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Homogeneous Equations of Algebraic Petri Nets
[article]

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 . ...

##
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Homogeneous Equations of Algebraic Petri Nets

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). ...

##
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Piecewise linear concave dynamical systems appearing in the microscopic traffic modeling

2011
*
Linear Algebra and its Applications
*

The main interest

doi:10.1016/j.laa.2011.03.002
fatcat:akfhyrs5pzavriyblkls2mouna
*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. ...##
###
About Dynamical Systems Appearing in the Microscopic Traffic Modeling
[article]

2010
*
arXiv
*
pre-print

The dynamics

arXiv:0911.4672v2
fatcat:jrwx7lxkufac7m3sjhjxtlrckm
*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. ...##
###
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]

2012
*
Petri Nets - Manufacturing and Computer Science
*

Performance Evaluation

doi:10.5772/48498
fatcat:5uhwbiyjkvhfrfqlzikrfbzbom
*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*...##
###
Petri Algebras
[chapter]

2005
*
Lecture Notes in Computer Science
*

This class

doi:10.1007/11523468_60
fatcat:sqifufxgvzgzrc2526na5y4uhy
*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. ...##
###
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

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. ...

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

1995
*
IFIP Advances in Information and Communication Technology
*

a

doi:10.1007/978-0-387-34878-0_38
fatcat:lbbhxtqa3nednkagjdhbmuchmm
*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. ...##
###
OPTIMAL CONTROL SYNTHESIS IN INTERVAL DESCRIPTOR SYSTEMS APPLICATION TO TIME STREAM EVENT GRAPHS

2005
*
IFAC Proceedings Volumes
*

A motivation for the current study is the modelling

doi:10.3182/20050703-6-cz-1902.00287
fatcat:dkgqdwg6j5ca5n5ifgd3acxvte
*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. ...##
###
Timed-event graphs with multipliers and homogeneous min-plus systems

1998
*
IEEE Transactions on Automatic Control
*

Abstract| We study uid analogues

doi:10.1109/9.718621
fatcat:66jf33pgprag5kimpobo4y34fy
*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. ...##
###
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. ...

##
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ON VERIFICATION OF FORMAL MODELS OF COMPLEX SYSTEMS

2018
*
The Turkish Online Journal of Design Art and Communication
*

The paper considers the application

doi:10.7456/1080mse/141
fatcat:xopbcpk45rfdrjiv2kklfmpgby
*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*...
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