Computational analysis of LED circuits based on partial quasi‐group rings

Abstract

Since the original idea of Claude Shannon about describing switching circuits by means of Boolean algebras, the working of devices within electric circuits has been modeled in the literature by means of different types of algebras. This paper delves into this topic by dealing with the synthesis and computational analysis of light-emitting diode (LED) circuits through which the electric current is regulated by a set of devices (voltage regulators, single-pole double-throw relays, analog multipliers, capacitors, resistors, and push buttons) whose working is uniquely described by a given partial quasi-group ring, or, equivalently, by a partial Latin square. Some results on the existing relationship among the designed circuits and these algebraic and combinatorial structures are exposed. Furthermore, to illustrate this relationship, we introduce a light switching game whose goal is lighting all the LEDs within a circuit based on a given partial quasi-group ring. The solvability of the game is analyzed by making use of computational algebraic geometry.