- •CONTENTS
- •PREFACE
- •LIST OF FIGURES
- •INTRODUCTION
- •1.1 WHAT IS TIME?
- •1.2 SIMULATION
- •1.3 TESTING
- •1.4 VERIFICATION
- •1.6 USEFUL RESOURCES
- •2.1 SYMBOLIC LOGIC
- •2.1.1 Propositional Logic
- •2.1.2 Predicate Logic
- •2.2 AUTOMATA AND LANGUAGES
- •2.2.1 Languages and Their Representations
- •2.2.2 Finite Automata
- •2.3 HISTORICAL PERSPECTIVE AND RELATED WORK
- •2.4 SUMMARY
- •EXERCISES
- •3.1 DETERMINING COMPUTATION TIME
- •3.2 UNIPROCESSOR SCHEDULING
- •3.2.1 Scheduling Preemptable and Independent Tasks
- •3.2.2 Scheduling Nonpreemptable Tasks
- •3.2.3 Nonpreemptable Tasks with Precedence Constraints
- •3.2.5 Periodic Tasks with Critical Sections: Kernelized Monitor Model
- •3.3 MULTIPROCESSOR SCHEDULING
- •3.3.1 Schedule Representations
- •3.3.3 Scheduling Periodic Tasks
- •3.4 AVAILABLE SCHEDULING TOOLS
- •3.4.2 PerfoRMAx
- •3.4.3 TimeWiz
- •3.6 HISTORICAL PERSPECTIVE AND RELATED WORK
- •3.7 SUMMARY
- •EXERCISES
- •4.1 SYSTEM SPECIFICATION
- •4.2.1 Analysis Complexity
- •4.3 EXTENSIONS TO CTL
- •4.4 APPLICATIONS
- •4.4.1 Analysis Example
- •4.5 COMPLETE CTL MODEL CHECKER IN C
- •4.6 SYMBOLIC MODEL CHECKING
- •4.6.1 Binary Decision Diagrams
- •4.6.2 Symbolic Model Checker
- •4.7.1 Minimum and Maximum Delays
- •4.7.2 Minimum and Maximum Number of Condition Occurrences
- •4.8 AVAILABLE TOOLS
- •4.9 HISTORICAL PERSPECTIVE AND RELATED WORK
- •4.10 SUMMARY
- •EXERCISES
- •VISUAL FORMALISM, STATECHARTS, AND STATEMATE
- •5.1 STATECHARTS
- •5.1.1 Basic Statecharts Features
- •5.1.2 Semantics
- •5.4 STATEMATE
- •5.4.1 Forms Language
- •5.4.2 Information Retrieval and Documentation
- •5.4.3 Code Executions and Analysis
- •5.5 AVAILABLE TOOLS
- •5.6 HISTORICAL PERSPECTIVE AND RELATED WORK
- •5.7 SUMMARY
- •EXERCISES
- •6.1 SPECIFICATION AND SAFETY ASSERTIONS
- •6.4 RESTRICTED RTL FORMULAS
- •6.4.1 Graph Construction
- •6.5 CHECKING FOR UNSATISFIABILITY
- •6.6 EFFICIENT UNSATISFIABILITY CHECK
- •6.6.1 Analysis Complexity and Optimization
- •6.7.2 Timing Properties
- •6.7.3 Timing and Safety Analysis Using RTL
- •6.7.5 RTL Representation Converted to Presburger Arithmetic
- •6.7.6 Constraint Graph Analysis
- •6.8 MODECHART SPECIFICATION LANGUAGE
- •6.8.1 Modes
- •6.8.2 Transitions
- •6.9.1 System Computations
- •6.9.2 Computation Graph
- •6.9.3 Timing Properties
- •6.9.4 Minimum and Maximum Distance Between Endpoints
- •6.9.5 Exclusion and Inclusion of Endpoint and Interval
- •6.10 AVAILABLE TOOLS
- •6.11 HISTORICAL PERSPECTIVE AND RELATED WORK
- •6.12 SUMMARY
- •EXERCISES
- •7.1.1 Timed Executions
- •7.1.2 Timed Traces
- •7.1.3 Composition of Timed Automata
- •7.1.4 MMT Automata
- •7.1.6 Proving Time Bounds with Simulations
- •7.2.1 Untimed Traces
- •7.2.2 Timed Traces
- •7.3.1 Clock Regions
- •7.3.2 Region Automaton
- •7.4 AVAILABLE TOOLS
- •7.5 HISTORICAL PERSPECTIVE AND RELATED WORK
- •7.6 SUMMARY
- •EXERCISES
- •TIMED PETRI NETS
