PI-BEAM CALCULUS: THEORY AND APPLICATIONS
PI-BEAM CALCULUS: THEORY AND APPLICATIONS
Desheng Li
School of AI Engineering
Guangzhou College of Technology and Business
Copyright © 2026 by Cayley Nielson Press, Inc.
ISBN: 978-1-957274-28-7
Cayley Nielson Press Scholarly Monograph Series Book Code No.: 216-3-2
US$168.50
Preface
Based on the previous research, this Monograph uses Pi calculus and its extension as a formal tool to discuss the main issues in the service life cycle including service modeling, selection, combination, and verification. The specific contents include the following:
(1) Study the definitions, categories, methodologies and technologies of formalization of Web services at home and abroad, and clarify the research direction of service composition.
(2) Study the relevant theories and techniques of the formal method Pi calculus at home and abroad, and master the grammatical semantics and typed techniques of Pi calculus.
(3) Type extension of traditional Pi calculus for the characteristics of service composition: grammar extension has constrained channel, logical parallel and logical selection; semantic extension has beam channel link semantic rule, logical parallel and logical selection transformation rule.
(4) As a structured formal modeling language, although all Pi calculus versions can easily represent the operational semantics of concurrent processes, they are not as intuitive as Petri nets. Therefore, in order to accommodate the new primitives that extend the Pi calculus, we design a graphical representation notation APG to explicitly assign concurrency and logical relationships. Although it is not possible to fully represent the semantics of Pi calculus, it is helpful to understand and analyze Pi calculus and modeling Web services.
(5) Based on the extended Pi-Beam calculus, a detailed rationality discussion of the type system is given, and a strict proof is given.
(6) Based on the extended Pi-Beam calculus, the atomic services and composite services of Web services are modeled, and the related combination paradigm is proposed. Based on the paradigm, two rationalities of type rationality and process rationality are proposed, and the definition and determination methods of deadlock, deadlock freedom, livelock and livelock freedom are realized. In addition, based on the correctness guarantee, an automatic service combination algorithm using heuristic reasoning technology is proposed. It is used to automate combinatorial algorithms with polynomial time complexity.
(7) An extended cost Pi calculus is proposed, which can transform the search process of evolutionary algorithms such as PSO into its built-in primitives. Then a detailed scheme is proposed for the design pattern of discretized PSO. Based on the language, a PSO-based QoS-aware Web service selection method based on abstract syntax tree is developed.
The content is supported partly by the 2025 Guangdong Provincial Ordinary University Characteristic Innovation Project, Natural Science Category (Project No. 2025KTSCX205), and the 2024 Foshan Self-Funded Science and Technology Innovation (Project No. 2420001004401), the Natural Science Foundation of Anhui Province (Project No. 1708085MF161), KeyProject of Supporting Program for Outstanding Young Talents in Universities of 2016 (Project No. Gxyqzd2016214).
The content is supported partly by the 2025 Guangdong Provincial Ordinary University Characteristic Innovation Project, Natural Science Category (Project No. 2025KTSCX205), and the 2024 Foshan Self-Funded Science and Technology Innovation (Project No. 2420001004401), the Natural Science Foundation of Anhui Province (Project No. 1708085MF161), KeyProject of Supporting Program for Outstanding Young Talents in Universities of 2016 (Project No. Gxyqzd2016214).
Desheng Li
School of AI Engineering
Guangzhou College of Technology and Business
Foshan, Guangdong, China
January, 2026
Contents
Preface I
Authors Biography III
Chapter 1 Introduction 1
1.1 Process Algebra 1
1.2 Pi Calculus 5
Chapter 2 Extended Pi Calculus: Pi-Beam 15
2.1 Language 15
2.1.1 Syntax 15
2.1.1.1 Constrained Channel Bundle 19
2.1.1.2 Logical Parallel Links and Logical Selection 27
2.1.2 Semantics 32
2.1.2.1 Structure Congruence 32
2.1.2.2 Reduction Semantics 36
2.1.2.3 LTS 36
2.1.3 Type System 38
2.1.3.1 Type 38
2.1.3.2 Typing 39
2.1.3.3 Running Error 40
2.2 Soundness 42
2.2.1 Soundness of Typing System 42
2.2.2 Soundnesses of Beam Channel 48
2.2.3 Balance Soundness of Process' Beam Channel 49
2.3 Equivalence 49
Chapter 3 Graphical Representation of Pi-Beam 54
3.1 Related Graphical Representation 54
3.2 Label Connection Process Diagram 57
3.3 Summary 59
Chapter 4 Pi Calculus Experimental Environment 61
4.1 Overall Structure 61
4.2 Pi Calculus Compilation Execution Environment 63
4.2.1 Package Structure Diagram 63
4.2.2 Compiler Front End 65
4.2.3 Compiler Backend 69
4.3 Summary 69
Chapter 5 Pi-Beam-Cost Calculus 71
5.1 Problem Description 71
5.1.1 QoS of Service 71
5.1.2 Qos-Aware Service Composition Problem 74
5.1.3 Qos-Aware Service Composition Method 78
5.1.4 Formal Method of Intelligent System Based on Process Algebra 80
5.2 Language 84
5.2.1 Syntax 84
5.2.2 Semantics 85
5.2.2.1 Structured Congruence 86
5.2.2.2 LTS 87
5.2.2.3 Cost Measure Operator 90
5.2.2.4 Cost Measurement of Equivalent Services 94
5.2.2.5 PSO Meta-Control Process 96
Chapter 6 Modeling and Design of Qos-Aware Web Service Selection 101
6.1 Scenes 101
6.2 Pi-Beam-Cost for Qos-Aware Web Service Composition 103
6.2.1 PSO Optimization Process 113
6.2.1 DPSO Design of Model 116
6.2.1.1 DPSO Introduction 116
6.2.1.2 Representation of the Solution 116
6.2.1.3 Physical Representation of Particles 117
6.2.1.4 Particle Dynamics Definition 120
6.2.1.5 Fitness Function Design and Calculation 122
6.2.1.6 The Main Process of DPSO 124
6.3 Simulation 128
6.3.1 Establishment of Simulation Platform 128
6.3.2 Experimental Result 128
6.4 Summary 130
Appendix I: Symbol Table 133
References 134
Readership
This book should be useful for students, scientists, engineers and professionals working in the areas of optoelectronic packaging, photonic devices, semiconductor technology, materials science, polymer science, electrical and electronics engineering. This book could be used for one semester course on adhesives for photonics packaging designed for both undergraduate and graduate engineering students.
