht and G. Rozenberg [Ehrenfeucht Rozenberg 1990a, b] and finally to the research two of the authors of this paper are doing together with L. Bernardinello and S. Vigna on the structural properties of Elementary ....

[Article contains additional citation context not shown here]

Nielsen, M., Rozenberg, G., Thiagarajan, P.S. Elementary Transition Systems, TCS 96/1, 1992.

....a task flow graph for an Ada program. No efficient technique for deriving a PN is used. We think that our technique for synthesis of PNs can provide an efficient machinery for the analysis of concurrent programs. 1. 3 Related Work The concept of regions was introduced in [24] and developed in [42], 3] 6] 21] 40] as a fundamental link between state based and event based specifications. A comprehensive review of the theory of regions can be found in [4] State in safe Petri Nets is distributed among places: Each state is a set of marked places, and each place is marked in a set of ....

....all statements in Sections 3 and 4 (except for Theorem 3.3 which is fully proven) are only given with only informal proofs. The details can be found in the technical report [17] which is the extended version of this paper. 2MODELS 2. 1 Transition Systems A transition system (TS) is a quadruple [42] TS = S, E, T, s in ) where S is a nonempty set of states, E is a set of events, T # S # E # S is a transition relation, and s in is an initial state. The elements of T are called the transitions of TS and will be often denoted by ss e # # instead of (s, e, s#) A transition system is finite ....

[Article contains additional citation context not shown here]

# M. Nielsen, G. Rozenberg, and P.S. Thiagarajan, "Elementary Transition Systems," Theoretical Computer Science, vol. 96, pp. 3-33, 1992.

....regions. A region in a TS is a set of states corresponding to a place in a PN. Transitions in and out of this set of states mimic the PN firing behavior (which un marks predecessor places and marks successor places of a transition) The notion of regions was introduced in [15] and developed in [1, 3, 12, 24, 27]) as a basic intermediate object between state based and event basedspecifications. This papers have been limited with the so called class of elementary TSs which allow for PN representation with uniquely labeled transitions (each event has only one occurrence in the PN) We have shown [10] how ....

....is not limited to elementary TSs, which are quite restricted; we can handle the full class of TSs by means of label splitting. In the following sections we will briefly and informally review the theory behind petrify. 3. 1 Basic models: Petri Nets and Transition Systems Informally, a TS ([27]) can be represented as an arc labeled directed graph. A simple example of a TS is shown in Figure 2 (the left part) A TS is called deterministic if for each state s and each label a there can be at most one state s 0 such that s a s 0 . A TS is called commutative if whenever two actions ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, 96:3--33, 1992.

....morphism is a partial finitary function, and vice versa. Moreover, #b = # b # # B # #b # = b in this case. ## Nielsen et al. used transposes of partial functions to establish an adjunction between the category of elementary nets and the category of elementary transition systems, see [10]. They also underly major part of the material presented in [15] Thus, flat meet preserving morphisms have already found their way to categorical investigations of Petri nets. It seems, that the more general class of meet preserving additive functions has not yet been used in the area. The next ....

....Then M ## is closed with respect to binary meets, so that its atoms are irreducible (Lemma 2.6) This makes the decomposition unique (Lemma 2. 5) The class of meet preserving morphisms is wider than the class of commutative monoid homomorphisms underlying the results of Nielsen et al. [10]. Nevertheless, to insist that all binary meets be preserved is too stringent a condition to establish finite completeness of many interesting categories of Petri nets. Luckily, in the proof of Prop. 3.4 it is not important that the morphisms being equalized preserve all binary meets. What really ....

[Article contains additional citation context not shown here]

M. Nielsen, G. Rozenberg, and P. S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, vol. 96, pp. 3--33, 1992.

....be familiar with Petri nets, a formalism used to specify concurrent systems. We refer to [9] for a general tutorial on Petri nets. Lazy transition systems and lazy state graphs were introduced in more detail in [3] 2. 1 Transition Systems and State Graphs A transition system (TS) is a quadruple [13] TS = #S;E;T;s in #,whereSis a non empty set of states, E is a set of events, T # S#E#S is a transition relation, and s in is an initial state. The elements of T are called the transitions of TS and will be often denoted by s e s 0 instead of #s; e; s 0 #. State Graphs are binary ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, 96:3--33, 1992.

