Quantum algorithms for topological data analysis (TDA) seem to provide an exponential
advantage over the best classical approach while remaining immune to dequantization …

Tools of topological data analysis provide stable summaries encapsulating the shape of the
considered data. Persistent homology, the most standard and well-studied data summary …

For several computational problems in homotopy theory, we obtain algorithms with running
time polynomial in the input size. In particular, for every fixed k≥2, there is a polynomial-time …

We prove the NP-hardness of computing homology groups of simplicial complexes when the
size of the input complex is measured by the number of maximal faces or the number of …

We present the design and implementation of a C++ class for reliability analysis of multi-
state systems using an algebraic approach based on monomial ideals. The class is …

The algebraic approach to the analysis of system reliability associates an algebraic object, a
monomial ideal, to a coherent system (CS), and studies the reliability of the system using the …

We consider the problem of exact probabilistic inference for Union of Conjunctive Queries
(UCQs) on tuple-independent databases. For this problem, two approaches currently …

We study the problem of counting answers to unions of conjunctive queries (UCQs) under
structural restrictions on the input query. Concretely, given a class C of UCQs, the problem# …

The interplay between supersymmetry and classical and quantum computation is discussed.
First, it is shown that the problem of computing the Witten index of $\mathcal N\leq 2 …

In this paper, we explore whether a data structure for representing Boolean functions
(namely, Binary Decision Diagrams) can be useful to detect, in an efficient way, the acyclicity …