Gajendra Pratap Singh

Boolean Petri Nets

Petri net is a graphical tool invented by Carl Adam Petri [13]. These are used for describing, designing and studying discrete event-driven dynamical systems that are characterized as being concurrent, asynchronous, distributed, parallel, random and/or nondeterministic. As a graphical tool, Petri net can be used for planning and designing a system with given objectives, more practically effective than flowcharts and block diagrams. As a mathematical tool, it enables one to set up state equations, algebraic equations and other mathematical models which govern the behavior of discrete dynamical systems. Still, there is a drawback inherent in representing discrete event-systems. They suffer from the state explosion problem as what will happen when a system is highly populated, i.e., initial state consists of a large number of places that are nonempty. This phenomenon may lead to an exponential growth of its reachability graph. This makes us to study the safe systems. The aim of this chapter is to present some basic results on 1-safe Petri nets that generate the elements of a Boolean hypercube as marking vectors. Complete Boolean hypercube is the most popular interconnection network with many attractive and well known properties such as regularity, symmetry, strong connectivity, embeddability, recursive construction, etc. For brevity, we shall call a 1-safe Petri net that generates all the binary n-vectors as marking vectors a Boolean Petri net. Boolean Petri nets are not only of theoretical interest but also are of practical importance, required in practice to construct control systems [1]. In this chapter, we will consider the problems of characterizing the class of Boolean Petri nets as also the class of crisp Boolean Petri nets, viz., the Boolean Petri nets that generate all the binary n-vectors exactly once. We show the existence of a disconnected Boolean Petri net whose reachability tree is homomorphic to the n-dimensional complete lattice Ln. Finally, we observe that characterizing a Boolean Petri net is rather intricate.

Wormhole Detection and Prevention using Profile base Mechanism in MANET

A Mobile Ad hoc Network (MANET) is a collection of selfconfigurable mobile node connected through wireless links. Absence of central controller it is difficult to determine the reliable & secure communication in Mobile Ad hoc network. Worm hole attack that are work as to established path in between sender and receiver but if the sender has start data transmission then in that case the worm hole attacker has create a direct link, referred to as a wormhole tunnel between them, it means more of the number of trusted nodes it means higher successful data communication process rates may well expected. In this desertion we proposed detection as well as prevention technique against wormhole attack, for detection we use profile base detection technique and get attacker node information like node number, number of attack packet, attack time etc. after that we prevent wormhole attack using neighbor trust worthy base technique and secure the mobile ad-hoc network communication, through our proposal we provide secure as well as reliable communication and simulate through network simulator-2 and analyze the network behavior in attack and prevention case.

Construction of a Crisp Boolean Petri Net from a 1-safe Petri Net

The concept of a Petri net, a tool for the study of certain discrete dynamical systems, was invented in 1939 by Carl Adam Petri. In the attempt to characterize Boolean Petri nets, we discovered a subclass of Boolean Petri net called the crisp Boolean Petri net, viz., the one that generates every binary vector as its marking vectors exactly once. In this paper, the construction of a crisp Boolean Petri net from a 1-safe Petri net has been shown.

A Disconnected 1-Safe Petri Net Whose Reachability Tree Is Homomorphic to a Complete Boolean Lattice

Petri nets generating all the 2^n binary n-vectors as their marking vectors are not only of theoretical interest but also are of practical importance. In this note, we demonstrate the existence of a disconnected 1-safe Petri net whose reachability tree is homomorphic to the n-dimensional complete lattice L_n. This makes the problem of characterizing the 1-safe Petri nets that generate all the binary n-vectors as marking vectors exactly once appear more intricate.

Applications of Petri nets in electrical, electronics and optimizations

The main objective of this paper is to discuss the basic concepts of Petri net for students, researchers and industrialists. Petri nets are used in the discrete event driven dynamical system and governed by the set of events. The study of Petri nets forms one of its most vibrant areas of research due to its applications in all branches of engineering and sciences [9]. One of the most active fields of current research in mathematics is the subject of discrete dynamical system as Petri nets, whose structures form directed bipartite graphs, together with an initial marking. Petri nets have a well known graphical representation in which transitions are represented as boxes and places as circles with directed arcs interconnecting them, to represent the flow relation between them. This paper describes the diverse applications of Petri nets in electrical, electronics and to optimization of dynamic systems.

Basic Results on Crisp Boolean Petri Nets

The concept of Petri net as a discrete event-driven dynamical system was invented by Carl Adam Petri in his doctoral thesis ‘Communication with Automata’ in 1962. Petri nets are one of the best defined approach to modeling of discrete and concurrent systems. The dynamics of Petri nets represent the long-term behavior of the modeled system. Petri nets combine mathematical concepts with a pictorial representation of the dynamical behavior of the modeled systems. A Petri net is a bipartite directed graph consisting of two type of nodes, namely, place nodes and transition nodes. Directed arcs connect places to transitions and transitions to places to represent flow relation. In this paper, we present some basic results on 1-safe Petri net that generates every binary n-vector exactly once as marking vectors in its reachability tree, known as crisp Boolean Petri net. These results can be used for characterizing crisp Boolean Petri nets.

A New Algorithm for Web Log Mining

The enormous content of information on the World Wide Web makes it obvious candidate for data mining research. Data Mining Technique application is used to the World Wide Web referred as Web mining where this term has been used in three distinct ways; , Web Structure Mining, Web Content Mining and Web Usage Mining. Web Log Mining is one of the Web based application where it will facing with large amount of log data. In order to produce the web log through portal usage patterns and user behaviors, this research work implements the high level process of Web Log mining technique using basic rules. Web Log Mining consists of three main phases, namely Data Preprocessing, Pattern filtering and Pattern Analysis. As we know that server log files become a set of raw data where it’s must go through with all the Web Log Mining phases to producing the final results. Here, Web Log mining, approach has been combining with the basic rules, to optimize the total execution time. Finally, this work wills present an overview of results analysis and Web Log Mining can use the findings for the suitable valuable actions.

Embedding an Arbitrary 1-safe Petri Net into a Boolean Petri Net

Petri nets are powerful mathematical formalism for designing and studying behaviors of a wide range of discrete dynamical event driven systems. The aim of this paper is to show that an arbitrary1safe Petri net can be embedded as an induced subnet of a Boolean Petri net, viz., the one that generates every binary n-vector as its marking vector.

Existence and Uniqueness of a Minimum Crisp Boolean Petri Net

In the continuing research towards characterizing 1-safe Petri nets with n-places and generating all the 2 n binary n-vectors as marking vectors exactly once, the problem of determine minimum Petri nets; ‘minimum’ in the sense that the number of transitions is kept minimum possible for the generation of all the 2 n binary n-vectors has been found. In this paper, the existence and uniqueness of a minimum Petri net which generates all the 2 n binary n-vectors exactly once has been shown. For brevity, a 1-safe Petri net that generate all the binary n-vectors as marking vectors is called a Boolean Petri net and a 1-safe Petri net that generates all the binary n-vectors exactly once is called crisp Boolean Petri net.