....Pool and Signal are compared in Figure 2. Apart from the new classification scheme, the major contributions of this paper are following: i) The construction of a Petri net specification of the two slot Signal type ACM using the synthesis methodology based on theory of regions in state graphs [14, 13]. The promotion of this methodology into the practice of designing protocols and asynchronous circuits is crucial in paving the way for the new generation of CAD tools capable of synthesising concurrent systems in general. ii) The implementation of the Petri net model as an asynchronous control ....

....in [13] Informally, such synthesis is a decomposition, or distribution, of global states of the state graph into local states of the system that can be associated with places in the Petri net. More formally, synthesis is based on the concept of regions in transition systems, originating from [14], and regions have one to one correspondence to places in the synthesised net. A region is a subset of states in which all arcs labelled with the same event e have exactly the same exit entry internal relationship. Depending on this relation to a particular event e a region r is called a preregion ....

Nielsen, M., Rozenberg, G. and P.S. Thiagarajan, "Elementary transition systems", Theoretical Computer Science, Vol. 96, pp. 3-33, 1992.

....systems (called respectively TSENIapost and TSENI transition systems) Keywords: causality partial order theory of concurrency, analysis and synthesis, structure and behaviour of nets. 1 Introduction Elementary Net Systems with Inhibitor Arcs are an extension of the Elementary Net Systems of [6], where in addition to the flow relation there is an inhibitor relation between some conditions and events. An example of such a net is shown in figure 1(a) The meaning of all the elements of N is standard except for the inhibitor arc (with the small circle at the end) between condition b 4 and ....

....of TS . The first asserts that event e appearing in definition 1 is always unique. Intuitively, this corresponds to the property of Petri nets that the sets of tokens consumed by concurrently executed events are disjoint. The second re establishes some of the properties of regions formulated in [6], for the Elementary Transition Systems, and re proved for the TSENI transition systems in [7] They hold for the TSENI apost transition systems as well. Proposition 3. There exists exactly one event e 2 u which satisfies definition 1(1) or 1(2) ut Synthesis of Net Systems with Inhibitor Arcs ....

[Article contains additional citation context not shown here]

Nielsen M., Rozenberg G., Thiagarajan P.S.: Elementary transition systems. Theoretical Computer Science 96 (1992), 3-33.

....M that consist of all maximal elements of Q only. 2. 3 Comparison with elementary transition systems The theory of concrete asynchronous systems subsumes, in the sense discussed below, the theory of elementary transition systems developed by Ehrenfeucht and Rozenberg, and their followers, e.g. cf. [5,11]. We believe that the results presented below should extend from elementary transition systems to the category of asynchronous systems used for synthesis by Winskel and Nielsen, see [14] A region R in a transition system S = #S, s, #, T # is a set of states, R # S, such that given a ....

M. Nielsen, G. Rozenberg, and P. S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, vol. 96: pp. 3--33, 1992.

....systems described above. Indeed, the notion proposed by Winskel does satisfy the above criterion. Some years later another class of morphisms was distinguished in an attempt to describe a coreflection between a category of elementary net systems and a category of elementary transition systems, cf. [11]. The morphisms introduced by Nielsen et al. form a subclass of Winskel morphisms (well, not quite, this is the price to pay for disallowing isolated places in nets) As such they also satisfy the criterion. The existence of the case graph functor prompts a natural question. Namely, is it ....

....Conversely, the regions of an elementary transition system taken as places provide a simple synthesis of a net. This construction was generalized later in various ways. From our point of view it is important that some of these generalizations attempted to make the constructions functorial, cf. [11, 6]. Thus, implicitly, the idea was to synthesize not only Petri nets from transition systems, but also Petri net morphisms from morphisms of the underlying transition systems. So far, all functors were based on the idea that all regions should become places of the net constructed. The nets ....

