Problem Solving: Methods, Programming and Future Concepts (eBook)

Front Cover 1
Problem Solving: Methods, Programming and Future Concepts 4
Copyright Page 5
CONTENTS 8
PREFACE 6
CONTENTS 8
INTRODUCTION 14
Conception of the book 23
The history of the subject 26
State of the art 33
CHAPTER 0. PROBLEM CLASSIFICATION. INTRODUCTION TO THE SOLVING METHODS 46
0.1 What is a problem? 46
0.2 Problem classification 50
0.3 An approach to building an interpretation calculus 51
0.4 Finding a solution by means of theorem proving 74
0.5 Finding an optimum interpretation 93
0.6 Psychological aspects 109
0.7 Conclusion 109
CHAPTER 1. ELEMENTS OF PROBLEM SOLVING THEORY: APPLICATION OF CUTTING STRATEGIES 110
1.1 Introduction 110
1.2 The properties of a solution's elements 112
1.3 A system of axioms for incompatibility calculus 114
1.4 An algorithm for searching for maximum-size zero submatrix 134
1.5 On the minimum-size cover problem (MSCP) 152
1.6 Precedence and incompatibility 158
1.7 Prohibition 160
1.8 Conditional executability 163
1.9 Other examples 167
1.10 Conclusion 169
CHAPTER 2. SOLVING DISCRETE OPTIMIZATION PROBLEMS ON THE BASIS OF .-TRANSFORM METHOD 170
2.1 .-transform method 171
2.2 Some important cases of the analytical representation of the .(q)-function 174
2.3 A general scheme for the discrete . 
179 
2.4 An approximate solution to F-indefinite static optimization problems 194
2.5 Conclusion 212
CHAPTER 3. WEAK METHODS AND HEURISTIC REASONING 214
3.1 Specific features of solving tasks by weak methods 214
3.2 Control of the solving process 217
3.3 Models of heuristic-based solution searching 223
3.4 Try-and-test procedures with cutting 226
3.5 Intermediate remarks on heuristics utilization 239
3.6 Examples of problem solving principles 240
3.7 Solution tree 245
3.8 Principle of dominance and choice function 279
3.9 An example of mechanization of heuristics 285
3.10 Conclusion 293
CHAPTER 4. LOGIC-BASED PROBLEM SOLVERS: APPROACHES AND NEW METHODS 296
4.1 Introduction 296
4.2 Logical problem solvers 297
4.3 Group resolution principle in predicate calculus 310
4.4 Implementation of group resolution principle 321
4.5 Reduction algorithm with term re-writing 327
4.6 Conclusion 337
CHAPTER 5. PROGRAMMING CONCEPTS IN PROBLEM SOLVING 338
5.1. Programming or theorem proving? 338
5.2 Universal algorithm paradigm 352
5.3 Computer mathematics 360
5.4 Expert systems 360
5.5 Evolutionary problem solution synthesis (EPSS) concept 369
5.6 Mathematical induction and pattern recognition approaches 371
5.7 Intellectual support concept in the problem solving system 373
5.8 Making a semantic structure of the problem 390
5.9 Conclusion 397
CHAPTER 6. FUTURE CONCEPTS: SOME PHILOSOPHICAL ISSUES 400
6.1 Universal problem solving approach restoration 400
6.2 Weak methods become strong 405
6.3 The role of formal logic in future developments 407
6.4 The human factor 410
6.5 Are there other paradigms? 414
6.6 Conclusive remarks 416
REFERENCES 418
GLOSSARY 424
INDEX 432