TY - GEN

T1 - Polynomial Terse Sets

AU - Amihood, A.

AU - .Gasarch, W. I

N1 - Place of conference:Ithaca, New York

PY - 1987

Y1 - 1987

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.

UR - https://scholar.google.co.il/scholar?q=Polynomial+Terse+Sets&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

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

ER -