Polynomial Terse Sets

A. Amihood; W. I .Gasarch

Polynomial Terse Sets

A. Amihood
, W. I .Gasarch

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Let A be a set and k ∈ N be such that we wish to know the answers to x1 ∈ A?, x2 ∈ A?, …, xk ∈ A? for various k-tuples 〈x1, x2, …, xk〉. If this problem requires k queries to A in order to be solved in polynomial time then A is called polynomial terse or pterse. We show the existence of both arbitrarily complex pterse and non-pterse sets; and that P ≠ NP iff every NP-complete set is pterse. We also show connections with p-immunity, p-selective, p-generic sets, and the boolean hierarchy. In our framework unique satisfiability (and a variation of it called kSAT is, in some sense, “close” to satisfiability.

Original language	American English
Title of host publication	2nd Annual Structure in Complexity Theory Conference (STRUCTURES)
State	Published - 1987

Bibliographical note

Place of conference:Ithaca, New York

Cite this

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title = "Polynomial Terse Sets",

abstract = "Let A be a set and k ∈ N be such that we wish to know the answers to x1 ∈ A?, x2 ∈ A?, …, xk ∈ A? for various k-tuples 〈x1, x2, …, xk〉. If this problem requires k queries to A in order to be solved in polynomial time then A is called polynomial terse or pterse. We show the existence of both arbitrarily complex pterse and non-pterse sets; and that P ≠ NP iff every NP-complete set is pterse. We also show connections with p-immunity, p-selective, p-generic sets, and the boolean hierarchy. In our framework unique satisfiability (and a variation of it called kSAT is, in some sense, “close” to satisfiability.",

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AU - .Gasarch, W. I

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N2 - Let A be a set and k ∈ N be such that we wish to know the answers to x1 ∈ A?, x2 ∈ A?, …, xk ∈ A? for various k-tuples 〈x1, x2, …, xk〉. If this problem requires k queries to A in order to be solved in polynomial time then A is called polynomial terse or pterse. We show the existence of both arbitrarily complex pterse and non-pterse sets; and that P ≠ NP iff every NP-complete set is pterse. We also show connections with p-immunity, p-selective, p-generic sets, and the boolean hierarchy. In our framework unique satisfiability (and a variation of it called kSAT is, in some sense, “close” to satisfiability.

AB - Let A be a set and k ∈ N be such that we wish to know the answers to x1 ∈ A?, x2 ∈ A?, …, xk ∈ A? for various k-tuples 〈x1, x2, …, xk〉. If this problem requires k queries to A in order to be solved in polynomial time then A is called polynomial terse or pterse. We show the existence of both arbitrarily complex pterse and non-pterse sets; and that P ≠ NP iff every NP-complete set is pterse. We also show connections with p-immunity, p-selective, p-generic sets, and the boolean hierarchy. In our framework unique satisfiability (and a variation of it called kSAT is, in some sense, “close” to satisfiability.

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M3 - Conference contribution

BT - 2nd Annual Structure in Complexity Theory Conference (STRUCTURES)

ER -

Polynomial Terse Sets

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Bibliographical note

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