Boolean Petri Nets

Kansal, Sangita; Acharya, Mukti; Singh, Gajendra Pratap

doi:10.5772/50354

Cited by 12 publications

(4 citation statements)

References 6 publications

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“…There are several types of Petri net to deal with a different system like Boolean Petri nets, Colored Petri net, Fuzzy Petri net, Timed Petri net etc. (Kansal et al, 2010(Kansal et al, , 2012(Kansal et al, and 2015Jenson and Rozenberg, 2012;Rosen and Krithivasan, 2012;Gupta et al, 2019a). Previously in (Kansal et al, 2011b), characterization of a specific class in Petri nets is being discussed which are known as Boolean Petri net (BPN).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we propose the structure of some forbidden subnets which hinders any 1-safe Petri net to be a CBPN. These forbidden digraphs interrupt in the generation of all the binary -vectors exactly once in its reachability tree as its marking vector (Pastor et al, 1994;Kansal et al, 2012). Petri net modeling has other applications too, like it can behave as a recommender system or can be modeled for many biological networks which can be proven very helpful to study the complex biological networks or disease networks (Kumar et al, 2018;Gupta et al, 2019b;Singh and Gupta, 2019;.…”

Section: Introductionmentioning

confidence: 99%

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Existence of Forbidden Digraphs for Crisp Boolean Petri Nets

Singh¹,

Singh²,

Jha³

2019

Int J Math, Eng, Manag Sci

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Boolean Petri net (BPN) and Crisp Boolean Petri net (CBPN) is a well-studied graph model since 2010 which has several applications in mathematical modeling of complex or tricky networks. Modeling any network with Petri net which can generate binary numbers as marking vectors in its reachability tree is still has much uses. In CBPN with a minimum number of transition and minimum number of steps of reachability tree, minimal execution time to run the machine has not been noted till date, thus it’s necessary to sort out this problem. Possibly it may occur due to some forbidden structure which hinders any 1-safe Petri net to be a CBPN. In this paper, we present some forbidden digraphs whose presence interrupts the generation of binary n-vectors exactly once. Any 1-safe Petri net is not a CBPN if it contains any of the subnet induced to the four forbidden structures discussed in this paper.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Existence of Forbidden Digraphs for Crisp Boolean Petri Nets

Singh¹,

Singh²,

Jha³

2019

Int J Math, Eng, Manag Sci

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“…The 'net-like' representation of these logical tools came into the existence in his doctoral thesis "Communication with Automata" at the Technical University of Darmstadt, Germany, in 1962 [1]. Petri nets are very reliable tool to model and study the structure of the discrete event-driven systems with large population or heavy traffic appear frequently in many fields such as manufacturing processes, logistics, telecommunication systems, traffic systems etc [2]. Of all existing models, Petri nets and their extensions are of undeniable fundamental interest because they define easy graphical support for the representation and the understanding of basic mechanism and behaviors.…”

Section: Introductionmentioning

confidence: 99%

A Wheel 1-Safe Petri Net Generating all the {0; 1}^n Sequences

Singh¹

2013

IJCA

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Petri nets are a graphic and mathematic modeling tool which is applicable to several systems and to all those systems presenting particular characteristics such as concurrency, distribution, parallelism, non-determinism and/or stochastically. In this paper, a wheel Petri net whose reachability tree contains all the binary ntuples or sequences as marking vectors has been defined. The result is proved by the using of the Principle of Mathematical Induction (PMI) on |P | = n.

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“…In [1], the authors proposed a 1-safe star Petri net S n , with |P | = n and |T | = n + 1, having a central transition, that generates all the binary n-vectors, as its marking vectors. For brevity, a 1-safe Petri net that generates all the binary n-vectors as marking vectors will be called a Boolean Petri net [2] and a 1-safe Petri net that generates all the binary n-vectors exactly once as marking vectors a crisp Boolean Petri net [2].…”

Section: Introductionmentioning

confidence: 99%