Proceedings of 37th Conference on Foundations of Computer Science (1996)

Burlington, VT

Oct. 14, 1996 to Oct. 16, 1996

ISBN: 0-8186-7594-2

pp: 108

G. Kogan , Dept. of Comput. Sci., Technion-Israel Inst. of Technol., Haifa, Israel

ABSTRACT

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(AAT - I) ≤ 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(AAT - I) ≥ 2 implies NP = R. As a byproduct we obtain that computing per(A) for a matrix A such that rg(AAT - I) ≥ 2 is #P(mod3) complete.

INDEX TERMS

computational complexity; complexity; permanents; fields of characteristic 3; polynomial time algorithm; polynomial-time algorithm; matrix

CITATION

G. Kogan, "Computing permanents over fields of characteristic 3: where and why it becomes difficult,"

*Proceedings of 37th Conference on Foundations of Computer Science(FOCS)*, Burlington, VT, 1996, pp. 108.

doi:10.1109/SFCS.1996.548469

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