This paper is a survey of the upper bounds on the complexity of basic algebraic and
geometric operations with Pfaffian and Noetherian functions, and with sets definable by …

A bstract Inspired by the notion that physical systems can contain only a finite amount of
information or complexity, we introduce a framework that allows for quantifying the amount of …

BETTI NUMBERS OF SEMIALGEBRAIC AND SUB-PFAFFIAN SETS Page 1 J. London Math.
Soc. (2) 69 (2004) 27–43 Cо2004 London Mathematical Society DOI: 10.1112/S0024610703004939 …

We prove new upper bounds on homotopy and homology groups of o‐minimal sets in terms
of their approximations by compact o‐minimal sets. In particular, we improve the known …

We present a new, far simpler family of counter-examples to Kushnirenko's Conjecture.
Along the way, we illustrate a computer-assisted approach to finding sparse polynomial …

The o-minimal structure generated by the restricted Pfaffian functions, known as restricted
sub-Pfaffian sets, admits a natural measure of complexity in terms of a format, recording …

We present an algorithm for simplifying a large class of elementary functions in the presence
of branch cuts. This algorithm works by:(a) verifying that the proposed simplification is …

A PREPARATION THEOREM FOR WEIERSTRASS SYSTEMS Introduction Given a real analytic
function f : U → R defined on an open neighbo Page 1 TRANSACTIONS OF THE AMERICAN …

In this paper we prove tight bounds on the combinatorial and topological complexity of sets
dened in terms of n denable sets belonging to some fixed denable family of sets in an o …

Consider a system F of n polynomials in n variables, with a total of n+ k distinct exponent
vectors, over any local field L. We discuss conjecturally tight bounds on the maximal number …