On the Structure, Complexity, and Depth of the Circuits over the Basis {&, ∨} Realizing Step Boolean Functions

The step Boolean function is a function of the algebra of logic of n Boolean variables, n = 1, 2, … , reducing to 1 on all of the sets of an n -dimensional unit cube, the ordinal numbers of which are not lower than the given set. In this paper, the problem of synthesis of circuits over the basis {&a...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki Jg. 162; H. 3; S. 335 - 349
Hauptverfasser: Lozhkin, S.A., Kinzhikeyeva, D.S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Kazan Federal University 01.01.2020
Schlagworte:
basis {& ∨}
boolean circuits
complexity and depth minimization
step boolean functions
structure of minimal circuits
ISSN:2541-7746, 2500-2198
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The step Boolean function is a function of the algebra of logic of n Boolean variables, n = 1, 2, … , reducing to 1 on all of the sets of an n -dimensional unit cube, the ordinal numbers of which are not lower than the given set. In this paper, the problem of synthesis of circuits over the basis {&, ∨} realizing step Boolean functions was considered. The optimized structure of the given circuits was studied with regard to complexity and depth. Step functions often appear in theoretical and applied tasks as an auxiliary subfunctions. For instance, an n- bit adder contains such a subfunction.
ISSN:2541-7746
2500-2198
DOI:10.26907/2541-7746.2020.3.335-349