Andrei Karatkevich

Application of comparability graphs in decomposition of Petri nets

In the article we present a new algorithm of Petri net decomposition into State Machine Components (SMCs). The idea bases on the application of the comparability graph theory. The comparability graphs are classified as a subclass of the perfect graphs and have unique properties. If a graph belongs to the comparability class, many problems (like graph coloring, maximal clique problem) can be solved in polynomial time. Therefore, if the sequentiality graph of a Petri net belongs to comparability class, the whole decomposition process turns to be polynomial. The preliminary experiments have demonstrated the effectiveness of the proposed idea. Over 90% of concurrency and sequentiality graphs of tested benchmarks belong to the comparability class. The efficiency is even higher if the Petri net class is reduced to the EFC (Extended Free-Choice).

On macroplaces in Petri nets

This article deals with hierarchical decomposition of Petri nets. The following question is considered: which conditions a subnet should satisfy to make possible its replacement by a macroplace? A general class of such subnets is defined. The theoretical results related to such kind of decomposition are presented. Application of the decomposition to verification of systems, which are specified by means of Petri nets, is considered.

Deadlock detection in Petri nets: One trace for one deadlock?

Formal verification of specifications of digital devices, such as logical controllers, is an important part of the design process. Deadlock detection is one of the fundamental tasks of formal verification. There exist classical methods of deadlock detection in the concurrent discrete systems, which allow obtaining paths to every reachable deadlock without complete state space exploration. In the paper a method is proposed allowing further reduction of the size of explored state space during deadlock detection. The method is presented for the Petri nets.

A Method of Analysis of Operational Petri Nets

Petri nets, a popular discrete automaton model, are convenient for describing some parallel operations. A net used for such purpose cannot be a closed system but has to contain input and output places. Such a model is defined here as an operational Petri net.

FPGA-based embedded Logic Controllers

In general case, reconfigurable logic controllers (RLC) are included into reactive digital embedded systems, carrying out control for several processes proceeding concurrently. The paper presents a practical application of a formal, rule-based specification language in Gentzen sequent logic, which is used as an intermediate textual description of a control interpreted Petri net. On the other hand exactly the same description serves also as logic design expressions, related with different versions of functionally equivalent concurrent state machine models, considered on Register Transfer Level. The symbolic rule-based specification of Petri net-based embedded Logic Controllers (LCs) can be step-by step formally transformed into the final specification of concurrent state machine model, closely related with VHDL description, suitable for a direct mapping in reconfigurable logic devices. In this paper it is proposed novel compact form of logic descriptions, directly based on event-oriented specification, where it is assumed that macrocells can be implicitly formed by synthesis tool as containing virtual T flip-flops.

Analysis of Petri nets by means of concurrent simulation

In the paper the task of concurrent analysis of a Petri net is considered. A Petri net is given, and several processes able to simulate transition firings. The methods of analysis described in this paper are based on the original approach to net decomposition and oriented for the so-called operational nets and a class of cyclic Petri nets. The methods analyze the nets by reduced state space construction; both their sequential and parallel versions are described. Also the algorithm of decomposition oriented to concurrent analysis is described. The suggested methods of analysis can be implemented as a multithreaded application.

Modeling of production processes using UML and Petri nets

Abstract The paper proposes combined use of UML and Petri nets to model production processes which will be useful for designers of production processes in any area of industry. In practice, the specification of a normal operation cycle is presented by a technical drawing. It is known that UML helps to present the concept and various aspects of a system, and Petri nets can provide information about faults. A major challenge in modeling a production process with dynamic models of activity diagrams such as UML 2.0 and PNs is cooperation of these two different methods and conversion between them. The meta-model can be used to control the effects of modifications made in the system. These methods have been widely applied in different areas, but being applied together they can produce new results. This will be demonstrated on a practical example.

Design of Reconfigurable Logic Controllers

This bookpresents the original concepts and modern techniques for specification, synthesis, optimisation and implementation of parallel logical control devices. It deals with essential problems of reconfigurable control systems like dependability, modularity and portability. Reconfigurable systems require a wider variety of design and verification options than the application-specific integrated circuits. The book presents a comprehensive selection of possible design techniques. The diversity of the modelling approaches covers Petri nets, state machines and activity diagrams. The preferences of the presented optimization and synthesis methods are not limited to increasing of the efficiency of resource use. One of the biggest advantages of the presented methods is the platform independence, the FPGA devices and single board computers are some of the examples of possible platforms. These issues and problems are illustrated with practical cases of complete control systems. If you expect a new look at the reconfigurable systems designing process or need ideas for improving the quality of the project, this book is a good choice.g process or need ideas for improving the quality of the project, this book is a good choice.

Hierarchical Decomposition of Petri Nets for Digital Microsystems Design

In this paper an approach to hierarchical decomposition of Petri nets and of specification of a digital system behavior by means of hierarchical Petri nets is proposed.

Prototyping of Concurrent Control Systems With Application of Petri Nets and Comparability Graphs

This paper shows a novel prototyping technique for concurrent control systems described by interpreted Petri nets. The technique is based on the decomposition of an interpreted Petri net into concurrent sequential automata. In general, minimum decomposition requires runtime that is exponential in the number of Petri net places. We show that in many cases, including the real-life ones, the minimum decomposition problem can be solved in polynomial time. The proposed method allows implementing a concurrent control system using minimal number of sequential components, which requires polynomial time and can be applied to most of the considered cases. The presented concept is illustrated by a real-life industrial example of a beverage production and distribution machine implemented in a field programmable gate array.