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A new parallel vector model, with exact characterizations of NC k
 in Proc. 11th Annual Symposium on Theoretical Aspects of Computer Science
, 1994
"... This paper develops a new and natural parallel vector model, and shows that for all k ≥ 1, the languages recognizable in O(log k n) time and polynomial work in the model are exactly those in NC k. Some improvements to other simulations in parallel models and reversal complexity are given. 1 ..."
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Cited by 5 (4 self)
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This paper develops a new and natural parallel vector model, and shows that for all k ≥ 1, the languages recognizable in O(log k n) time and polynomial work in the model are exactly those in NC k. Some improvements to other simulations in parallel models and reversal complexity are given. 1
LinearTime Algorithms in Memory Hierarchies
, 1994
"... This paper studies lineartime algorithms on a hierarchical memory model called Block Move (BM), which extends the Block Transfer (BT) model of Aggarwal, Chandra, and Snir, and which is more stringent than a pipelining model studied recently by Luccio and Pagli. Upper and lower bounds are shown for ..."
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This paper studies lineartime algorithms on a hierarchical memory model called Block Move (BM), which extends the Block Transfer (BT) model of Aggarwal, Chandra, and Snir, and which is more stringent than a pipelining model studied recently by Luccio and Pagli. Upper and lower bounds are shown for various dataprocessing primitives, and some interesting open problems are given. 1 Introduction Recent years have seen marked dissatisfaction with the computational realism of the classic machine models, such as Turing machines or the standard integer RAM (see [13, 12]). Many algorithms that theoretically run in linear time on the RAM scale nonlinearly when it comes time to implement them. Cook [5, 6] proposed replacing the usual unitcost RAM measure by the logcost criterion, by which an operation that reads an integer i stored at address a is charged log i+log a time units. Aggarwal, Alpern, Chandra, and Snir [1] went further by introducing a parameter ¯ : N ! N called a memory access...
Descriptive Complexity, Lower Bounds and Linear Time
 In Proceedings of the 12th International Workshop on Computer Science Logic (CSL’98
, 1998
"... This paper surveys two related lines of research: ffl Logical characterizations of (nondeterministic) linear time complexity classes, and ffl nonexpressibility results concerning sublogics of existential secondorder logic. Starting from Fagin's fundamental work there has been steady progress in ..."
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This paper surveys two related lines of research: ffl Logical characterizations of (nondeterministic) linear time complexity classes, and ffl nonexpressibility results concerning sublogics of existential secondorder logic. Starting from Fagin's fundamental work there has been steady progress in both fields with the effect that the weakest logics that are used in characterizations of linear time complexity classes are closely related to the strongest logics for which inexpressibility proofs for concrete problems have been obtained. The paper sketches these developments and highlights their connections as well as the obstacles that prevent us from closing the remaining gap between both kinds of logics. 1 Introduction The theory of computational complexity is quite successful in classifying computational problems with respect to their intrinsic consumption of ressources. Unfortunately it is until now much less successful in proving that the complexity classes that are used for these...
On superlinear lower bounds in complexity theory
 In Proc. 10th Annual IEEE Conference on Structure in Complexity Theory
, 1995
"... This paper first surveys the neartotal lack of superlinear lower bounds in complexity theory, for “natural” computational problems with respect to many models of computation. We note that the dividing line between models where such bounds are known and those where none are known comes when the mode ..."
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This paper first surveys the neartotal lack of superlinear lower bounds in complexity theory, for “natural” computational problems with respect to many models of computation. We note that the dividing line between models where such bounds are known and those where none are known comes when the model allows nonlocal communication with memory at unit cost. We study a model that imposes a “fair cost ” for nonlocal communication, and obtain modest superlinear lower bounds for some problems via a Kolmogorovcomplexity argument. Then we look to the larger picture of what it will take to prove really striking lower bounds, and pull from ours and others’ work a concept of information vicinity that may offer new tools and modes of analysis to a young field that rather lacks them.
Algebraic and Logical Characterizations of Deterministic Linear Time Classes
 In Proc. 14th Symposium on Theoretical Aspects of Computer Science STACS 97
, 1996
"... In this paper an algebraic characterization of the class DLIN of functions that can be computed in linear time by a deterministic RAM using only numbers of linear size is given. This class was introduced by Grandjean, who showed that it is robust and contains most computational problems that are usu ..."
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In this paper an algebraic characterization of the class DLIN of functions that can be computed in linear time by a deterministic RAM using only numbers of linear size is given. This class was introduced by Grandjean, who showed that it is robust and contains most computational problems that are usually considered to be solvable in deterministic linear time. The characterization is in terms of a recursion scheme for unary functions. A variation of this recursion scheme characterizes DLINEAR, the class which allows polynomially large numbers. A second variation defines a class that still contains DTIME(n), the class of functions that are computable in linear time on a Turing machine. From these algebraic characterizations, logical characterizations of DLIN and DLINEAR as well as complete problems (under DTIME(n) reductions) are derived. 1 Introduction Although deterministic linear time is a frequently used notion in the theory of algorithms it still does not have a universally accept...