Propositional temporal logic is not suitable for expressing properties on the evolution of dynamically allocated entities over time. In particular, it is not possible to trace such...
We extend the lower bounds on the complexity of computing Betti numbers proved in [6] to complex algebraic varieties. More precisely, we first prove that the problem of deciding ...
The “XL-algorithm” is a computational method to solve overdetermined systems of polynomial equations which is based on a generalization of the well-known method of linearizatio...
Often, high dimensional data lie close to a low-dimensional submanifold and it is of interest to understand the geometry of these submanifolds. The homology groups of a manifold a...
Sivaraman Balakrishnan, Alessandro Rinaldo, Don Sh...
The notion of interval sets is introduced as a new kind of sets, represented by a pair of sets, namely, the lower and upper bounds. The interval-set algebra may be regarded as a c...