We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We p...
We study the complexity of deciding whether a given homogeneous multivariate polynomial has a nontrivial root over a finite field. Given a homogeneous algebraic circuit C that com...
We present an approach that extends the BentleyOttmann sweep-line algorithm [3] to the exact computation of the topology of arrangements induced by non-singular algebraic curves o...
We reexamine what it means to compute Nash equilibria and, more generally, what it means to compute a fixed point of a given Brouwer function, and we investigate the complexity o...
We present computational techniques for automatically generating algebraic (polynomial equality) invariants for algebraic hybrid systems. Such systems involve ordinary differentia...