M. A. Bednarczyk and A. M. Borzyszkowski. Concurrent realizations of reactive systems. In P. R. M. Hofmann, D. Pavlovic, ed., Proc. Category Theory in Computer Science, 8th Conf., Edinburgh, vol. 29 of Electronic Notes in Theoretical Computer Science, pp. 1--19. Elsevier, 1999. Home/Search Document Details and Download
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General Morphisms of Petri Nets (Extended Abstract) - Bednarczyk, al. (1999) (Correct)
....of general Petri nets and their labelled counterparts are shown to admit products. Also, there are enough general morphisms to make the construction of a labelled state machine out of a transition system functorial. This simple observation has important consequences. In a companion paper, see [4], the authors show how the notions and the results presented here can be used to develop a functorial synthesis procedure for a wide class of concurrent behaviours. This procedure works for a class of asynchronous systems, cf. 13, 2] namely those which can be presented as rigid or mixed product ....
....here can be used to develop a functorial synthesis procedure for a wide class of concurrent behaviours. This procedure works for a class of asynchronous systems, cf. 13, 2] namely those which can be presented as rigid or mixed product of (sequential) transition systems, see [7, 16, 10] In [4] we show that the rigid product of Petri net realizations of a family of transition systems is a realization of the rigid product of the family. Thus, in the light of the results presented here, it is indeed su#cient to provide just a functorial realization of sequential systems. The full version ....
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M. A. Bednarczyk and A. M. Borzyszkowski. Concurrent realizations of reactive systems, 1999. Submitted.
On Concurrent Realization of Reactive Systems - And Their Morphisms Self-citation (Bednarczyk Borzyszkowski) (Correct)
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M. A. Bednarczyk and A. M. Borzyszkowski. Concurrent realizations of reactive systems. In P. R. M. Hofmann, D. Pavlovic, ed., Proc. Category Theory in Computer Science, 8th Conf., Edinburgh, vol. 29 of Electronic Notes in Theoretical Computer Science, pp. 1--19. Elsevier, 1999.
Finite Completeness of Categories of Petri Nets - Bednarczyk, Borzyszkowski, Somla (2000) Self-citation (Bednarczyk Borzyszkowski) (Correct)
....in which markings are elements of an arbitrary monoid. Here, we are only concerned with Petri nets over free monoids. Let us motivate the work by explaining our reasons for getting involved in the subject. Other potential applications of limits other than products are indicated in Section 7. In [3] the first two authors describe a method to synthesize a labelled 1 safe Petri net as an asynchronous realization of a concurrent behaviour described as an asynchronous system, cf. 1, 11] In [8] Morin introduced a class of good asynchronous systems, which he calls concrete. Namely, an ....
....in [2] and rigid products were shown to exist. In fact, rigid morphisms were identified there as a subclass of morphisms more general than those introduced and studied by Winskel. The same generalization, although for a di#erent purpose, was investigated earlier by Vogler, see [12] Finally, in [3], a notion of labelled 1 safe Petri net realizing behavior described as an asynchronous system was proposed. The crucial result there, cf. 3, Theorem 2.13] says that the rigid product of Petri nets, each realizing a given asynchronous system, is a realization of the rigid product of these ....
[Article contains additional citation context not shown here]
M. A. Bednarczyk and A. M. Borzyszkowski. Concurrent realizations of reactive systems. In M. Hofmann, ed., Proc. Category Theory in Computer Science, Edinburgh, vol. 29 of Electronic Notes in Theoretical Computer Science, pp. 1--19. Elsevier, 1999.
Equalizing Morphisms of Petri Nets - Bednarczyk, Borzyszkowski, Somla (1999) Self-citation (Bednarczyk Borzyszkowski) (Correct)
....workpackage within the CRIT 2 project funded by ESPRIT and INCO programmes, and by State Committee for Scientific Research grants 8 T11C 018 11 and 8 T11C 037 16 1 Introduction Let us start, by explaining why have we got interested in the problem of completeness of categories of Petri nets. In [2] the first two authors describe a method to synthesize a labelled 1safe Petri net to realize a given asynchronous system, see [7, 1] To explain our interest in completeness we present the main ideas underlying the construction in terms of the notions and terminology introduced in [2] Most of ....
....nets. In [2] the first two authors describe a method to synthesize a labelled 1safe Petri net to realize a given asynchronous system, see [7, 1] To explain our interest in completeness we present the main ideas underlying the construction in terms of the notions and terminology introduced in [2]. Most of these notions are irrelevant for the purpose of this paper and therefore we refrain from providing their formal definitions 1 . First, in [5] Morin characterized the class of good asynchronous systems. Namely, a good asynchronous system, which he calls concrete, is the one that arises ....
M. A. Bednarczyk and A. M. Borzyszkowski. Concurrent realizations of reactive systems. In Proc. CTCS '99. Elsevier, 1999.
Equalizing Morphisms of Petri Nets (Extended Abstract) - Bednarczyk, al. Self-citation (Bednarczyk) (Correct)
....showed that Petri nets admit finite products, with the empty net being a terminal object. He also showed general Petri nets do not admit coproducts, whereas coproducts of 1 safe nets always exist. It seems, though, that nobody has investigated the existence of other kinds of limits or colimits. In [3] the first two authors describe a method to synthesize a labelled 1 safe Petri net to realize a given asynchronous systems, a model introduced indpendently by Bednarczyk and Shields, cf. 1] and [9] To explain our interest in completeness let us present the main ideas of [3] in terms of the ....
....limits or colimits. In [3] the first two authors describe a method to synthesize a labelled 1 safe Petri net to realize a given asynchronous systems, a model introduced indpendently by Bednarczyk and Shields, cf. 1] and [9] To explain our interest in completeness let us present the main ideas of [3] in terms of the notions and terminology introduced there. Most of these are irrelevant for the purpose of this paper and therefore we refrain from providing their formal definitions. The interested reader is asked to consult the original paper available at http: www.ipipan.gda.pl. # Partially ....
[Article contains additional citation context not shown here]
M. A. Bednarczyk and A. M. Borzyszkowski. Concurrent realizations of reactive systems. In Proc. CTCS '99, Edinburgh, pp.:1-19, 1999. To appear in ENTCS.
General Morphisms of Petri Nets - Bednarczyk, Borzyszkowski (1999) (2 citations) Self-citation (Bednarczyk Borzyszkowski) (Correct)
....nets are shown to admit products. Labelled general Petri nets admit rigid products. 7 Also, there are enough general morphisms to make the construction of a labelled state machine out of a transition system functorial. This simple observation has important consequences. In a companion paper, see [3], the authors show how the notions and the results presented here can be used to develop a functorial synthesis procedure for a wide class of concurrent behaviours. This procedure works for a class of asynchronous systems, cf. 12, 2] namely those which can be presented as rigid or mixed product ....
....here can be used to develop a functorial synthesis procedure for a wide class of concurrent behaviours. This procedure works for a class of asynchronous systems, cf. 12, 2] namely those which can be presented as rigid or mixed product of (sequential) transition systems, see [6, 15, 9] In [3] we show that the rigid product of Petri net realizations of a family of transition systems is a realization of the rigid product of the family. Thus, in the light of the results presented here, it is indeed su#cient to provide just a functorial realization of sequential systems. 1.1 ....
[Article contains additional citation context not shown here]
M. A. Bednarczyk and A. M. Borzyszkowski. Concurrent realizations of reactive systems, 1999. Submitted, Available as ftp://ftp.ipipan.gda.pl/andrzej/papers/concur.ps.gz.
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