We present symbolic algorithms for computing the g-asymptotes, or generalized asymptotes, of a plane algebraic curve, C, implicitly parametrically defined. The g-asymptotes generalize classical concept asymptotes curve. Both notions have been previously studied analyzing geometry and topology curve at infinity points, as well to detect symmetries that can occur in coordinates far from origin. T...

In this paper we present our personal view of what should be the next step in the development of symbolic computation systems. The main point is that future systems should integrate the power of algebra and logic. We identify four gaps between the future ideal and the systems available at present: the logic, the syntax , the mathematics, and the prover gap, respectively. We discuss higher order...

We consider Markov decision processes (MDPs) with ω-regular specifications given as parity objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. The algorithms for the computation of the almost-sure winning set for parity objectives iteratively use the solutions for the almost-sure winning set for Büchi...

The construction of computational cognitive models integrating the connectionist and symbolic paradigms of artificial intelligence is a standing research issue in the field. The combination of logic-based inference and connectionist learning systems may lead to the construction of semantically sound computational cognitive models in artificial intelligence, computer and cognitive sciences. Over...

Using Computer Algebra Software (CAS) we obtained the reproduction rate of an Epidemic Propagation in a circular habitat, for two cases, in the first one the boundary has an endemic condition, in the other one it presents an infectious transference from other territories through its boundary. We transformed the initial equation into Laplace Domain, and then we solved the simplified differential...

We consider Markov decision processes (MDPs) with ω-regular specifications given as parity objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. The algorithms for the computation of the almost-sure winning set for parity objectives iteratively use the solutions for the almost-sure winning set for Büchi...