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Homogeneous Equations of Algebraic Petri Nets [article]

Marvin Triebel, Jan Sürmeli
2016 arXiv   pre-print
Algebraic Petri nets are a formalism for modeling distributed systems and algorithms, describing control and data flow by combining Petri nets and algebraic specification.  ...  One way to specify correctness of an algebraic Petri net model N is to specify a linear equation E over the places of N based on term substitution, and coefficients from an abelian group G.  ...  Algebraic Petri Nets An algebraic Petri net structure consists of places P and transitions T .  ... 
arXiv:1606.05490v3 fatcat:doq5fctxejdxhf4keed34nmngy

Homogeneous Equations of Algebraic Petri Nets

Marvin Triebel, Jan Sürmeli, Marc Herbstritt
2016 International Conference on Concurrency Theory  
Algebraic Petri nets are a formalism for modeling distributed systems and algorithms, describing control and data flow by combining Petri nets and algebraic specification.  ...  One way to specify correctness of an algebraic Petri net model N is to specify a linear equation E over the places of N based on term substitution, and coefficients from an abelian group G.  ...  C O N C U R 2 0 1 6 14:12 Homogeneous Equations of Algebraic Petri Nets ▸ Definition 43 (Spanning Set).  ... 
doi:10.4230/lipics.concur.2016.14 dblp:conf/concur/TriebelS16 fatcat:hvsqmznhtngpxalnce5wvjz4zi

Piecewise linear concave dynamical systems appearing in the microscopic traffic modeling

N. Farhi, M. Goursat, J.-P. Quadrat
2011 Linear Algebra and its Applications  
The main interest of the PH equation is that we can derive macroscopic laws like the fundamental diagram from its solution.  ...  The Prigogine-Herman (PH) model [48] (kinetic model) gives the evolution of the density of particles ρ(t, x, v) as a function of t, x and v, where v is the speed of particles.  ...  Petri net dynamics Autonomous Petri nets Let us give, in minplus-times algebra, a presentation of timed continuous Petri nets with weights.  ... 
doi:10.1016/j.laa.2011.03.002 fatcat:akfhyrs5pzavriyblkls2mouna

About Dynamical Systems Appearing in the Microscopic Traffic Modeling [article]

Nadir Farhi, Maurice Goursat, Jean-Pierre Quadrat
2010 arXiv   pre-print
The dynamics of these Petri nets are well-defined and may be described by a generalized matrix with a submatrix in the standard algebra with possibly negative entries, and another submatrix in the minplus  ...  We introduce a deterministic Petri net extension where edges may have negative weights.  ...  Autonomous Petri nets We present, in min-plus-times algebra, timed continuous Petri nets with weights.  ... 
arXiv:0911.4672v2 fatcat:jrwx7lxkufac7m3sjhjxtlrckm

Page 2926 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
Since the early 1990s, the development of the Petri box calculus has shown how to define an algebra of labelled Petri nets to- gether with a corresponding process algebra to compositionally and hierarchically  ...  Indeed, the authors delineate a class of Petri net operators such that one can systemat- ically derive through the general refinement mechanism an algebra of nets with a corresponding SOS semantics and  ... 

Page 1085 of Automation and Remote Control Vol. 53, Issue 7 [page]

1992 Automation and Remote Control  
This system leads to a system of linear algebraic equations that must be “If the net is unbounded, this construction is hypothetical.  ...  These conditions are checked by analyzing at most n + m — 1] linear algebraic equations and inequalities, where n and m respectively are the number of places and the number of transitions in the Petri  ... 

Performance Evaluation of Timed Petri Nets in Dioid Algebra [chapter]

Samir Hamaci, Karim Labadi, A. Moumen
2012 Petri Nets - Manufacturing and Computer Science  
Performance Evaluation of Timed Petri Nets in Dioid Algebra Petri Nets -Manufacturing and Computer Science  ...  After recalling in Section 2 some properties of Petri nets, we present in Section 3, modeling the dynamic behavior of TEGM, which are a class of Petri nets, in dioid algebra, precisely in (min, +) algebra  ... 
doi:10.5772/48498 fatcat:5uhwbiyjkvhfrfqlzikrfbzbom

Petri Algebras [chapter]

Eric Badouel, Jules Chenou, Goulven Guillou
2005 Lecture Notes in Computer Science  
This class of nets is universal in the sense that any net associated with some Petri algebras can be simulated by a lexicographic Petri net.  ...  We identify a class of residuated commutative monoids, called Petri algebras, for which one can mimic the token game of Petri nets to define the behaviour of generalized Petri net whose flow relation and  ...  The first author thanks Nikolaos Galatos for fruitful discussions on totally ordered commutative GMV algebras. The second author was supported by a grant from the University of Douala, Cameroon.  ... 
doi:10.1007/11523468_60 fatcat:sqifufxgvzgzrc2526na5y4uhy

