LIST OF FIGURES

xx

LIST OF FIGURES

3.5

EDF schedule

53

3.6

Infeasible RM schedule

54

3.7

RM schedule

55

3.8

EDF schedule

55

3.9

Schedule for example task set using approach 1

56

3.10

Schedule for example task set using approach 2

57

3.11

Schedule for example task set using approach 3: deferred server

57

3.12

Scheduling algorithm A for tasks with precedence constraints

59

3.13

Precedence graph

60

3.14

Scheduling algorithm B for tasks with precedence constraints

60

3.15

Schedule for tasks with precedence constraints

61

3.16

Schedule for tasks with precedence constraints after shifting tasks

61

3.17

Scheduling algorithm for tasks with rendezvous constraints

62

3.18

Infeasible EDF schedule for tasks with rendezvous constraints

63

revising deadlines

64

3.20

Infeasible EDF schedule for tasks with critical sections

64

3.21

Scheduling algorithm for tasks with critical sections

65

3.22

Schedule for tasks with critical sections

65

3.23

Gantt chart

66

3.24

Timing diagram

66

3.25

Scheduling game board

67

3.26

Game board showing deadline miss

68

3.27

Game board showing a feasible schedule

69

3.28

Schedule for four periodic tasks on two processors

71

4.1

CTL structure for the railroad crossing system

88

4.2

BDD for formula ( p q) (r s) (t u)

117

4.3

BDD for formula ( p q) (r s) (t u)

118

4.4

Algorithm restrict

119

4.5

Symbolic model checking algorithm

120

4.6

Minimum delay algorithm

122

4.7

Maximum delay algorithm

122

4.8

Minimum condition-counting algorithm

124

4.9

Maximum condition-counting algorithm

124

4.10

TTG minimum delay algorithm

126

5.1

Special events, conditions, and actions

136

5.2

Two Statecharts of the behavior of a car’s pedals

137

5.3

Statechart A of a solution to the mutual exclusion problem

138

LIST OF FIGURES

xxi

5.4

Statechart B of a solution to the mutual exclusion problem

138

5.5

Module-chart of a simplified car

141

6.1

Constructing the constraint graph corresponding to example

156

6.2

Worst-case search tree for example

159

6.3

Rearranging positive cycles to trim the search tree

161

6.4

Modechart 1

172

6.5

Modechart 2

173

6.6

Algorithm for checking minimum distance

178

6.7

Algorithm for checking maximum distance

179

7.1

Automaton α1 for automatic air conditioning and heating system

196

7.2

Automaton α2 for message sending and acknowledgment

198

7.3

Clock regions for two clocks, ci = 1 and c j = 2

203

7.4

Automaton α3

204

7.5

Verification algorithm

205

8.1

Petri net of a three-process mutual exclusion algorithm

213

8.2

Sample ER net

220

8.3

Partial TERN for a smart traffic light system

221

9.1

CCS laws

240

9.2

ACSR-specific laws

251

9.3

Differences between ACSR and VERSA

253

10.1

A real-time decision system

261

10.2

State-space graph of a real-time decision program

270

10.3

Development of real-time decision systems

272

10.4

Computer-aided design tools for real-time decision systems

274

example2

279

10.6

A two-counter machine for testing odd input

281

functions q1 and q2

299

10.8

Overview of the analysis methodology

303

10.9

The Estella-General Analysis Tool

305

components

327

10.11

The high-level dependency graph construction procedure

337

10.12

The HLD graph of Program

1

339

10.13

Algorithm

A

343

10.14

The ME graph of Program

2

344

xxii

LIST OF FIGURES

10.15

Depth-first-search algorithm

349

10.16

Algorithm

D

350

10.17

(a) The RD graph of Program

3. (b) The SRD graph of Program

3

351

10.18

Traversing orders by the subrule 11

352

10.19

The ME graph of Program

3

352

10.20

The general analysis algorithm

353

10.21

Rule enabling patterns

356

10.22

VM cycles

359

11.1

An example of a Rete network

372

11.2

State-space graph of an OPS5 program

374

11.3

Enabling relation with pessimistic estimation

392

11.4

CPU timing report of the OMS expert system

399

11.5

Test results of the OMS expert system

399

11.6

PI graph cycle classification

403

11.7

PI graph of Waltz program segment

405

11.8

Algorithm

A

410

11.9

The Rete network for r4

413

11.10

Algorithm

M

417

11.11

The Rete network for the Waltz program segment

418

11.12

ri dis-instantiates r j

420

response time

421

11.14

Old PI graph of Waltz

425

11.15

New PI graph of Waltz

428

12.1

An example of the EQL(B) rule-based expert system

441

12.2

An EQL program-based decision system

441

12.3

State-space graph for the EQL(B) program in Figure 12.1

443

12.4

Derivation of fixed-point assertion F P2

445

12.5

General optimization schema

446

dependency graph (b) for the EQL(B) program in Figure 12.1

447

12.7

Bottom-up generation of an optimized transition system

448

generated from the EQL(B) program in Figure 12.1 using the BU

algorithm. xxxd denotes all eight states for which the value of

variable d is equal to 1

449

is based on an equally labeled single-rule transition to a single state.

The transformation is initiated with a call to Transform BU

449

LIST OF FIGURES

xxiii

derivation of equivalent states

450

from the EQL(B) program in Figure 12.1, using the ES algorithm

451

generation of equivalent states and multiple-rule transitions

452

from the EQL(B) program in Figure 12.1, using the ESM algorithm

452

{c} {b,a}

{a,b,c}

(b)

453

S2c −→ S2b −→ S2a

−→ S1

12.1, using either the BU or ES algorithm

455

12.1, using the ESM algorithm

455