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- Guillaume Malod, Natacha Portier
- MFCS
- 2006

Valiant introduced 20 years ago V P and V NP : an algebraic analogue to the classes P and NP . They are defined via non-uniform sequences of arithmetic circuits and are especially useful to study the… (More)

- Bruno Grenet, Pascal Koiran, Natacha Portier
- MFCS
- 2010

The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable… (More)

- Vincent D. Blondel, Emmanuel Jeandel, Pascal Koiran, Natacha Portier
- SIAM J. Comput.
- 2005

We study the following decision problem: is the language recognized by a quantum finite automaton empty or nonempty? We prove that this problem is decidable or undecidable depending on whether… (More)

- Bruno Grenet, Pascal Koiran, Natacha Portier
- J. Complexity
- 2013

The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable… (More)

- Guillaume Malod, Natacha Portier
- J. Complexity
- 2008

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 classes… (More)

- Pascal Koiran, Vincent Nesme, Natacha Portier
- Theor. Comput. Sci.
- 2007

Simon in his FOCS’94 paper was the first to show an exponential gap between classical and quantum computation. The problem he dealt with is now part of a well-studied class of problems, the hidden… (More)

We show that the problem of determining if a given integer linear recurrent sequence has a zero – a problem that is known as “Pisot’s problem” – is NP-hard. With a similar argument we show that the… (More)

- Pascal Koiran, Vincent Nesme, Natacha Portier
- ICALP
- 2005

We present general methods for proving lower bounds on the query complexity of nonadaptive quantum algorithms. Our results are based on the adversary method of Ambainis.

- Pascal Koiran, Natacha Portier, Sébastien Tavenas
- J. Symb. Comput.
- 2015

According to the real τ -conjecture, the number of real roots of a sum of products of sparse univariate polynomials should be polynomially bounded in the size of such an expression. It is known that… (More)

We present an algorithm which computes the multilinear factors of bivariate lacunary polynomials. It is based on a new Gap theorem which allows to test whether… (More)