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...

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Published in:Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki Vol. 162; no. 3; pp. 335 - 349
Main Authors: Lozhkin, S.A., Kinzhikeyeva, D.S.
Format: Journal Article
Language:English
Published: Kazan Federal University 01.01.2020
Subjects:
basis {& ∨}
boolean circuits
complexity and depth minimization
step boolean functions
structure of minimal circuits
ISSN:2541-7746, 2500-2198
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Abstract 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.
AbstractList 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.
Author Lozhkin, S.A.
Kinzhikeyeva, D.S.
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SubjectTerms basis {& ∨}
boolean circuits
complexity and depth minimization
step boolean functions
structure of minimal circuits
Title On the Structure, Complexity, and Depth of the Circuits over the Basis {&, ∨} Realizing Step Boolean Functions
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