Selection Criteria for Rational Forms of Representing Logical Functions in Applied Problems of Discrete Mathematics

Abstract

The article substantiates that mastering the criteria for selecting rational forms of representing logical functions is a core competency. It enables future specialists not only to understand the theoretical foundations of computing systems but also to optimize applied developments under real technical constraints. The research aims to justify the methodical expediency of using problems with combinatorial and applied content in the process of studying methods for constructing normal forms of truth-table-defined logical functions to develop students' critical thinking. To achieve this goal, the following methods were used: analysis of scientific literature, generalization of pedagogical experience in higher education institutions, surveys, and questionnaires. The proposed techniques were tested during a pedagogical experiment at the Faculty of Information Technology and Mathematics of Lesya Ukrainka Volyn National University.

Key results. The study substantiates that the absence of a unique way to represent a Boolean function as an arbitrary DNF (Disjunctive Normal Form) or CNF (Conjunctive Normal Form) significantly complicates the verification of logical equivalence. This necessitates the transition to canonical forms (PDNF and PCNF), which guarantee a unique representation for each specific function. It is proved that, despite the existence of well-defined construction algorithms, a key aspect of training future specialists should be the development of the ability to consciously choose the canonical form that is appropriate to synthesize in a specific case. Preliminary analysis of the truth table structure ensures process optimization before the calculation phase, promoting a transition from mechanical reproduction of algorithms to a conscious analytical assessment of the computational expediency of the chosen method. The authors established that using problems with combinatorial and applied content facilitates the transformation of formal knowledge into an effective analytical tool.

Conclusions. The use of problems with combinatorial and applied content in the study of methods for constructing normal forms of truth-table-defined logical functions increases the motivation of future mathematicians and develops their critical thinking skills.