# On the Structure of Polynomial Time Reducibility

@article{Ladner1975OnTS,
title={On the Structure of Polynomial Time Reducibility},
journal={J. ACM},
year={1975},
volume={22},
pages={155-171}
}
Two notions of polynomml time reduclbihty, denoted here by ~ T e and <.~P, were defined by Cook and Karp, respectively The abstract propertms of these two relatmns on the domain of computable sets are investigated. Both relations prove to be dense and to have minimal pairs. Further , there is a strictly ascending sequence with a minimal pair of upper bounds to the sequence. Our method of showing density ymlds the result that if P ~ NP then there are members of NP -P that are not polynomml…
757 Citations
• A. Selman
• Mathematics
Mathematical systems theory
• 2005
It is proved that for every tally language set in NP there exists a polynomial time equivalent set inNP that isp-selective, and it follows that if NEXT ≠ DEXT, then polynometric time Turing and many-one reducibilities differ onNP.
It is proved that for m every tally language set in NP there exists a polynomial time equivalent set inNP that is p-selective, and from this result it follows that if NEXT ~ DEXT, then polynometric time Turing and many-one reducibilities differ on NP.
• K. Ambos-Spies
• Mathematics, Computer Science
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It is shown that any class, which in the relativized case collapses to P with probability one, is actually contained in BPP, the class of problems which can be probabilisticly solved with uniformly bounded error probability in polynomial time.
• Computer Science
• 1993
In the setting of the parametrized reducibilities introduced by the second author and Mike Fellows, we prove a number of decidability and definability results. In particular the undecidability of the
It is shown that for every recursive set A∉P there is a recursive set B such that A and B form a minimal pair and similar results for pairs without greatest predecessors are proved.
A polynomial time enumeration reducibility is defined that retains the character of enumeration Redux and it is shown that it is equivalent to conjunctive non‐deterministic polynometric time reducible.
• Philosophy
Mathematical systems theory
• 2005
The method used is applicable to questions regarding the comparison of a wide range of pairs of classes of formal languages specified by machines whose computational resources are bounded in time or space.

## References

SHOWING 1-10 OF 28 REFERENCES

• Computer Science
STOC '74
• 1974
Comparison of the polynomial-time-bounded reducibilities introduced by Cook [1] and Karp] leads naturally to the definition of several intermediate truth-tableredcibilities, and it is noted that all redu cibilities of this type which do not have obvious implication relationships are in fact distinct in a strong sense.
• S. Cook
• Mathematics, Computer Science
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 a
• V. Pratt
• Mathematics, Computer Science
SIAM J. Comput.
• 1975
It remains an open problem whether a prime n can be recognized in only $\log _2^\alpha n$ operations of a Turing machine for any fixed $\alpha$.
• Computer Science
• 1954
The concept 'degree of recursive unsolvability' was introduced briefly in Post [16]. In his abstract [17] the concept was formulated precisely via an extension of [15], and a resulting partial scale
• Computer Science, Mathematics
STOC
• 1973
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.
Introduction. Recent developments of symbolic logic have considerable importance for mathematics both with respect to its philosophy and practice. That mathematicians generally are oblivious to the
Kleene makes a new attempt at a classification of general recursive functions, by using the notion of relative primitive recursiveness and of the uniform effective enumerability of the functions primitive recursive in an assumed function.
A sequence of classes of computable functions for which a prediction of the complexity of the calculation may be made in a comparatively simple fashion, each defined as the class of functions whose computational complexity is "predictable" by a function in the preceding class.
• Mathematics
SWAT
• 1969
D density is not a measure invariant property of ΣΦ or ΩΦ, but ΩL is not dense in ΣL, and these are the first examples of important structural properties of these families of Φ-complexity classes which are not measure invariants.