TY - JOUR
T1 - Polynomial terse sets
AU - Amir, Amihood
AU - Gasarch, William I.
PY - 1988/4
Y1 - 1988/4
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 - http://www.scopus.com/inward/record.url?scp=0141626517&partnerID=8YFLogxK
U2 - 10.1016/0890-5401(88)90044-2
DO - 10.1016/0890-5401(88)90044-2
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0141626517
SN - 0890-5401
VL - 77
SP - 37
EP - 56
JO - Information and Computation
JF - Information and Computation
IS - 1
ER -