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Theoretical Computer Science
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The complexity of the parity function in unbounded fan-in, unbounded depth circuits

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1991 English Publisher:Elsevier BVJournal:Theoretical Computer Science, volume 85, pages 155-170 (issn: 0304-3975, Copyright policy )
Authors: Ingo Wegener;

doi: 10.1016/0304-3975(91)90052-4

The complexity of the parity function in unbounded fan-in, unbounded depth circuits

Abstract

An involved study of the complexity of the parity function \(f_ n\) of \(n\) variables realised by unbounded fan-in Boolean circuits is presented. The number of gates of a circuit is considered as the main complexity measure, but the number of wires is also investigated in some cases. Several optimal and almost optimal (lower and upper) bounds on the complexity of \(f_ n\) for distinct bases are established. The proof techniques used include several nice ideas, and are interesting for everybody working in Boolean function complexity theory.

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Keywords

unbounded fan-in Boolean circuits, Analysis of algorithms and problem complexity, Switching theory, application of Boolean algebra; Boolean functions, Boolean function complexity theory, complexity measure, complexity of the parity function, Theoretical Computer Science, Computer Science(all)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
20
Top 10%
Top 10%
Average
hybrid