Valiant introduced 20 years ago an algebraic complexity theory to study the complexity of polynomial families. The basic computation model used is the arithmetic circuit, which makes these classesâ€¦ (More)

We consider the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of monomials. We show that these problems areâ€¦ (More)

We study the arithmetic complexity of iterated matrix multiplication. We show that any multilinear homogeneous depth 4 arithmetic formula computing the product of <i>d</i> generic matrices of sizeâ€¦ (More)

This work deals with the power of linear algebra in the context of multilinear computation. By linear algebra we mean algebraic branching programs (ABPs) which are known to be computationallyâ€¦ (More)

In this paper we suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x; y) which statesâ€¦ (More)

We study the link between the complexity of a polynomial and that of its coefficient functions. Valiant's theory is a good setting for this, and we start by generalizing one of Valiant'sâ€¦ (More)

Nisan (STOC 1991) exhibited a polynomial which is computable by linear-size non-commutative circuits but requires exponential-size non-commutative algebraic branching programs. Nisanâ€™s hardâ€¦ (More)

In the setting of non-commutative arithmetic computations, we define a class of circuits that generalize algebraic branching programs (ABP). This model is called unambiguous because it captures theâ€¦ (More)