Switching Systems Synthesis Method Using Permuted Gray Code Tables (PGC Method)

  • Cesar Troya-Sherdek International University of Ecuador
  • Valentin Salgado-Fuentes Technical University of Denmark
  • Jaime Molina Kachariy Higher Technical Institute
  • Gustavo Moreno Kachariy Higher Technical Institute
Keywords: Boolean functions, discrete problems, Gray Code, Hamiltonian Paths, hypercube, switching systems


Finding the shortest function on switching systems is a necessity for the development of efficient automatic systems. Currently, several methodologies aim to solve this need with different techniques. This article proposes a new methodology to find a propositional formula that describes a switching system problem using several truth tables which are based on an original one; these tables are generated using Gray Code principles and permutations. As it will be shown, the used code has a direct relation to the Hamiltonian paths, where each permutation is a different connection in a hypervolume, and each node is represented as a bit combination. An algorithm was developed using MATLAB and compared with the solutions from the software Boole-Deusto to verify and validate the applicability and implementation of the method. Finally, examples of execution, computational cost comparison and future work proposals are presented.


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