TY - JOUR

T1 - Language complexity on the synchronous anonymous ring

AU - Attiya, Hagit

AU - Mansour, Yishay

PY - 1987

Y1 - 1987

N2 - A set of n nondistinct processors, organized as a ring and operating synchronously, have to compute a function of their initial values. Every computable function can be computed with O(n log n) messages, while some functions can be computed with as few as O(n) messages. We prove a necessary and sufficient condition for a regular language to be recognized with O(n) messages. Languages that do not satisfy this condition are 'hard' to compute, i.e., their recognition requires Ω(n log n) message. The condition is an extension of the notion of counter-free regular languages. These results give a gap theorem for recognizing regular languages on the synchronous anonymous ring. In contrast, we show a family of nonregular languages, computing thresholds, that obtain any intermediate complexity in the range Θ{round}(n) to Θ{round}(n log n).

AB - A set of n nondistinct processors, organized as a ring and operating synchronously, have to compute a function of their initial values. Every computable function can be computed with O(n log n) messages, while some functions can be computed with as few as O(n) messages. We prove a necessary and sufficient condition for a regular language to be recognized with O(n) messages. Languages that do not satisfy this condition are 'hard' to compute, i.e., their recognition requires Ω(n log n) message. The condition is an extension of the notion of counter-free regular languages. These results give a gap theorem for recognizing regular languages on the synchronous anonymous ring. In contrast, we show a family of nonregular languages, computing thresholds, that obtain any intermediate complexity in the range Θ{round}(n) to Θ{round}(n log n).

UR - http://www.scopus.com/inward/record.url?scp=0023538151&partnerID=8YFLogxK

U2 - 10.1016/0304-3975(87)90062-4

DO - 10.1016/0304-3975(87)90062-4

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AN - SCOPUS:0023538151

SN - 0304-3975

VL - 53

SP - 169

EP - 185

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 2-3

ER -