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Dynamic word problems

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3 Author(s)
Frandsen, G.S. ; Dept. of Comput. Sci., Aarhus Univ., Denmark ; Miltersen, P.B. ; Skyum, S.

Let M be a fixed finite monoid. We consider the problem of implementing a data type containing a vector x=(x1,x2 ,...,xn)∈Mn, initially (1,1,...,1) with two kinds of operations, for each i∈{1,...,n}, a∈M, an operation changei,a which changes xi to a and a single operation product returning Πi=1nxi . This is the dynamic word problem. If we in addition for each j∈{1,...,n} have an operation prefixj returning Πi=1jxi, we talk about the dynamic prefix problem. We analyze the complexity of these problems in the cell probe or decision assignment tree model for two natural cell sizes, 1 bit and log n bits. We obtain a classification of the complexity based on algebraic properties of M

Published in:

Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on

Date of Conference:

3-5 Nov 1993

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