The Formalization of Decision-Free Petri Net

In this article we formalize the definition of Decision-Free Petri Net (DFPN) presented in [19]. Then we formalize the concept of directed path and directed circuit nets in Petri nets to prove properties of DFPN. We also present the definition of firing transitions and transition sequences with natural numbers marking that always check whether transition is enabled or not and after firing it only removes the available tokens (i.e., it does not remove from zero number of tokens). At the end of this article, we show that the total number of tokens in a circuit of decision-free Petri net always remains the same after firing any sequences of the transition.Shah Pratima K. - Shinshu University Nagano, JapanKawamoto Pauline N. - Shinshu University Nagano, JapanGiero Mariusz - University of Białystok PolandGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Pauline N. Kawamoto, Yasushi Fuwa, and Yatsuka Nakamura. Basic Petri net concepts. Formalized Mathematics, 3(2):183-187, 1992.Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.Robert Milewski. Subsequences of almost, weakly and poorly one-to-one finite sequences. Formalized Mathematics, 13(2):227-233, 2005.Karol Pak. Continuity of barycentric coordinates in Euclidean topological spaces. Formalized Mathematics, 19(3):139-144, 2011. doi:10.2478/v10037-011-0022-5.Andrzej Trybulec. On the decomposition of finite sequences. Formalized Mathematics, 5 (3):317-322, 1996.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Jiacun Wang. Timed Petri Nets, Theory and Application. Kluwer Academic Publishers, 1998.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990

A Petri Nets-based Scheduling Methodology forMultipurpose Batch Plants.

This article presents an optimization methodology of batch production processes assembled by shared resources which rely on a mapping of state-events into time-events allowing in this way the straightforward use of a well consolidated scheduling policies developed for manufacturing systems. A technique to generate the timed Petri net representation from a continuous dynamic representation (Differential-Algebraic Equations systems (DAEs)) of the production system is presented together with the main characteristics of a Petri nets-based tool implemented for optimization purposes. This paper describes also how the implemented tool generates the coverability tree and how it can be pruned by a general purpose heuristic. An example of a distillation process with two shared batch resources is used to illustrate the optimization methodology proposed

Reliability models for dataflow computer systems

The demands for concurrent operation within a computer system and the representation of parallelism in programming languages have yielded a new form of program representation known as data flow (DENN 74, DENN 75, TREL 82a). A new model based on data flow principles for parallel computations and parallel computer systems is presented. Necessary conditions for liveness and deadlock freeness in data flow graphs are derived. The data flow graph is used as a model to represent asynchronous concurrent computer architectures including data flow computers

On the Formal Verification of Petri Net Properties using a Mechanized Proof Checker Approach （プルーフチェッカーシステムを用いたペトリネットの性質の形式的検証について）

信州大学(Shinshu university)博士（工学）ThesisPRATIMA KUMARI　SHAH . On the Formal Verification of Petri Net Properties using a Mechanized Proof Checker Approach （プルーフチェッカーシステムを用いたペトリネットの性質の形式的検証について）. 信州大学, 2014, 博士論文. 博士（工学）, 甲第616号, 平成26年9月30日授与.doctoral thesi

Construction of formal models and verifying property specifications through an example of railway interlocking systems

Abstract The use of formal modeling has seen an increasing interest in the development of safety-critical, embedded microcomputer-controlled railway interlocking systems, due to its ability to specify the behavior of the systems using mathematically precise rules. The research goal is to prepare a specification-verification environment, which supports the developer of the railway interlocking systems in the creation of a formally-proven correct design and at the same time hides the inherent mathematical-computer since related background knowledge. The case study is presented with the aim to summarize the process of formalizing a domain specification, and to show further application possibilities (e.g. verification methods)