Polynomial Sufficient Conditions of Well-Behavedness and Home Markings in Subclasses of Weighted Petri Nets

2014 ◽  
Vol 13 (4s) ◽  
pp. 1-25 ◽  
Author(s):  
Thomas Hujsa ◽  
Jean-Marc Delosme ◽  
Alix Munier-Kordon
Keyword(s):  
Petri Nets ◽  
Sufficient Conditions

Algorithms of reduced complexity to design control sequences for untimed Petri nets in varying and uncertain environments

2018 ◽  
Vol 232 (6) ◽  
pp. 638-651
Author(s):  
Dimitri Lefebvre
Keyword(s):  
Petri Nets ◽  
Flexible Manufacturing ◽  
Manufacturing Systems ◽  
Discrete Event ◽  
Sufficient Conditions ◽  
Reference Value ◽  
Computational Effort ◽  
Scheduling Problems ◽  
Reachability Graph ◽  
Control Sequences

Petri nets have been widely used for the modelling, analysis, control and optimization of discrete event systems with shared resources in the domains of engineering. This article concerns the design of control sequences for such systems modelled with untimed Petri nets. The aim of the controller is to incrementally compute sequences of transition firings with minimal size. Such sequences aim to move the marking from an initial value to a reference value. The resulting trajectory must avoid some forbidden markings and limit as possible the exploration of non-promising branches. For this purpose, the approach explores a small part of the reachability graph in the neighbourhood of the current marking. Then from the explored markings, it estimates a distance to the reference. The main contributions are (a) to reduce the explored part of the reachability graph according to a double limitation in breadth and in depth in order to provide solutions with a low computational effort; (b) to provide conditions to ensure the converge and optimality of the proposed algorithms and derive necessary and sufficient conditions for reachability; and (c) to include the firing sequence design in a global control schema suitable for reactive scheduling problems in uncertain and perturbed environments. The main application concerns deadlock-free scheduling problems in the domain of flexible manufacturing systems, but the approach is also applicable for systems in computer science and transportation.

scholarly journals PATH DECOMPOSITION AND SEMILINEARITY OF PETRI NETS

2009 ◽  
Vol 20 (04) ◽  
pp. 581-596 ◽  
Author(s):  
HSU-CHUN YEN
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Sufficient Conditions ◽  
Formal Languages ◽  
Path Decomposition ◽  
Reachability Sets ◽  
Reachability Set

Semilinearity plays a key role not only in formal languages but also in the study of Petri nets. Although the reachability set of a Petri net may not be semilinear in general, there are a wide variety of subclasses of Petri nets which enjoy having semilinear reachability sets. In this paper, we develop sufficient conditions for Petri nets under which semilinearity is guaranteed. Our approach, based on the idea of path decomposition, can be used for consolidating several existing semilinearity results as well as for deriving new results all under the same framework.

scholarly journals Sufficient Conditions and Sensor Placement for Structural Fault Diagnosis in a class of Timed Continuous Petri Nets

2018 ◽  
Vol 51 (13) ◽  
pp. 61-66
Author(s):  
R. Casas-Carrillo ◽  
O. Begovich ◽  
J. Ruiz-León ◽  
A. Ramírez-Treviño
Keyword(s):  
Fault Diagnosis ◽  
Petri Nets ◽  
Sensor Placement ◽  
Sufficient Conditions ◽  
Continuous Petri Nets

Liveness and boundedness analysis of Petri net synthesis

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
CHUANLIANG XIA
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Manufacturing System ◽  
Flexible Manufacturing System ◽  
Dynamic Properties ◽  
Synthesis Method ◽  
Sufficient Conditions ◽  
Sufficient And Necessary Conditions ◽  
Petri Net Synthesis

We provide motivation for and then study the synthesis of Petri nets. Synthesis can avoid the state exploration problem by guaranteeing correctness for the Petri net. We propose conditions to be imposed on a synthesis shared pb-type subnet for systems specified in Petri nets that ensure the preservation of the liveness and boundedness structural properties. Specifically, we propose a group of sufficient conditions, or both sufficient and necessary conditions, for liveness preservation and boundedness preservation. Possible applications of this synthesis method are illustrated through an example in the form of a flexible manufacturing system. These results are useful for studying the static and dynamic properties of Petri nets for analysing the properties of large complex systems.

Sufficient conditions for loop resource subsets to derive strict minimal siphons in class of Petri nets

2014 ◽  
Vol 50 (1) ◽  
pp. 25-27 ◽  
Author(s):  
Miao Liu ◽  
ShouGuang Wang ◽  
Zhiwu Li
Keyword(s):  
Petri Nets ◽  
Sufficient Conditions

scholarly journals An effective fixpoint semantics for linear logic programs

2001 ◽  
Vol 2 (1) ◽  
pp. 85-122 ◽  
Author(s):  
MARCO BOZZANO ◽  
GIORGIO DELZANNO ◽  
MAURIZIO MARTELLI
Keyword(s):  
Logic Programming ◽  
Petri Nets ◽  
Abstract Interpretation ◽  
Theoretical Foundation ◽  
Linear Logic ◽  
Sufficient Conditions ◽  
Logic Programs ◽  
Bottom Up ◽  
Interesting Class ◽  
Fixpoint Semantics

In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of TP working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming (Minker et al., 1991). Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete (Cousot & Cousot, 1977; Giacobazzi & Ranzato, 1997) for an interesting class of LO programs encoding Petri Nets.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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