- •8.1 UNTIMED PETRI NETS
- •8.2 PETRI NETS WITH TIME EXTENSIONS
- •8.2.1 Timed Petri Nets
- •8.2.2 Time Petri Nets
- •8.3 TIME ER NETS
- •8.3.1 Strong and Weak Time Models
- •8.5.1 Determining Fireability of Transitions from Classes
- •8.5.2 Deriving Reachable Classes
- •8.6 MILANO GROUP’S APPROACH TO HLTPN ANALYSIS
- •8.6.1 Facilitating Analysis with TRIO
- •8.7 PRACTICALITY: AVAILABLE TOOLS
- •8.8 HISTORICAL PERSPECTIVE AND RELATED WORK
- •8.9 SUMMARY
- •EXERCISES
- •PROCESS ALGEBRA
- •9.1 UNTIMED PROCESS ALGEBRAS
- •9.2 MILNER’S CALCULUS OF COMMUNICATING SYSTEMS
- •9.2.1 Direct Equivalence of Behavior Programs
- •9.2.2 Congruence of Behavior Programs
- •9.2.3 Equivalence Relations: Bisimulation
- •9.3 TIMED PROCESS ALGEBRAS
- •9.4 ALGEBRA OF COMMUNICATING SHARED RESOURCES
- •9.4.1 Syntax of ACSR
- •9.4.2 Semantics of ACSR: Operational Rules
- •9.4.3 Example Airport Radar System
- •9.5 ANALYSIS AND VERIFICATION
- •9.5.1 Analysis Example
- •9.5.2 Using VERSA
- •9.5.3 Practicality
- •9.6 RELATIONSHIPS TO OTHER APPROACHES
- •9.7 AVAILABLE TOOLS
- •9.8 HISTORICAL PERSPECTIVE AND RELATED WORK
- •9.9 SUMMARY
- •EXERCISES
- •10.3.1 The Declaration Section
- •10.3.2 The CONST Declaration
- •10.3.3 The VAR Declaration
- •10.3.4 The INPUTVAR Declaration
- •10.3.5 The Initialization Section INIT and INPUT
- •10.3.6 The RULES Section
- •10.3.7 The Output Section
- •10.5.1 Analysis Example
- •10.6 THE ANALYSIS PROBLEM
- •10.6.1 Finite Domains
- •10.6.2 Special Form: Compatible Assignment to Constants,
- •10.6.3 The General Analysis Strategy
- •10.8 THE SYNTHESIS PROBLEM
- •10.8.1 Time Complexity of Scheduling Equational
- •10.8.2 The Method of Lagrange Multipliers for Solving the
- •10.9 SPECIFYING TERMINATION CONDITIONS IN ESTELLA
- •10.9.1 Overview of the Analysis Methodology
- •10.9.2 Facility for Specifying Behavioral Constraint Assertions
- •10.10 TWO INDUSTRIAL EXAMPLES
- •10.10.2 Specifying Assertions for Analyzing the FCE Expert System
- •Meta Rules of the Fuel Cell Expert System
- •10.11.1 General Analysis Algorithm
- •10.11.2 Selecting Independent Rule Sets
- •10.11.3 Checking Compatibility Conditions
- •10.12 QUANTITATIVE TIMING ANALYSIS ALGORITHMS
- •10.12.1 Overview
- •10.12.2 The Equational Logic Language
- •10.12.3 Mutual Exclusiveness and Compatibility
- •10.12.5 Program Execution and Response Time
- •10.12.8 Special Form A and Algorithm A
- •10.12.9 Special Form A
- •10.12.10 Special Form D and Algorithm D
- •10.12.11 The General Analysis Algorithm
- •10.12.12 Proofs
- •10.13 HISTORICAL PERSPECTIVE AND RELATED WORK
- •10.14 SUMMARY
- •EXERCISES
- •11.1 THE OPS5 LANGUAGE
- •11.1.1 Overview
- •11.1.2 The Rete Network
- •11.2.1 Static Analysis of Control Paths in OPS5
- •11.2.2 Termination Analysis
- •11.2.3 Timing Analysis
- •11.2.4 Static Analysis
- •11.2.5 WM Generation
- •11.2.6 Implementation and Experiment
- •11.3.1 Introduction
