Axiomatizing the algebra of net computations and processes:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Stanford, Calif.
1990
|
| Schriftenreihe: | Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL
90,12 |
| Schlagwörter: | |
| Abstract: | Abstract: "Descriptions of concurrent behaviors in terms of partial orderings (called nonsequential processes or simply processes in Petri net theory) have been recognized as superior when information about distribution in space, about causal dependency or about fairness must be provided. However, at least in the general case of Place/Transition (P/T) nets, the proposed models lack a suitable, general notion of sequential composition. In this paper, a new algebraic axiomatization is proposed, where, given a net N, a term algebra P[N] with two operations of parallel and sequential composition is defined. The congruence classes generated by a few simple axioms are proved isomorphic to slight refinement of classical processes Actually, P[N] is a symmetric monoidal category, parallel composition is the monoidal operation on morphisms and sequential composition is morphism composition. Besides P[N], we introduce a category S[N] containing the classical occurrence and step sequences. The term algebras of P[N] and of S[N] are in general incomparable, and thus we introduce two more categories K[N] and T[N] providing an upper and a lower bound, respectively. A simple axiom expressing the functoriality of parallel composition allows us to map K[N] to P[N] and S[N] to T[N], while commutativity of parallel composition maps K[N] to S[N] and P[N] to T[N] (see Figure 4) Morphisms of K[N] constitute a new notion of concrete net computation, while the strictly symmetric monoidal category T[N] was introduced previously by two of the authors as a new algebraic foundation for P/T nets [13]. In the context of the present paper, the morphisms of T[N] are proved isomorphic to the processes recently defined in terms of the 'swap' transformation by Best and Devillers [4]. Thus the diamond of the four categories gives a full account in algebraic terms of the relations between interleaving and partial ordering observations of P/T net computations. |
| Umfang: | 23 S. |
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| 100 | 1 | |a Degano, Pierpaolo |d 1950- |e Verfasser |0 (DE-588)115394869 |4 aut | |
| 245 | 1 | 0 | |a Axiomatizing the algebra of net computations and processes |c Pierpaolo Degano, José Meseguer, and Ugo Montanari |
| 264 | 1 | |a Stanford, Calif. |c 1990 | |
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| 490 | 1 | |a Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL |v 90,12 | |
| 520 | 3 | |a Abstract: "Descriptions of concurrent behaviors in terms of partial orderings (called nonsequential processes or simply processes in Petri net theory) have been recognized as superior when information about distribution in space, about causal dependency or about fairness must be provided. However, at least in the general case of Place/Transition (P/T) nets, the proposed models lack a suitable, general notion of sequential composition. In this paper, a new algebraic axiomatization is proposed, where, given a net N, a term algebra P[N] with two operations of parallel and sequential composition is defined. The congruence classes generated by a few simple axioms are proved isomorphic to slight refinement of classical processes | |
| 520 | 3 | |a Actually, P[N] is a symmetric monoidal category, parallel composition is the monoidal operation on morphisms and sequential composition is morphism composition. Besides P[N], we introduce a category S[N] containing the classical occurrence and step sequences. The term algebras of P[N] and of S[N] are in general incomparable, and thus we introduce two more categories K[N] and T[N] providing an upper and a lower bound, respectively. A simple axiom expressing the functoriality of parallel composition allows us to map K[N] to P[N] and S[N] to T[N], while commutativity of parallel composition maps K[N] to S[N] and P[N] to T[N] (see Figure 4) | |
| 520 | 3 | |a Morphisms of K[N] constitute a new notion of concrete net computation, while the strictly symmetric monoidal category T[N] was introduced previously by two of the authors as a new algebraic foundation for P/T nets [13]. In the context of the present paper, the morphisms of T[N] are proved isomorphic to the processes recently defined in terms of the 'swap' transformation by Best and Devillers [4]. Thus the diamond of the four categories gives a full account in algebraic terms of the relations between interleaving and partial ordering observations of P/T net computations. | |
| 650 | 4 | |a Petri nets | |
| 700 | 1 | |a Meseguer, José |e Verfasser |4 aut | |
| 700 | 1 | |a Montanari, Ugo |d 1943- |e Verfasser |0 (DE-588)134068815 |4 aut | |
| 830 | 0 | |a Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL |v 90,12 |w (DE-604)BV008930658 |9 90,12 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-005926171 | |
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| author | Degano, Pierpaolo 1950- Meseguer, José Montanari, Ugo 1943- |
| author_GND | (DE-588)115394869 (DE-588)134068815 |
