## A Sheaf Semantics for Petri Nets (1993)

Citations: | 2 - 0 self |

### BibTeX

@TECHREPORT{Lilius93asheaf,

author = {Johan Lilius},

title = {A Sheaf Semantics for Petri Nets},

institution = {},

year = {1993}

}

### OpenURL

### Abstract

: The semantics of Petri Nets are discussed within the "Objects are sheaves" paradigm. Transitions and places are represented as sheaves and nets are represented as diagrams of sheaves. Both an interleaving semantics, and a non-interleaving semantics are shown to arise as the limit of the sheaf diagram representing the net. This work was supported by the Information Technology Promotion Agency, Japan, as part of the R & D of Basic Technology for Future Industries "New Models of Software Architecture" project sponsored by NEDO (New Energy and Industrial Technology Developments Organization). Printing: TKK Monistamo; Otaniemi 1993 Helsinki University of Technology Phone: 90 +358--0 4511 Department of Computer Science Digital Systems Laboratory Telex: 125 161 htkk sf Otaniemi, Otakaari 1 Telefax: +358--0--465 077 SF--02150 ESPOO, FINLAND E-mail: lab@hutds.hut.fi -- 1 -- 1 Introduction Sheaf theory is a mathematical tool that has been successfully applied to the solution of difficult m...

### Citations

577 |
Petri Nets, An Introduction
- Reisig
- 1985
(Show Context)
Citation Context ...ram of sheaves and the behavior of the net to the limit of the diagram. Before we go into details, we need some definitions from Net theory and some notation. The standard reference for Net theory is =-=[8]-=-. The following is a slightly massaged definition of a Place/Transition net [7] without capacities. Definition 5 A Place/Transition net N is a quadruple hT; P; '; oi where T is the set of transitions,... |

45 | Sheaf semantics for concurrent interacting objects
- Goguen
- 1992
(Show Context)
Citation Context ... The behavior of a system is calculated by taking the limit of the diagram of its subcomponents, and colimits are used to connect systems. This paradigm was later extended to models of concurrency in =-=[4] and used -=-to give a semantics for the FOOPS language in [10]. This paper is an application of the "Objects are sheaves" paradigm as formulated in [4] to one specific model of concurrency, namely Petri... |

37 |
Categorical foundations for general systems theory
- Goguen
- 1973
(Show Context)
Citation Context ...], Gray surveys applications to complex analysis, algebraic geometry, differential equations, and category theory. Sheaf theory has also been used in a general formulation of systems theory by Goguen =-=[2, 3, 5]-=-. The basic building blocks of this categorical formulation of General Systems Theory besides sheaves are the categorical notions of diagram, limit and colimit. The behavior of a component or system i... |

20 |
A categorical approach to general systems theory
- Goguen, Ginali
- 1978
(Show Context)
Citation Context ...], Gray surveys applications to complex analysis, algebraic geometry, differential equations, and category theory. Sheaf theory has also been used in a general formulation of systems theory by Goguen =-=[2, 3, 5]-=-. The basic building blocks of this categorical formulation of General Systems Theory besides sheaves are the categorical notions of diagram, limit and colimit. The behavior of a component or system i... |

11 |
An Algebraic Semantics for Transition Systems and Logic Programming
- Corradini
- 1990
(Show Context)
Citation Context ...gle transition and three places. It is customary to assume that the functions ' and o are injective so as to rule out transitions with identical sets of input and output places. In the terminology of =-=[1] P/T nets -=-are "extensional transition systems". The following notations will be useful, where t 2 T and p 2 P . The preset or set of input places of a transition t is defined as ffl t = fp j '(t)(p)s1... |

5 |
Elementary net systems,” in Petri nets: central models and their properties
- Thiagarajan
- 1986
(Show Context)
Citation Context ...cally. To simplify the presentation we will restrict our nets so that all places have a capacity of one and all arcs have a weight of one, making the nets essentially Elementary Net (EN) systems (cf. =-=[9]-=-). When talking about EN-systems, it is customary to call places conditions, and transitions events. Elementary Net systems are essentially a modern version of Condition/Event systems (cf. [8] chapter... |

5 |
A sheaf semantics for FOOPS expressions
- WOLFRAM, GOGUEN
- 1992
(Show Context)
Citation Context ... of the diagram of its subcomponents, and colimits are used to connect systems. This paradigm was later extended to models of concurrency in [4] and used to give a semantics for the FOOPS language in =-=[10]. This pap-=-er is an application of the "Objects are sheaves" paradigm as formulated in [4] to one specific model of concurrency, namely Petri Nets. The main result of this paper is that two well known ... |

2 |
Fragments of the history of sheaf theory. Applications of Sheaves
- Gray
- 1979
(Show Context)
Citation Context ... SF--02150 ESPOO, FINLAND E-mail: lab@hutds.hut.fi -- 1 -- 1 Introduction Sheaf theory is a mathematical tool that has been successfully applied to the solution of difficult mathematical problems. In =-=[6]-=-, Gray surveys applications to complex analysis, algebraic geometry, differential equations, and category theory. Sheaf theory has also been used in a general formulation of systems theory by Goguen [... |

1 |
Place/transition systems. Petri Nets: Central Models and Their Properties
- Reisig
- 1986
(Show Context)
Citation Context ...we go into details, we need some definitions from Net theory and some notation. The standard reference for Net theory is [8]. The following is a slightly massaged definition of a Place/Transition net =-=[7]-=- without capacities. Definition 5 A Place/Transition net N is a quadruple hT; P; '; oi where T is the set of transitions, P is the set of places, and '; o : T ! [P ! N ] are the input and output weigh... |