Comparison of polynomial-time reducibilities

@inproceedings{Ladner1974ComparisonOP,
  title={Comparison of polynomial-time reducibilities},
  author={Richard E. Ladner and Nancy A. Lynch and Alan L. Selman},
  booktitle={STOC '74},
  year={1974}
}
Comparison of the polynomial-time-bounded reducibilities introduced by Cook [1] and Karp [4] leads naturally to the definition of several intermediate truth-table reducibilities. We give definitions and comparisons for these reducibilities; we note, in particular, that all reducibilities of this type which do not have obvious implication relationships are in fact distinct in a strong sense. Proofs are by simultaneous diagonalization and encoding constructions. Work of Meyer and Stockmeyer [7… Expand
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  • Computer Science
  • Mathematical systems theory
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  • Mathematics, Computer Science
  • [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
  • 1988
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References

SHOWING 1-10 OF 12 REFERENCES
Polynominal time reducibility
  • R. Ladner
  • Computer Science, Mathematics
  • STOC
  • 1973
TLDR
Several of the results that appear in [4] are stated to be true of polynominal time reducibility (≤p) but are not proved explicitly but are proved with the hope of shedding some light on the “determinism vs. nondeterminism” problem. Expand
RELATIVIZATION OF THE THEORY OF COMPUTATION COMPLEXITY
Blum''s machine-independent treatment of the complexity of partial recursive functions is extended to relative algorithms (as represented by Turing machines with oracles). We prove relativizations ofExpand
The complexity of theorem-proving procedures
  • S. Cook
  • Computer Science, Mathematics
  • STOC
  • 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 aExpand
Word problems requiring exponential time(Preliminary Report)
TLDR
A number of similar decidable word problems from automata theory and logic whose inherent computational complexity can be precisely characterized in terms of time or space requirements on deterministic or nondeterministic Turing machines are considered. Expand
Theory of Recursive Functions and Effective Computability
Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular. A second group of topics has to do with generalizationsExpand
Computational Work and Time on Finite Machines
TLDR
In this paper, measures of the computational work and computational delay required by ms chines to compute functions are given and many e~ change inequalities involving storage, time, and other important parameters of computation are developed. Expand
Reducibility among combinatorial problems in log n space
  • Proceedings of Seventh Annual Princeton Conference on Information Sciences and Systems
  • 1973
Word problems requiring exponential time
  • Fifth Annual Symposium on Theory of Computing
  • 1973
Relativization of the Theorv of computational complexity
  • Relativization of the Theorv of computational complexity
  • 1972
...
1
2
...