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.

Research Articles for the Regular Issue