Constraint Theory [electronic resource] : Multidimensional Mathematical Model Management /
Friedman, George.author.
The enormous potential of digital computation to manage new complex systems is impeded by exponential increases in complexity. As the model's dimensionality increases from hundreds to thousands of variables, and as submodels constructed by diverse technical teams are integrated into the total model, the model is likely to become inconsistent and even more likely, the computational requests on the model become unallowable. This text analyzes the way constraint theory employs bipartite graphs and constraint matrices to detect and correct these well-posed problems. It also presents the process of locating the "kernel of constraint", literally trillions of times faster than a random search, determining consistency and compatibility within seconds. This text is an invaluable reference for all engineers, mathematicians and managers concerned with modeling. "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory." --Cornelius T. Leondes, UCLA "Groundbreaking work. ... Friedman's accomplishment represents engineering at its finest. ... The credibility of the theory rests upon the formal proofs which are interspersed among the illuminating hypothetical dialog sequences between manager and analyst, which bring out distinctions that the organization must face, en route to accepting Friedman's work as essential to achieve quality control in developing and applying large models." --John N. Warfield.
Description based upon print version of record.
Includes bibliographical references (p. [181]-182) and index.
Motivations: What is Constraint Theory and why is it important?- The Four-fold way: How to Perceive Complex Mathematical Models and Well-Posed Problems -- General Results: From Protomath to Math to Metamath -- Regular Relations: Searching for the Kernels of Constraint -- Discrete and Interval Relations: The Diminished Utility of Metamodels -- The Logical Structure of Constraint: Theory A Compact Summary -- Examples of Constraint Theory Applied to Real-World Problems -- Manager and Analyst Meet Again: Gists and Schizophrenia.
The enormous potential of digital computation to manage new complex systems is impeded by exponential increases in complexity. As the model's dimensionality increases from hundreds to thousands of variables, and as submodels constructed by diverse technical teams are integrated into the total model, the model is likely to become inconsistent and even more likely, the computational requests on the model become unallowable. This text analyzes the way constraint theory employs bipartite graphs and constraint matrices to detect and correct these well-posed problems. It also presents the process of locating the "kernel of constraint", literally trillions of times faster than a random search, determining consistency and compatibility within seconds. This text is an invaluable reference for all engineers, mathematicians and managers concerned with modeling. "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory." --Cornelius T. Leondes, UCLA "Groundbreaking work. ... Friedman's accomplishment represents engineering at its finest. ... The credibility of the theory rests upon the formal proofs which are interspersed among the illuminating hypothetical dialog sequences between manager and analyst, which bring out distinctions that the organization must face, en route to accepting Friedman's work as essential to achieve quality control in developing and applying large models." --John N. Warfield.
Applied mathematics.
Engineering mathematics.
Mathematical models.
Computational intelligence.
Computer science—Mathematics.
Artificial intelligence.
Mathematical and Computational Engineering.
Mathematical Modeling and Industrial Mathematics.
Computational Intelligence.
Mathematics of Computing.
Artificial Intelligence.
IFSR International Series on Systems Science and Engineering