Semidefinite programming and arithmetic circuit evaluation
Abstract
A rational number can be naturally presented by an arithmetic computation (AC): a sequence of elementary arithmetic operations starting from a fixed constant, say 1. The asymptotic complexity issues of such a representation are studied e.g. in the framework of the algebraic complexity theory over arbitrary field. Here we study a related problem of the complexity of performing arithmetic operations and computing elementary predicates, e.g. ``='' or ``>'', on rational numbers given by AC. In the first place, we prove that AC can be efficiently simulated by the exact semidefinite programming (SDP). Secondly, we give a BPPalgorithm for the equality predicate. Thirdly, we put ``>''predicate into the complexity class PSPACE. We conjecture that ``>''predicate is hard to compute. This conjecture, if true, would clarify the complexity status of the exact SDP  a well known open problem in the field of mathematical programming.
 Publication:

arXiv eprints
 Pub Date:
 December 2005
 DOI:
 10.48550/arXiv.cs/0512035
 arXiv:
 arXiv:cs/0512035
 Bibcode:
 2005cs.......12035T
 Keywords:

 Computer Science  Computational Complexity;
 F.1.3
 EPrint:
 Submitted to Special issue of DAM in memory of L.Khachiyan