Pattern theory in algorithm design

Pattern theory is an analytical approach for mathematically sifting the essential “pattern-ness” from a function or algorithm. Elements of function decomposition theory are used to minimize the mathematical representation of a function by iteratively searching for the minimal algorithm which will generate a particular function. Minimality is defined in terms of decomposed function cardinality (DFC), a general measure of the complexity of a function. By acquiring the minimal (or quasi-minimal) algorithm of a function, significant improvements in execution time and computer memory requirements of on-board avionics systems can be obtained. To this end, pattern theory is an algorithm design paradigm. This paper shows some of the theoretical foundations of pattern theory and describes how pattern theory techniques have been applied to small binary problems in machine learning, circuit design, data compression, algorithm design, and image processing. Pattern theory is compared with conventional artificial intelligence approaches for algorithm/machine learning (e.g., neural networks) and experimental results are discussed