# P-Selective Sets, Tally Languages, and the Behavior of Polynomial Time Reducibilities on NP

@inproceedings{Selman1979PSelectiveST,
title={P-Selective Sets, Tally Languages, and the Behavior of Polynomial Time Reducibilities on NP},
author={Alan L. Selman},
booktitle={ICALP},
year={1979}
}
• A. Selman
• Published in ICALP 16 July 1979
• Mathematics, Computer Science
The notion of p-selective sets, and tally languages, are used to study polynomial time reducibilities on NP. P-selectivity has the property that a set A belongs to the class P if and only if both A NP A and A is p-selective. We prove that for m every tally language set in NP there exists a polynomial time equivalent set in NP that is p-selective. From this result it follows that if NEXT ~ DEXT , then polynomial time Turing and many-one reducibilities differ on NP.

#### Topics from this paper

On sets turing reducible to p-selective sets
• Computer Science, Mathematics
• Theory of Computing Systems
• 2007
It is shown that EXP cannot be reduced to the p-selective sets under 2lin time reductions with at mostnk queries for any fixed k ε N. Expand
Selectivity: Reductions, Nondeterminism, and Function Classes 1
A set is P-selective [Sel79] if there is a polynomial-time semi-decision algorithm for the set|an algorithm that given any two strings decides which is \more likely" to be in the set. This paperExpand
Polynomial-Time Semi-Rankable Sets
• Mathematics
• 1996
We study the polynomial-time semi-rankable sets (P-sr), the ranking analog of the P-selective sets. We prove that P-sr is a strict subset of the P-selective sets, and indeed that the two classesExpand
Polynomial-Time Semi-Rankable
We study the polynomial-time semi-rankable sets (P-sr), the ranking analog of the P-selective sets. We prove that P-sr is a strict subset of the P-selective sets, and indeed that the two classesExpand
On Self-Reducibility and Weak P-Selectivity
• K. Ko
• Computer Science, Mathematics
• J. Comput. Syst. Sci.
• 1983
It is proved that self-reducible sets are not polynomial-time Turing reducible to these sets, and weakly p -selective sets are introduced as a generalization of p - selective sets based on this characterization. Expand
Nondeterministically Selective Sets
NP-selective sets (formally, sets that are selective via NPSVt functions) are studied as a natural generalization of P-selectives, and it is shown that, assuming P≠NP∩coNP, the class of NP- selective sets properly contains the class that is implicit in Karp and Lipton’s seminal result on nonuniform classes. Expand
Selectivity and Self-reducibility: New Characterizations of Complexity Classes
It is known that a set is in P ii it is p-time Turing self-reducible and p-selective 2] and a p-time Turing self-reducible set is in NP \ coNP ii it is NP-selective 4]. We generalize these newExpand
Approximable sets
• Computer Science
• Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory
• 1994
In a relativized world, a d-self-reducible set in NP-P is constructed that is polynomial-time 2-tt reducible to a p-selective set, and no easily countable set is NP-hard under Turing reductions unless P=NP. Expand
Analogues of Semicursive Sets and Effective Reducibilities to the Study of NP Complexity
• A. Selman
• Computer Science, Mathematics
• Inf. Control.
• 1982
The structure of NP <~-degrees is similar to the one of r, and the reducibilities formulated by Cook (1971) and Karp (1973) are just the restrictions to polynomial time of Turing and many-one reducibility, respectively. Expand
Approximable Sets Universitt at Karlsruhe
Much structural work on NP-complete sets has exploited SAT's d-self-reduci-bility. In this paper we exploit the additional fact that SAT is a d-cylinder to show that NP-complete sets are p-superterseExpand

#### References

SHOWING 1-10 OF 13 REFERENCES
On the Structure of Polynomial Time Reducibility
• Mathematics, Computer Science
• JACM
• 1975
The method of showing density ymlds the result that if P ~ NP then there are members of NP -P that are not polynomml complete is shown, which means there is a strictly ascending sequence with a minimal pair of upper bounds to the sequence. Expand
Relationship Between Density and Deterministic Complexity of NP-Complete Languages
The main theorem of this paper establishes that if CLIQUE has some f-sparse translation into another set, which is calculable by a deterministic Turing machine in time bounded by f, then all the sets belonging to NP are calculable in time bound by a function polynomially related to f. Expand
On Languages Accepted in Polynomial Time
• R. V. Book
• Mathematics, Computer Science
• SIAM J. Comput.
• 1972
The family NP (P) of languages accepted by nondeterministic (deterministic) Turing machines operating in polynomial time is distinct from many well-known families of languages defined by tape-boundedExpand
Tally Languages and Complexity Classes
The following statements are shown to be equivalent: (i) Every language accepted by a nondeterministic Turing machine which operates within time bound 2 cn for some c > 0 is also accepted by aExpand
Comparing Complexity Classes
• R. V. Book
• Computer Science, Mathematics
• J. Comput. Syst. Sci.
• 1974
The results do not establish the existence of possible relationships between these classes; rather, they show the consequences of such relationships, in some cases offering circumstantial evidence that these relationships do not hold and that certain pairs of classes are set-theoretically incomparable. Expand
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
Turing Machines and the Spectra of First-Order Formulas
• Computer Science
• 1974
It is shown that spectra and context sensitive languages are closely related, and that their open questions are merely special cases of a family of open questions which relate to the difference between deterministic and nondeterministic time or space bounded Turing machines. Expand
Every Prime has a Succinct Certificate
• 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 $\alpha$. Expand
Characterizations of Pushdown Machines in Terms of Time-Bounded Computers
A class of machines called auxiliary pushdown machines is introduced, characterized in terms of time-bounded Turing machines, and corollaries are derived which answer some open questions in the field. Expand
A Comparison of Polynomial Time Reducibilities
• Computer Science, Mathematics
• Theor. Comput. Sci.
• 1975
Abstract Various forms of polynomial time reducibility are compared. Among the forms examined are many-one, bounded truth table, truth table and Turing reducibility. The effect of introducingExpand