TY - GEN

T1 - Some connections between bounded query classes and nonuniform complexity

AU - Amihood, A.

AU - Beigel, Richard

AU - Gasarch, William I.

N1 - Place of conference:Barcelona, Spain

PY - 1990

Y1 - 1990

N2 - It is shown that if there is a polynomial-time algorithm that tests k(n)=O(log n) points for membership in a set A by making only k(n)-1 adaptive queries to an oracle set X, then A belongs to NP/poly intersection co-NP/poly (if k(n)=O(1) then A belong to P/poly). In particular, k(n)=O(log n) queries to an NP-complete set (k(n)=O(1) queries to an NP-hard set) are more powerful than k(n)-1 queries, unless the polynomial hierarchy collapses. Similarly, if there is a small circuit that tests k(n) points for membership in A by making only k(n)-1 adaptive queries to a set X, then there is a correspondingly small circuit that decides membership in A without an oracle. An investigation is conducted of the quantitatively stronger assumption that there is a polynomial-time algorithm that tests 2/sup k/ strings for membership in A by making only k queries to an oracle X, and qualitatively stronger conclusions about the structure of A are derived: A cannot be self-reducible unless A in P, and A cannot be NP-hard unless P=NP. Similar results hold for counting classes. In addition, relationships between bounded-query computations, lowness, and the p-degrees are investigated.

AB - It is shown that if there is a polynomial-time algorithm that tests k(n)=O(log n) points for membership in a set A by making only k(n)-1 adaptive queries to an oracle set X, then A belongs to NP/poly intersection co-NP/poly (if k(n)=O(1) then A belong to P/poly). In particular, k(n)=O(log n) queries to an NP-complete set (k(n)=O(1) queries to an NP-hard set) are more powerful than k(n)-1 queries, unless the polynomial hierarchy collapses. Similarly, if there is a small circuit that tests k(n) points for membership in A by making only k(n)-1 adaptive queries to a set X, then there is a correspondingly small circuit that decides membership in A without an oracle. An investigation is conducted of the quantitatively stronger assumption that there is a polynomial-time algorithm that tests 2/sup k/ strings for membership in A by making only k queries to an oracle X, and qualitatively stronger conclusions about the structure of A are derived: A cannot be self-reducible unless A in P, and A cannot be NP-hard unless P=NP. Similar results hold for counting classes. In addition, relationships between bounded-query computations, lowness, and the p-degrees are investigated.

UR - https://scholar.google.co.il/scholar?q=Some+Connections+between+Bounded+Query+Classes+and+Non-Uniform+Complexity&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

BT - Structure in Complexity Theory Conference, 1990, Proceedings., Fifth Annual

PB - IEEE

ER -