Locally computable coding for unary operations

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Abstract

Coding plays an important role in the design of parallel algorithms. When each digit of a result of a desired operation depends only on a part of digits of operands under a coding scheme, we say the operation is locally computable under the coding scheme. There is a closed relation between local computability and redundancy of codes. Several excellent algorithms utilizing local computability by redundant coding schemes are developed and used practically. The problem to examine the relation among coding schemes, local computability and algebraic structures of target operations is a basic problem on the design of parallel algorithms. In this paper, we discuss a relation between redundancy of coding schemes and local computability of unary operations defined on finite sets. We show that it is generally impossible to realize local computability by nonredundant coding schemes. If we introduce redundancy into coding, we can construct a coding under which every digit of a result depends only on 2 digits of an operand for any unary operations. These results are closely related with a state assignment problem of finite state machines. The above 2-locally computable coding derives a state assignment of a pipelined sequential circuit for an arbitrary sequential machine.

Original languageEnglish
Title of host publicationConcurrency
Subtitle of host publicationTheory, Language, and Architecture - UK/Japan Workshop, Proceedings
EditorsTakayasu Ito, Akinori Yonezawa
PublisherSpringer Verlag
Pages312-323
Number of pages12
ISBN (Print)9783540464525
DOIs
Publication statusPublished - Jan 1 1991
Externally publishedYes
EventUK/Japan Workshop on Concurrency Theory, 1989 - Oxford, United Kingdom
Duration: Sep 25 1989Sep 27 1989

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume491 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherUK/Japan Workshop on Concurrency Theory, 1989
CountryUnited Kingdom
CityOxford
Period9/25/899/27/89

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yasuura, H. (1991). Locally computable coding for unary operations. In T. Ito, & A. Yonezawa (Eds.), Concurrency: Theory, Language, and Architecture - UK/Japan Workshop, Proceedings (pp. 312-323). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 491 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-53932-8_58