 
Summary: The Bit Complexity of the Predecessor
Problem
Y. Afek, M. Cohen, E. Haalman
Computer Science Department
TelAviv University
Israel 69978
Abstract
Tight bound of 2n \Gamma 1 bits on the communication complexity of ``The Pre
decessor'' problem in a synchronous ring (previously known as ``The last in
a synchronous ring'' problem) is presented.
Key Words: Distributed Computing, Unidirectional, Anonymous Ring.
1 Introduction
In [6] the following question, which we call the ``predecessor problem'', in
distributed computing on a unidirectional ring was raised: In a unidirec
tional ring of finite automata, design an algorithm by which a designated
node, v, distinguishes the node preceding it from all other nodes. A solu
tion to the predecessor problem plays a key roll in distributed algorithms for
unidirectional networks. In particular it serves as a basic building block in
algorithms for Depth First Search [1], Leader Election [6], Firing Squad Syn
chronization [4, 8], and recently for selfstabilization in Unidirectional rings
