Dynamic Word Problems

Let M be a fixed finite monoid. We consider the problem of implementing a data type containing a vector x ϭ ( x1, x2, . . . , xn) ʦ Mn , initially (1, 1, . . . , 1), with two kinds of operations, for each i ʦ {1, . . . , n} and a ʦ M, an operation changei,a which changes xi to a and a single operation product returning ͟iϭ1 n xi. This is the dynamic word problem for M. If we in addition for each j ʦ {1, . . . , n} have an operation prefixj returning ͟iϭ1 j xi, we get the dynamic prefix problem for M. 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 partial classification of the complexity based on algebraic properties of M.

• Type: Conference
• Year: 1993
• Where: FOCS
• Authors: Gudmund Skovbjerg Frandsen, Peter Bro Miltersen, Sven Skyum
• Keywords: Dynamic Prefix Problem, Dynamic Word Problem, FOCS 1993, Single Operation Product, Theoretical Computer Science