## Circuits versus Trees in Algebraic Complexity (2000)

Venue: | In Proc. STACS 2000 |

Citations: | 5 - 4 self |

### BibTeX

@INPROCEEDINGS{Koiran00circuitsversus,

author = {Pascal Koiran},

title = {Circuits versus Trees in Algebraic Complexity},

booktitle = {In Proc. STACS 2000},

year = {2000},

pages = {35--54},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

. This survey is devoted to some aspects of the \P = NP ?" problem over the real numbers and more general algebraic structures. We argue that given a structure M , it is important to nd out whether NPM problems can be solved by polynomial depth computation trees, and if so whether these trees can be eciently simulated by circuits. Point location, a problem of computational geometry, comes into play in the study of these questions for several structures of interest. 1 Introduction In algebraic complexity one measures the complexity of an algorithm by the number of basic operations performed during a computation. The basic operations are usually arithmetic operations and comparisons, but sometimes transcendental functions are also allowed [21-23, 26]. Even when the set of basic operations has been xed, the complexity of a problem depends on the particular model of computation considered. The two main categories of interest for this paper are circuits and trees. In section 2 and...