- •11.3.3 Response Time of OPS5 Systems
- •11.3.4 List of Symbols
- •11.3.5 Experimental Results
- •11.3.6 Removing Cycles with the Help of the Programmer
- •11.4 HISTORICAL PERSPECTIVE AND RELATED WORK
- •11.5 SUMMARY
- •EXERCISES
- •12.1 INTRODUCTION
- •12.2 BACKGROUND
- •12.3 BASIC DEFINITIONS
- •12.3.1 EQL Program
- •12.3.4 Derivation of Fixed Points
- •12.4 OPTIMIZATION ALGORITHM
- •12.5 EXPERIMENTAL EVALUATION
- •12.6 COMMENTS ON OPTIMIZATION METHODS
- •12.6.1 Qualitative Comparison of Optimization Methods
- •12.7 HISTORICAL PERSPECTIVE AND RELATED WORK
- •12.8 SUMMARY
- •EXERCISES
- •BIBLIOGRAPHY
- •INDEX
236 TIMED PETRI NETS
the types of tokens for enabling the transitions and the types of tokens produced by the firing.
To extend ER nets to specify the notions of time, a variable chronos is used to represent the time-stamp of the token in each environment. This time-stamp gives the time when the token is produced. The time-stamps of the tokens put in output places are produced by the actions associated with the transitions and are based on the values of the environments of the selected input enabling tuple.
EXERCISES
1.Explain the difference between an untimed Petri net and a timed/time Petri net.
2.Consider the Petri net in Figure 8.1 modeling three tasks competing to execute the critical section. There are 10 places, one shared by all three tasks, and three places for each task. If we need to model an additional task, we need to add only three more places to model the internal events in this new task. Thus the size of the net is linearly proportional to the number of tasks. However, if we model this mutual-exclusion solution as a state-transition graph or Kripke structure (chapter 4), the number of states in this state graph grows exponentially as the number of modeled tasks increases. Explain why this is the case. On the other hand, a Statechart specification avoids this state explosion in its modeling of this mutualexclusion problem (chapter 5). Explain why this is the case.
3.Explain the differences between strong and weak time ER nets. Under what conditions should
(a)a strong time ER net be used?
(b)a weak time ER net be used?
4.Consider the ER net in Figure 8.2. Specify an alternate action with a predicate satisfying:
(a)token2 and token3.
(b)all 3 tokens.
5.Specify the car pedals system described as an MMT automaton using a time ER net.
6.Specify the hospital intensive care unit monitoring subsystem in chapter 6 (exercise 2) as a time ER net.
7.Construct a TERN corresponding to the example of the resource center with client requests (section 8.3).
8.Specify the smart airbag deployment system described in chapter 4 (exercise 6) as a TERN. Compare the expressiveness and space requirement for the TERN model and the timed transition graph model.
9.What is the run-time and space complexity of the Berthomieu–Diaz analysis algorithm?