A Survey of Russian Approaches to Perebor (Brute-Force Searches) Algorithms
@article{Trakhtenbrot1984ASO,
title={A Survey of Russian Approaches to Perebor (Brute-Force Searches) Algorithms},
author={Boris A. Trakhtenbrot},
journal={Annals of the History of Computing},
year={1984},
volume={6},
pages={384-400}
}Concerns about computational problems requiring brute-force or exhaustive search methods have gained particular attention in recent years because of the widespread research on the "P = NP?" question. The Russian word for "brute-force search" is "perebor. " It has been an active research area in the Soviet Union for several decades. Disputes about approaches to perebor had a certain influence on the development, and developers, of complexity theory in the Soviet Union. This paper is a personal…
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References
SHOWING 1-10 OF 67 REFERENCES
A Logical Approach to the Problem "P=NP?"
- MathematicsMFCS
- 1980
The Main Result of this paper states, for some natural theory T, unprovability of the assertion on exponential lower time complexity bound of acceptin6 NP-sets.
The consistency of "P = NP" and related problems with fragments of number theory
- MathematicsSTOC '80
- 1980
The main results of this paper demonstrate the consistency of “P &equil; NP” and a variant of “NP @@@@ coNP” with certain natural fragments of number theory to be defined precisely in the sequel.@@@@…
The complexity of theorem-proving procedures
- Mathematics, Computer ScienceSTOC
- 1971
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a…
Observations about the development of theoretical computer science
- Education20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
- 1979
A personal account of some developments in automata theory and computational complexity theory and discusses the underlying beliefs and philosophy which guided this research as well as the intellectual environment and the ideas and contacts which influenced it.
THE COMPLEXITY OF FINITE OBJECTS AND THE DEVELOPMENT OF THE CONCEPTS OF INFORMATION AND RANDOMNESS BY MEANS OF THE THEORY OF ALGORITHMS
- Computer Science
- 1970
The present article is a survey of the fundamental results connected with the concept of complexity as the minimum number of binary signs containing all the information about a given object that are sufficient for its recovery (decoding).
Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question
- Mathematics, Computer Science
- 1975
Relativized versions of the open question of whether every language accepted nondeterministically in polynomial time can be recognized deterministic in poynomial time are investigated.

