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Quantitative measures of the system property flexibility have long eluded systems analysts. This paper introduces a mathematical framework to define, measure, and analyze embedded system functional flexibility in a quantitative manner. The methodology employs a domain-specific ontology to encode a system's functions and its hardware resources in a natural and efficient manner, decoupling the logical and physical aspects of the system. The modeling of system functions is expressed in polynomial form and easily converted to matrix form for efficient mathematical and computational analysis. Algebraic, topological, and combinatorial methods are used to perturb a system's functions to explore its flexibility. Of special note, is the ability to mathematically vary a system's defined functionality in a manner that maintains logical similarity to its initial form. For the first time known, quantitative characterizations of these effects are derived, yielding measures that provide insights into a system's ability to admit change (flexibility) and its sensitivity to such changes. These measures of flexibility may be expressed as objective functions so that they may be integrated into design space exploration or optimization frameworks, thus allowing flexibility to be considered with other objectives in system trades.
Date of Publication: March 2011