Upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
Properties of complexity measures for prams and wrams
Theoretical Computer Science
Limits on the power of concurrent-write parallel machines
Information and Computation
Improved upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
SIAM Journal on Computing
On the degree of Boolean functions as real polynomials
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On the degree of polynomials that approximate symmetric Boolean functions (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Parallel Retrieval of Scattered Information
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Generic oracles and oracle classes
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Constant depth circuits, Fourier transform, and learnability
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Polynomial threshold functions, AC functions and spectrum norms
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Lower bounds for randomized exclusive write PRAMs
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
Computational bounds for fundamental problems on general-purpose parallel models
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
On the power of Las Vegas for one-way communication complexity, OBDDs, and finite automata
Information and Computation
Approximate Compaction and Padded-Sorting on Exclusive Write PRAMs
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
On the Power of Las Vegas II. Two-Way Finite Automata
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
On the Power of Randomized Pushdown Automata
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Gossiping and broadcasting versus computing functions in networks
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
On the power of nondeterminism and Las Vegas randomization for two-dimensional finite automata
Journal of Computer and System Sciences
On the power of randomized multicounter machines
Theoretical Computer Science - Insightful theory
Complementing two-way finite automata
Information and Computation
Pushdown automata and multicounter machines, a comparison of computation modes
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
On probabilistic pushdown automata
Information and Computation
Complementing two-way finite automata
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
Lower Bounds for Randomized Exclusive Write PRAMs
Theory of Computing Systems
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The time complexity of Boolean functions on abstract concurrent-read exclusive-write parallel random access machines (CREW PRAMs) is considered. We improve results of Cook, Dwork, and Reischuk (SIAM J. Comput.15 (1986), 87-97), and extend work of Kutylowski (SIAM J. Comput.20 (1991), 824-833), who proved a lower time bound for the OR function on such machines that equals the upper bound. We provide a general means for obtaining exact (i.e., correct up to an additive constant) lower bounds, which works for many Boolean functions, in particular all symmetric functions. The new approach is based on the fact that Boolean functions can be represented as polynomials with integer coefficients and that the degree of such a polynomial can be taken as a complexity measure. For some functions, e.g., AND and PARITY, the exact time bound also holds for nondeterministic machines. For probabilistic machines, we obtain exact lower time bounds for PARITY in the unbounded error model and, utilizing results by Szegedy (Ph.D. dissertation, University of Chicago, 1989), prove a general lower bound valid for all Boolean functions in the bounded error model. We further show that the (bounded error) probabilistic time complexity of Boolean functions on CREW PRAMs differs at most by a constant factor from the deterministic time complexity. We also obtain exact bounds for machines that allow a few processors to try to write to the same cell simultaneously. These bounds are stronger than those which follow automatically from the exclusive-write bounds. No tight bounds for this model were known before.