Fronticepiece	6
	Preface	8
	Acknowledgments	9
	Introduction	10
	A Warmup Problem in Complexity	14
	About the Authors	16
	Contents	18
	Chapter 1 MOTIVATIONS	21
	1.1 TRENDS AND PROBLEMS IN SYSTEM TECHNOLOGIES	21
	1.2 AN EXAMPLE OF LOW DIMENSION	24
	1.3 THE MANAGER AND ANALYST CONTINUE THEIR DIALOGUE	36
	1.4 PRELIMINARY CONCLUSIONS	40
	1.5 A LITTLE WINDOW INTO FUTURE CHAPTERS	42
	1.6 PROBLEMS FOR THE CURIOUS READER	43
	Chapter 2 THE FOUR-FOLD WAY	44
	2.1 PROLOGUE: THE MANAGER AND ANALYST DISCUSS THE ORIGINS OF MULTIDIMENSIONAL MODELS AND WELLPOSEDNESS	44
	2.2 THE FIRST VIEW: SET THEORETIC	47
	2.3 THE SECOND VIEW: FAMILY OF SUBMODELS	54
	2.4 THE THIRD VIEW: THE BIPARTITE GRAPH	57
	2.5 THE FOURTH VIEW: THE CONSTRAINT MATRIX	58
	2.6 MODEL CONSISTENCY AND COMPUTATIONAL ALLOWABILITY	59
	2.7 THE MANAGER AND ANALYST CONTINUE THEIR DIALOGUE	59
	2.8 CHAPTER SUMMARY	65
	2.9 PROBLEMS FOR THE INTERESTED STUDENT	67
	Chapter 3 GENERAL RESULTS	68
	3.1 LANGUAGE AND MATHEMATICS	68
	3.2 MOST GENERAL TRUSTWORTHY RESULTS	70
	3.3 CLASSES OF RELATIONS	75
	3.4 MANAGER AND ANALYST REVISITED	78
	3.5 CHAPTER SUMMARY	79
	3.6 PROBLEMS FOR THE GENERAL STUDENT	79
	Chapter 4 REGULAR RELATIONS	80
	4.1 COGNITIVE BARRIERS TO CIRCUITS	80
	4.2 NODE, KNOT AND BASIC NODAL SQUARE SANCTIFICATION	82
	4.3 USEFUL PROPERTIES OF BIPARTITE GRAPHS	91
	4.4 CORNERING THE CULPRIT KERNELS	98
	4.5 CONTINUING THE PURSUIT INSIDE THE CIRCUIT CLUSTERS (cc)	107
	4.6 LOCATING BNSs WITHIN A MODEL GRAPH	110
	4.7 QUERIES FOR THE REGULAR STUDENT	118
	Chapter 5 MODEL CONSISTENCY AND COMPUTATIONAL ALLOWABILITY	120
	5.1 ZERO CONSTRAINT ALL ALONG THE COMPUTATIONAL PATH	120
	5.2 RECAPITULATION OF COMPUTATIONAL FLOW	122
	5.3 GENERAL PROCEDURE FOR DETERMINING CONSISTENCY AND ALLOWABILITY IN A MODEL OF REGULAR RELATIONS	124
	5.4 DETECTION OF OVERLAPPING BNS	128
	5.5 RELIEF OF OVER-CONSTRAINT	133
	5.6 EXPANSION OF RESULTANT CONSTRAINT DOMAINS	134
	5.7 PROCESSING OF COMPUTATIONAL REQUESTS	143
	5.7.1 INITIAL SIMPLIFICATION OF MODEL GRAPH	143
	5.7.2 SIMPLIFYING MODEL GRAPH DURING CONSTRAINT PROPAGATION	145
	5.7.3 UNALLOWABLE COMPUTATIONAL REQUESTS	147
	5.7.3.1 OVER-CONSTRAINT OF NODES	147
	5.7.3.2 RELEVANCY OF DEPENDENT VARIABLES	148
	5.8 SUMMARY OF CHAPTER AND CONSTRAINT THEORY TOOLKIT	150
	5.9 QUERIES FOR THE REGULAR STUDENT	155
	Chapter 6 DISCRETE AND INTERVAL RELATIONS	156
	6.1 METAMODEL ISSUES AND PERSPECTIVES	156
	6.2 THE GENERAL TAXONOMY AND PRIMARY PROPERTY OF DISCRETE RELATIONS	157
	6.3 BOOLEAN RELATIONS	157
	6.4 TOPOLOGICAL IMPLICATIONS	164
	6.5 ALLOWABILITY OF DISCRETE COMPUTATIONS	166
	6.6 INEQUALITY RELATIONS	168
	6.7 SUMMARY	171
	6.8 PROBLEMS FOR THE DISCRETE STUDENT	173
	Chapter 7 THE LOGICAL STRUCTURE OF CONSTRAINT THEORY	174
	7.1 OVERVIEW	174
	7.2 POSTULATES AND PHILOSOPHICAL ASSUMPTIONS	174
	7.3 DEFINITIONS	175
	7.4 THEOREMS	175
	7.5 GRAPHS OF THE LOGICAL STRUCTURE OF CONSTRAINT THEORY	176
	7.6 COMPLETENESS	177
	Chapter 8 EXAMPLES OF CONSTRAINT THEORY APPLIED TO REAL-WORLD PROBLEMS	182
	8.1 APOLOGIES NOT REQUIRED	182
	8.2 COST AS AN INDEPENDENT VARIABLE (CAIV)	182
	8.3 THE KINEMATICS OF FREE-FALL WEAPONS	190
	8.4 THE DEFLECTION OF AN EARTH-THREATENING ASTEROID EMPLOYING MASS DRIVERS	195
	Chapter 9 MANAGER AND ANALYST MEET AGAIN	202
	Appendix A COMPUTATIONAL REQUEST DISAPPOINTMENTS	207
	Appendix B GRAPH THEORY OVERVIEW	215
	Appendix C THE LOGIC OF “IF” AND “IF AND ONLY IF”	219
	Appendix D ALGEBRAIC STRUCTURES	221
	References	228
	Index	231