Devising a method of figurative transformations for minimizing boolean functions in the implicative basis

Solomko, Mykhailo; Batyshkina, Iuliia; Voitovych, Ihor; Zubyk, Liudmyla; Babych, Stepaniia; Muzychuk, Kateryna

doi:10.15587/1729-4061.2020.220094

Cited by 1 publication

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…MODNF (23), obtained by the method of figurative transformations contains 12 literals and coincides with the MODNF obtained on the basis of the smallest maximum independent set [14].…”

Section: Table 10 Implicant Tablesupporting

confidence: 60%

See 1 more Smart Citation

Implementing the method of figurative transformations to minimize partially defined Boolean functions

Solomko

Antoniuk

Voitovych

et al. 2023

EEJET

View full text Add to dashboard Cite

This paper reports a research that established the possibility of increasing the effectiveness of the method of figurative transformations to minimize partially defined Boolean functions. The method makes it possible, without loss of functionality, to reduce the complexity of the minimization procedure, compared to sorting out binary definitions of partially defined Boolean functions. The interpretation of the result is that the 2-(n, b)-design, 2-(n, x/b)-design systems are a reflection of logical operations. Therefore, the identification of such combinatorial systems in the truth table of logical functions directly and unambiguously establishes the location of logical operations for equivalent transformations of Boolean expressions. This, in turn, implicates an algorithm for simplifying Boolean functions, including partially defined Boolean functions. Thus, the method of figurative transformations simplifies and speeds up the procedure for minimizing partially defined Boolean functions, compared to analogs. This indicates that the visual-matrix form of the analytical method still has the prospect of increasing its hardware capabilities, including in terms of minimizing partially defined Boolean functions. It has been experimentally confirmed that the method of figurative transformations increases the efficiency of minimizing partially defined Boolean functions, compared with analogs, by 100–200 %. There is reason to argue about the possibility of increasing the efficiency of minimizing partially defined Boolean functions in the main and polynomial bases by the specified method. The effectiveness of the method, in particular, is ensured by carrying out all operations of generalized gluing of variables for dead-end disjunctive normal forms (DNF), followed by the use of implicant tables; optimal combination of a sequence of logical operations for gluing variables

show abstract

“…MODNF (23), obtained by the method of figurative transformations contains 12 literals and coincides with the MODNF obtained on the basis of the smallest maximum independent set [14].…”

Section: Table 10 Implicant Tablesupporting

confidence: 60%

“…The mathematical apparatus for minimizing Boolean functions by the method of figurative transformations was considered in works [10,12,13,16,17,23,24], etc.…”

Section: Discussion Of Results Of Minimization Of Partially Defined B...mentioning

confidence: 99%

Implementing the method of figurative transformations to minimize partially defined Boolean functions

Solomko

Antoniuk

Voitovych

et al. 2023

EEJET

View full text Add to dashboard Cite

show abstract

Devising a method of figurative transformations for minimizing boolean functions in the implicative basis

Cited by 1 publication

References 17 publications

Implementing the method of figurative transformations to minimize partially defined Boolean functions

Implementing the method of figurative transformations to minimize partially defined Boolean functions

Contact Info

Product

Resources

About