Dynamic Word problems
Gudmund Skovbjerg Frandsen,Peter Bro Miltersen,Sven Skyum +2 more
- 01 May 1993
Vol. 22, Iss: 438
TL;DR: In this paper, the complexity of the dynamic prefix problem in the cell probe or decision assignment tree model for two natural cell sizes, 1 bit and log n bits, is analyzed.
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Abstract: Let M be a fixed finite monoid. We consider the problem of implementing a data type containing a vector x=(x_1, x_2, ..., x_n) in M^n, initially (1, 1, ..., 1) with two kinds of operations, for each i in {1, ..., n}, a in M, an operation change _{i,a} which changes x_i to a and a single operation product returning ½_{i=1}^j x_i. This is the dynamic word problem. If we in addition for each j in {1, ..., n} have an operation prefix_j returning ½_{i=1}^j x_i, 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 . f
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Citations
Optimal bounds for the predecessor problem and related problems
Paul Beame,Faith E. Fich +1 more
- 01 Aug 2002
TL;DR: The lower bounds are proved for a large class of problems, including both static and dynamic predecessor problems, in a much stronger communication game model, but they apply to the cell probe and RAM models.
Marked ancestor problems
Stephen Alstrup,Thore Husfeldt,Theis Rauhe +2 more
- 08 Nov 1998
TL;DR: The upper bounds improve algorithms from various fields, including coloured ancestor problems and maintenance of balanced parentheses and several problems from dynamic computational geometry, including segment intersection, interval maintenance, and ray shooting in the plane.
156
Temporal logic and semidirect products: an effective characterization of the until hierarchy
Denis Thérien,Thomas Wilke +1 more
- 14 Oct 1996
TL;DR: Applying deep results from finite semigroup theory, it is proved that each level of the until hierarchy is decidable.
37
Temporal Logic and Semidirect Products: An Effective Characterization of the Until Hierarchy
Denis Thérien,Thomas Wilke +1 more
TL;DR: Applying deep results from finite semigroup theory, it is proved that each level of the until hierarchy of linear temporal logic is decidable.
37
Dynamic Algorithms for the Dyck Languages
Gudmund Skovbjerg Frandsen,Thore Husfeldt,Peter Bro Miltersen,Theis Rauhe,Søren Skyum +4 more
- 16 Aug 1995
TL;DR: Both Las Vegas- and Monte Carlo-type randomised algorithms are given to achieve better running times, and lower bounds on the complexity for variants of the problems are presented.
30
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Observations on the Complexity of Generating Quasi-Gray Codes
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