ENGLISH

Cause-Effect Structures: An Algebra of Nets with Examples of Applications

By Ludwik Czaja

Book information

Publisher
Springer International Publishing
Year
2019
ISBN
978-3-030-20460-0;978-3-030-20461-7
Language
english
Format
PDF
Filesize
6 MB (6434079 bytes)
Series
Lecture Notes in Networks and Systems 45
Edition
1st ed.
Pages
XVII, 142\153
Time added
2019-09-18 12:19:19
Engineering; Computational Intelligence

Description

This book presents a new algebraic system whose interpretation coincides with the behaviour of Petri nets, enhanced with an inhibitory mechanism and four time models. Its goal is to provide a formal means of modelling dynamic tasks, and of testing and verifying properties, in contexts characterised by the parallel execution of actions. However, the task description differs from that of Petri nets. The algebra is a quasi-semiring, “quasi” because of its somewhat restricted distributivity axiom. Expressions of this algebra, the cause–effect structures, have a graphic presentation as nets, but with one kind of named nodes, each annotated by two expressions that specify the type of signal reception from predecessors and transmission to successors. Many structural and behavioural properties are stated with proofs, and illustrative sample tasks are included. The book is intended for all those interested or involved in parallel and distributed computing – students, researchers and practitioners alike. Front Matter ....Pages i-xvii Introductory Notes (Ludwik Czaja)....Pages 1-8 Basics of Elementary Cause-Effect Structures (Ludwik Czaja)....Pages 9-22 Extensions of Elementary Cause-Effect Structures: Inhibitors, Multi-valued Nodes with Capacities and Weighted Monomials (Ludwik Czaja)....Pages 23-28 Another Extension: Time in Elementary c-e Structures (Ludwik Czaja)....Pages 29-38 Rough Cause-Effect Structures (Ludwik Czaja)....Pages 39-44 Structural Properties—Lattice of c-e Structures (Ludwik Czaja)....Pages 45-51 Further Structural Properties—Decomposition (Ludwik Czaja)....Pages 53-62 Semantic Properties of c-e Structures (Ludwik Czaja)....Pages 63-74 Relation of Cause-Effect Structures to Petri Nets (Ludwik Czaja)....Pages 75-82 Processes in Elementary Cause-Effect Structures (Ludwik Czaja)....Pages 83-96 Monoid of Processes (Ludwik Czaja)....Pages 97-103 Languages of Processes: Analysis and Synthesis Problems (Ludwik Czaja)....Pages 105-117 Examples (Ludwik Czaja)....Pages 119-136 Back Matter ....Pages 137-142

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