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However, at least in the general case of Place/Transition (P/T) nets, the proposed models lack a suitable, general notion of sequential composition. In this paper, a new algebraic axiomatization is proposed, where, given a net N, a term algebra P[N] with two operations of parallel and sequential composition is defined. The congruence classes generated by a few simple axioms are proved isomorphic to slight refinement of classical processes</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">Actually, P[N] is a symmetric monoidal category, parallel composition is the monoidal operation on morphisms and sequential composition is morphism composition. Besides P[N], we introduce a category S[N] containing the classical occurrence and step sequences. The term algebras of P[N] and of S[N] are in general incomparable, and thus we introduce two more categories K[N] and T[N] providing an upper and a lower bound, respectively. 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| id | DE-604.BV008974619 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:29:45Z |
| institution | BVB |
| language | English |
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| physical | 23 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
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| series | Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL |
| series2 | Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL |
| spelling | Degano, Pierpaolo 1950- Verfasser (DE-588)115394869 aut Axiomatizing the algebra of net computations and processes Pierpaolo Degano, José Meseguer, and Ugo Montanari Stanford, Calif. 1990 23 S. txt rdacontent n rdamedia nc rdacarrier Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL 90,12 Abstract: "Descriptions of concurrent behaviors in terms of partial orderings (called nonsequential processes or simply processes in Petri net theory) have been recognized as superior when information about distribution in space, about causal dependency or about fairness must be provided. However, at least in the general case of Place/Transition (P/T) nets, the proposed models lack a suitable, general notion of sequential composition. In this paper, a new algebraic axiomatization is proposed, where, given a net N, a term algebra P[N] with two operations of parallel and sequential composition is defined. The congruence classes generated by a few simple axioms are proved isomorphic to slight refinement of classical processes Actually, P[N] is a symmetric monoidal category, parallel composition is the monoidal operation on morphisms and sequential composition is morphism composition. Besides P[N], we introduce a category S[N] containing the classical occurrence and step sequences. The term algebras of P[N] and of S[N] are in general incomparable, and thus we introduce two more categories K[N] and T[N] providing an upper and a lower bound, respectively. A simple axiom expressing the functoriality of parallel composition allows us to map K[N] to P[N] and S[N] to T[N], while commutativity of parallel composition maps K[N] to S[N] and P[N] to T[N] (see Figure 4) Morphisms of K[N] constitute a new notion of concrete net computation, while the strictly symmetric monoidal category T[N] was introduced previously by two of the authors as a new algebraic foundation for P/T nets [13]. In the context of the present paper, the morphisms of T[N] are proved isomorphic to the processes recently defined in terms of the 'swap' transformation by Best and Devillers [4]. Thus the diamond of the four categories gives a full account in algebraic terms of the relations between interleaving and partial ordering observations of P/T net computations. Petri nets Meseguer, José Verfasser aut Montanari, Ugo 1943- Verfasser (DE-588)134068815 aut Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL 90,12 (DE-604)BV008930658 90,12 |
| spellingShingle | Degano, Pierpaolo 1950- Meseguer, José Montanari, Ugo 1943- Axiomatizing the algebra of net computations and processes Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL Petri nets |
| title | Axiomatizing the algebra of net computations and processes |
| title_auth | Axiomatizing the algebra of net computations and processes |
| title_exact_search | Axiomatizing the algebra of net computations and processes |
| title_full | Axiomatizing the algebra of net computations and processes Pierpaolo Degano, José Meseguer, and Ugo Montanari |
| title_fullStr | Axiomatizing the algebra of net computations and processes Pierpaolo Degano, José Meseguer, and Ugo Montanari |
| title_full_unstemmed | Axiomatizing the algebra of net computations and processes Pierpaolo Degano, José Meseguer, and Ugo Montanari |
| title_short | Axiomatizing the algebra of net computations and processes |
| title_sort | axiomatizing the algebra of net computations and processes |
| topic | Petri nets |
| topic_facet | Petri nets |
| volume_link | (DE-604)BV008930658 |
| work_keys_str_mv | AT deganopierpaolo axiomatizingthealgebraofnetcomputationsandprocesses AT meseguerjose axiomatizingthealgebraofnetcomputationsandprocesses AT montanariugo axiomatizingthealgebraofnetcomputationsandprocesses |