On Randomized Algebraic Test Complexity

TitleOn Randomized Algebraic Test Complexity
Publication TypeTechnical Report
Year of Publication1992
AuthorsBürgisser P, Karpinski M, Lickteig TMichael
Other Numbers775

We investigate the impact of randomization on the complexity of deciding membership in a (semi-)algebraic subset X ? ?^m. Examples are exhibited where allowing for a certain error probability ? in the answer of the algorithms the complexity of decision problems decreases. A randomized (?^k,{=,?})-decision tree (k ? ? a subfield) over m will be defined as a pair (T, ?) where ? a probability measure on some ?^n and T is a (?^k,{=,?})-decision tree over m+n. We prove a general lower bound on the average decision complexity for testing membership in an irreducible algebraic subset X ? ?^m and apply it to k-generic complete intersection of polynomials of the same degree, extending results in [4, 6]. We also give applications to nongeneric cases, such as graphs of elementary symmetric functions, SL(m,?), and determinant varieties, extending results in [Li:90].

Bibliographic Notes

ICSI Technical Report TR-92-070

Abbreviated Authors

P. Buergisser, M. Karpinski, and T. Lickteig

ICSI Publication Type

Technical Report