Polynomial terse sets

Amihood Amir, William I. Gasarch

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


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 languageEnglish
Pages (from-to)37-56
Number of pages20
JournalInformation and Computation
Issue number1
StatePublished - Apr 1988
Externally publishedYes


Dive into the research topics of 'Polynomial terse sets'. Together they form a unique fingerprint.

Cite this