Automatic Verification of Sequential Infinite-State Processes

By: Olaf Burkart

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180 Pages

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A common approach in software engineering is to apply during the design phase a variety of structured techniques like top-down design, decomposition and abstraction, while only subsequently, in the implementation phase, is the design tested to ensure reliability. But this approach neglects that central aspects of software design and program development have a strong formal character which admits tool support for the construction of reliable and correct computer systems based on formal reasoning. This monograph provides much information both for theoreticians interested in algebraic theories, and for software engineers building practically relevant tools. The author presents the theoretical foundations needed for the verification of reactive, sequential infinite-state systems.

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Non-Fiction Computing & I.T.Computer Programming & Software Development Software Engineering Mathematics Computer Science Computer Architecture & Logic Design

Introduction	p. 1
Sequential Processes	p. 2
Model Checking	p. 3
Equivalence Checking	p. 5
Organisation of This Book	p. 6
Background	p. 9
Introduction	p. 9
Fixpoint Theory	p. 9
Ordered Sets	p. 9
Fixpoint Theorems	p. 12
Relations and Rewrite Systems	p. 13
Relations	p. 14
Rewrite Systems	p. 14
Context-Free Languages	p. 15
Processes and Labelled Transition Graphs	p. 17
Behavioural Equivalences	p. 20
Normedness and Determinism	p. 21
Context-Free Processes	p. 22
Syntax and Semantics	p. 23
Normedness	p. 28
Self-bisimulations	p. 30
Pushdown Processes	p. 33
Introduction	p. 33
Syntax and Semantics	p. 34
Expressiveness	p. 38
PDPA Laws	p. 40
Pushdown Normal Form	p. 43
Parallel Composition	p. 48
Example	p. 50
Parallel Decomposition and 2-PDNF	p. 51
Related work	p. 55
Context-Free Graphs	p. 56
Prefix Transition Graphs	p. 58
Pushdown Transition Graphs	p. 58
Equational graphs	p. 59
MSOL Definable Hypergraphs	p. 62
BPA with the state operator	p. 64
Model Checking	p. 67
Introduction	p. 67
The Modal µ-Calculus	p. 67
Syntax	p. 68
Semantics	p. 70
Continuity	p. 72
Alternation Depth	p. 73
Assertion-Based Semantics	p. 74
A Motivating Example	p. 75
Definition of Assertion-Based Semantics	p. 76
Properties of Assertion-Based Semantics	p. 77
Verifying Behavioural Properties	p. 96
Hierarchical Equational µ-Formulas	p. 96
The Model Checking Algorithm	p. 100
A Working Example	p. 110
Expressiveness of the modal µ-calculus	p. 111
Equivalence Checking	p. 115
Introduction	p. 115
The Bisimulation Equivalence Problem	p. 115
Separability	p. 116
Deciding Bisimilarity of Normed BPA	p. 124
A Bound for Separability	p. 130
The Algorithm	p. 137
Bisimulation Bases	p. 138
The Computation of an Initial Base	p. 140
The Branching Algorithm	p. 146
Summary of the Decision Procedure	p. 148
Summary and Perspectives	p. 151
Summary of the Main Results	p. 151
Perspectives	p. 152
Model Checking	p. 152
Equivalence Checking	p. 153
Regularity of Context-Free Processes	p. 154
Index	p. 161
Table of Contents provided by Publisher. All Rights Reserved.

Automatic Verification of Sequential Infinite-State Processes

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