TY - GEN

T1 - On the bit complexity of distributed computations in a ring with a leader

AU - Mansour, Y.

AU - Zaks, S.

N1 - Publisher Copyright:
© 1986 ACM.

PY - 1986/11/1

Y1 - 1986/11/1

N2 - We study the bit complexity of pattern recognition in a distributed ring with a leader. Each processor gets as input a letter from some alphabet, and these concatenated letters, starting at the leader, form the pattern of the ring. The leader initiates an algorithm that accepts or rejects this pattern. Thus each algorithm recognizes a language over a given alphabet. We prove the following (n is the size of the ring, not known a priori to any of the processors): (1) A language is recognized by an algorithm that uses O(n) bits if and only if it is regular. (2) Every non-regular language requires at least Ω(n logn) bits for its recognition (clearly, every language requires no more than O(n2) bits for its recognition). (3) For every function g(n), Ω.(n logn)≤g(n)≤O(n2), there is a language that requires Θ(g(n)) bits for its recognition.

AB - We study the bit complexity of pattern recognition in a distributed ring with a leader. Each processor gets as input a letter from some alphabet, and these concatenated letters, starting at the leader, form the pattern of the ring. The leader initiates an algorithm that accepts or rejects this pattern. Thus each algorithm recognizes a language over a given alphabet. We prove the following (n is the size of the ring, not known a priori to any of the processors): (1) A language is recognized by an algorithm that uses O(n) bits if and only if it is regular. (2) Every non-regular language requires at least Ω(n logn) bits for its recognition (clearly, every language requires no more than O(n2) bits for its recognition). (3) For every function g(n), Ω.(n logn)≤g(n)≤O(n2), there is a language that requires Θ(g(n)) bits for its recognition.

UR - http://www.scopus.com/inward/record.url?scp=85031731456&partnerID=8YFLogxK

U2 - 10.1145/10590.10603

DO - 10.1145/10590.10603

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AN - SCOPUS:85031731456

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 151

EP - 160

BT - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 5th Annual ACM Symposium on Principles of Distributed Computing, PODC 1986

Y2 - 11 August 1986 through 13 August 1986

ER -