Theoretical concepts asserted by Alan Turing are the basis of the computation and hence of machine intelligence. Turing Machine, the fundamental computational model, has been proven to be reducible to a logic circuit and, at the same time, portable into a computer program that can be expressed through a combination of fundamental programming language control structures. This work proposes a mathematical framework that analytically models logic gates employing Heaviside Step Function. The existence of a correspondence between a generic finite-time algorithm and the proposed mathematical formulation is proven. The proposed interpretation is given through a well-defined logical circuit analytical expression. Relevant geometrical applications, related to polygon processing, having wide implications in engineering branches are presented together with a new Penalty Method for constrained optimization problems handling. A detailed simulation campaign is conducted to assess the effectiveness of the applications derived from the proposed mathematical framework.
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