Computing permanents over fields of characteristic 3: Where and why it becomes difficult

Conference · Tue Dec 31 00:00:00 EST 1996

OSTI ID:457642

Kogan, G ^[1]

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1. Technion - Israel Institute of Technology, Haifa (Israel)

In this paper we consider the complexity of computing permanents over fields of characteristic 3. We present a polynomial time algorithm for computing per(A) for a matrix A such that the rank rg(AA{sup T} - I) {le} 1. On the other hand, we show that existence of a polynomial-time algorithm for computing per(A) for a matrix A such that rg(AA{sup T} - I) {ge} 2 implies NP = R. As a byproduct we obtain that computing per (A) for a matrix A such that rg(AA{sup T} - I) {ge} 2 is No. P (mod 3) complete.

• OSTI ID: 457642
• Report Number(s): CONF-961004-; TRN: 97:001036-0013
• Resource Relation: Conference: 37. annual symposium on foundations of computer science, Burlington, VT (United States), 13-16 Oct 1996; Other Information: PBD: 1996; Related Information: Is Part Of Proceedings of the 37th annual symposium on foundations of computer science; PB: 656 p.
• Country of Publication: United States
• Language: English

Related Subjects

99 MATHEMATICS
COMPUTERS
INFORMATION SCIENCE
MANAGEMENT
LAW
MISCELLANEOUS
MATRICES
ALGORITHMS
POLYNOMIALS
MATHEMATICAL LOGIC
UNITARITY
HAMILTONIANS