Page 1208 of Mathematical Reviews Vol. , Issue 83c [page]

1983 Mathematical Reviews  
Ehrich, Specifying algebraic data types by domain equations (pp. 120-129); Z. Esik, An axiomatization of regular forests in the language of algebraic theories with iteration (pp. 130-136); P.  ...  . 34-50); Miklos Bartha, An algebraic definition of attributed transformations (pp. 51-60); Franz-Josef Brandenburg, Analogies of PAL and COPY (pp. 61-70); Peter Burmeister, Quasi-equational logic for  ... 

Using linear programming in Petri net analysis

Jean B. Lasserre, Philippe Mahey
1989 Reserche operationelle  
Petri net analysis using linear algebra is based on the above équation. In the following, we consider some weighting or valuation function f: P ->• N.  ...  équation is: In fact, linear system theory is of limited help when dealing with Petri nets.  ...  vertices of the dual feasible set.  ... 
doi:10.1051/ro/1989230100431 fatcat:vgtzehczmnapzgdy6dsntwmffu

Integrated Analysis of Concurrent Distributed Systems using Markovian Process Algebra [chapter]

Marco Bernardo, Lorenzo Donatiello, Roberto Gorrieri
1995 IFIP Advances in Information and Communication Technology  
a homogeneous continuous time Markov chain (HCTMC), and a distributed model represented by a generalized stochastic Petri net (GSPN) [9] .  ...  of the stochastic process algebra into a generalized stochastic Petri net (GSPN), giving a distributed representation of the same concurrent system.  ... 
doi:10.1007/978-0-387-34878-0_38 fatcat:lbbhxtqa3nednkagjdhbmuchmm

OPTIMAL CONTROL SYNTHESIS IN INTERVAL DESCRIPTOR SYSTEMS APPLICATION TO TIME STREAM EVENT GRAPHS

Philippe Declerck, Mohamed Khalid Didi Alaoui
2005 IFAC Proceedings Volumes  
A motivation for the current study is the modelling of Time Petri nets like Time Stream Petri Nets and P-time Petri nets which extend Timed Petri Nets and generalize the semantic of its synchronization  ...  This paper presents a new class of model in the field of topical algebra whose time evolution belongs to intervals.  ...  Among these PNs, we can quote P-time Petri nets (P-time PNs), Time stream Petri nets (Time Stream PNs),.... which extend the application field of Timed Event Graphs.  ... 
doi:10.3182/20050703-6-cz-1902.00287 fatcat:dkgqdwg6j5ca5n5ifgd3acxvte

Timed-event graphs with multipliers and homogeneous min-plus systems

G. Cohen, S. Gaubert, J.P. Quadrat
1998 IEEE Transactions on Automatic Control  
Abstract| We study uid analogues of a subclass of Petri nets, called Fluid Timed Event Graphs with Multipliers, which are a timed extension of weighted T-Systems studied in the Petri Net literature.  ...  A subclass of dynamical systems in this algebra, which have a property of homogeneity, can be reduced to standard min-plus linear systems after a change of counting units.  ...  Recurrent Equations of Timed Event Graphs with Multipliers We begin by recalling the usual de nition of Timed Petri Nets and Event Graphs.  ... 
doi:10.1109/9.718621 fatcat:66jf33pgprag5kimpobo4y34fy

Page 4901 of Mathematical Reviews Vol. , Issue 88i [page]

1988 Mathematical Reviews  
of problems related to Petri nets.  ...  Advances in Petri nets 1987 (Oxford, 1986), 45-72, Lecture Notes in Comput. Sci., 266, Springer, Berlin-New York, 1987.  ... 

ON VERIFICATION OF FORMAL MODELS OF COMPLEX SYSTEMS

A. A.M. Smyrin, E.A. Lukyanova
2018 The Turkish Online Journal of Design Art and Communication  
The paper considers the application of the theory of Diophantine equations for the analysis of formal models of complex systems, in particular, Petri component models.  ...  After analyzing the work of the CN-net, taking into account the work of the component-place, we come to the conclusion that all the listed properties of the constructed model are preserved.  ...  In this case, when verifying Petri component models, it is necessary to solve both systems of linear homogeneous Diophantine equations (SLHDE), and systems of linear inhomogeneous Diophantine equations  ... 
doi:10.7456/1080mse/141 fatcat:xopbcpk45rfdrjiv2kklfmpgby
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