On the Structure of Polynomial Time Reducibility
@article{Ladner1975OnTS,
title={On the Structure of Polynomial Time Reducibility},
author={Richard E. Ladner},
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…
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References
SHOWING 1-10 OF 28 REFERENCES
Comparison of polynomial-time reducibilities
- Computer ScienceSTOC '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.
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…
Every Prime has a Succinct Certificate
- Mathematics, Computer ScienceSIAM 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 $.
Augmented Loop Languages and Classes of Computables Functions
- Mathematics, Computer ScienceJ. Comput. Syst. Sci.
- 1972
The Upper Semi-Lattice of Degrees of Recursive Unsolvability
- 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…
Word problems requiring exponential time(Preliminary Report)
- Computer Science, MathematicsSTOC
- 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.
Recursively enumerable sets of positive integers and their decision problems
- Mathematics
- 1944
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…
On a subrecursive hierarchy and primitive recursive degrees
- Computer Science
- 1959
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.
CLASSES OF PREDICTABLY COMPUTABLE FUNCTIONS
- Mathematics, Computer Science
- 1963
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.
Dense and Non-Dense Families of Complexity Classes
- MathematicsSWAT
- 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.