Algebraic Net Schemes
An algebraic net scheme is a pair consisting of an algebraic specification and a net with sorted places, with transtitions which have predicate (a set of equations) and with arcs marked with terms over the specification.
An algebraic net scheme consists in a basic coloured net where colours and firing rules are represented by interpretations of terms over a given algebraic specification.
(according to [dhp91])
An algebraic net scheme is a tuple N=(SPEC,X,P,T,Pre,Post,eqns,sort) where:
- SPEC=(SO,OP,EQ) is an algebraic specification of abstract data types
- X is a family of SO-sorted variables
- P and T are the sets of places and transitions
- Pre and Post are functions which assign a set of terms with variables to every pair place/transition
- eqns is a function which associates with each transition a set of equations
- sort is a function which assigns a sort SO to every place
Algebraic High-Level Nets
Algebraic high-level nets are couples (algebraic net scheme, algebra).
An algebraic high-level net (AHL net) is a tuple (N,A) where N is an algebraic net scheme and A is a SPEC-algebra.
The semantics of an algebraic high-level net is that of the associated coloured net where the terms and equations are interpreted in the given algebra.
PAPETRI, an integrated tool for editing and analysing Petri Nets.
SANDS-COOPN, a development system to construct Concurrent Object-Oriented Petri Net specifications based upon algebraic nets.
- J. Vautherin: Un modèle algébrique, basé sur les rèseaux de Petri, pour l'ètude des systèmes parallèles [vau85]
- J. Vautherin: Paralles Systems Specifications with Colored Petri Nets and Algebraic Specifications [vau87]
- U. Hummert: Algebraische Theorie von High-Level-Netzen [hum89]
- C. Dimitrovici, U. Hummert, L. Petrucci: Semantics, Composition and Net Properties of Algebraic High-level Nets [dhp91]