A direct version of Shamir and Snir's lower bounds on monotone circuit depth

We present direct proofs of the following results of Shamir and Snir [Mathematical System Theory 13 (1980) 301-322] on the depth of monotone arithmetic circuits over rings of characteristic 0: (1) an ω((log p)(log n)) lower bound for computing the product of p n × n matrices; and (2) an ω( n) lower...

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Bibliographic Details
Published inInformation processing letters Vol. 49; no. 5; pp. 243 - 248
Main Authors Tiwari, Prasoon, Tompa, Martin
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 11.03.1994
Elsevier Science
Elsevier Sequoia S.A
Subjects
Algorithms
Applied sciences
Arithmetic circuits
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Exact sciences and technology
Formula depth
Information processing
Parallel algorithms
Software
Studies
Theory
Formula depth
Parallel algorithms
Arithmetic circuits
Parallelism
Parallel algorithm
Arithmetic circuit
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Summary:We present direct proofs of the following results of Shamir and Snir [Mathematical System Theory 13 (1980) 301-322] on the depth of monotone arithmetic circuits over rings of characteristic 0: (1) an ω((log p)(log n)) lower bound for computing the product of p n × n matrices; and (2) an ω( n) lower bound for computing the permanent of an n × n matrix.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0020-0190
1872-6119
DOI:10.1016/0020-0190(94)90061-2