The recognition problem for the set of perfect squares

Authors:
Alan Cobham
Affiliations:
-
Venue:
SWAT '66 Proceedings of the 7th Annual Symposium on Switching and Automata Theory (swat 1966)
Year:
1966

Citing 0
Cited 9

Randomized Branching Programs

SAGA '01 Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications
Models of Computation, Riemann Hypothesis, and Classical Mathematics

SOFSEM '98 Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Nondeterministic Polynomial Time versus Nondeterministic Logarithmic Space: Time-Space Tradeoffs for Satisfiability

CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Comparison-based time-space lower bounds for selection

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
BDDs-design, analysis, complexity, and applications

Discrete Applied Mathematics
Comparison-based time-space lower bounds for selection

ACM Transactions on Algorithms (TALG)
Relationships between nondeterministic and deterministic tape complexities

Journal of Computer and System Sciences
Generic constant-round oblivious sorting algorithm for MPC

ProvSec'11 Proceedings of the 5th international conference on Provable security
Quantum and classical communication-space tradeoffs from rectangle bounds

FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Lower bounds on the capacity and on the product of capacity and computation time are obtained for machines which recognize the set of squares. The bound on capacity is approached to within a factor of four by a specific machine which carries out a test based on the fact that every non-square is a quadratic non-residue of some rational prime. A machine which carries out a test based on the standard root-extraction algorithm is substantially less efficient in this respect. For neither machine is the bound on the capacity-time product closely approached.