[Article contains additional citation context not shown here]

M. Nielsen, G. Rozenberg, and P. S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, vol. 96: pp. 3--33, 1992.

....if the original actions were fairly complex, and the overhead associated with function calls is unacceptable for the application 9 . Here we only summarize the basic results of the theory of regions, on which the optimization algorithm is based, and we refer the interested reader to [13, 8]. 3.1 S graphs and Petri Nets APN [14, 12] is a 4 tuple (P; T; F; m 0 ) in which P is a set of places, T is a set of transitions, and F (T Theta P ) P Theta T ) is the flow relation (P; T; F is a bipartite directed graph) and m 0 is the initial marking. A marking is a multi set of places. ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, 96:3--33, 1992.

....be familiar with Petri nets, a formalism used to specify concurrent systems. We refer to [9] for a general tutorial on Petri nets. Lazy transition systems and lazy state graphs were introduced in more detail in [3] 2. 1 Transition Systems and State Graphs A transition system (TS) is a quadruple [13] TS = S;E;T;s in ) where S is a non empty set of states, E is a set of events, T ae S Theta E Theta S is a transition relation, and s in is an initial state. The elements of T are called the transitions of TS and will be often denoted by s e s 0 instead of (s; e; s 0 ) State Graphs ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, 96:3--33, 1992.

....and F graphs. Moreover we discuss the relation to classical elementary net systems. The behavior and realization constructions we have introduced are compatible with corresponding constructions for elementary net systems (with initial state) and elementary transition systems in the sense of [NRT92] Keywords: place transition nets, elementary nets, uniform approach, realization problem, category theory 1 Introduction Petri nets are the most common approach to model concurrent and distributed systems within the true concurrency paradigm. Concurrency is considered to be a primitive ....

....and arcs that represent the ring of enabled transitions. On the other hand it is useful to characterize those graphs which realize the behavior of Petri nets. This realization problem was solved for elementary transition system, a restricted kind of graphs, yielding elementary net systems in [NRT92] The behavior and realization construction have been given as adjoint functors between the corresponding categories. In this paper we take the general idea of [NRT92] but consider Petri nets without initial state. We use category theory to de ne an abstract notion of Petri nets based on a ....

[Article contains additional citation context not shown here]

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan. Elementary transition systems. TCS, 96:3-33, 1992.

....concurrency, and conflict could mean. Fortunately, there is a fairly well understood construction, the so called regional construction, by which one can manufacture places (of a Petri net) out of concurrency models which have a natural transition relation associated with them. See, e.g. ER] [NRT], WN] HKT1] M] Definition 4.1 Let ES = E; C; be an L event structure. A region of ES is a function r : C [ E N [ N Theta N) satisfying the following conditions. 1) 8c 2 C: r(c) 2 N and 8e 2 E: r(e) 2 N Theta N. For e 2 E we write r(e) r e; e r ) 2) c u ) r(c) P ....

Nielsen, M., Rozenberg, G., and Thiagarajan, P.S., (1992), Elementary transition systems, Theoretical Computer Science 96, 3-33. 46

No context found.

Nielsen, M., G. Rozenberg, and P. S. Thiagarajan (1992). Elementary transition systems. Theoretical Computer Science 96.

No context found.

M. Nielsen, G. Rozenberg, and P. Thiagarajan. Elementary transition systems. TCS, 96:3--33, 1992.

No context found.

M. Nielsen, G. Rozenburg, and P.S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, 96, 3--33, 1992. (p 22)

No context found.

M. Nielsen, G. Rozenberg, and P. S. Thiagarajan. Elementary transition systems. Theoretical Computer Science, vol. 96: pp. 3--33, 1992.

No context found.

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan. Elementary transition systems. TCS, 96:3--33, 1992.

No context found.

M. Nielsen, G. Rozenberg & P.S. Thiagarajan (1992): Elementary transition systems. Theoretical Computer Science 96, pp. 3--33.

No context found.

Nielsen, M., Rozenberg, G., Thiagarajan, P.S.: Elementary transition systems. Theoretical Comp. Sci. 96/1 (1992) 3--33

First 50 documents  Next 50

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