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We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
A binary string of length $2^k$ induces the Boolean function of $k$ variables whose Shannon expansion is the given binary string. This Boolean function then is representable via a unique reduced ordered binary decision diagram (ROBDD). The…
Bayesian network classifiers provide a feasible solution to tabular data classification, with a number of merits like high time and memory efficiency, and great explainability. However, due to the parameter explosion and data sparsity…
We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time…
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and…
Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…
Verifying and explaining the behavior of neural networks is becoming increasingly important, especially when they are deployed in safety-critical applications. In this paper, we study verification problems for Binarized Neural Networks…
We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…
Deep neural networks are a family of computational models that are naturally suited to the analysis of hierarchical data such as, for instance, sequential data with the use of recurrent neural networks. In the other hand, ordinal regression…
We study the distributions of waiting times in variations of the negative binomial distribution of order $k$. One variation apply different enumeration scheme on the runs of successes. Another case considers binary trials for which the…
In this paper we review our current results concerning the computational power of quantum read-once branching programs. First of all, based on the circuit presentation of quantum branching programs and our variant of quantum fingerprinting…
A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) multivariate polynomials. The algorithm recasts the implicitly…
We give an algorithm that, for every fixed k, decides isomorphism of graphs of rank width at most k in polynomial time. As the clique width of a graph is bounded in terms of its rank width, we also obtain a polynomial time isomorphism test…
We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main…
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
Recently, a framework for analyzing time series by constructing an associated complex network has attracted significant research interest. One of the advantages of the complex network method for studying time series is that complex network…
We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and…
We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…
We propose a method for variable selection and basis learning for high-dimensional classification with ordinal responses. The proposed method extends sparse multiclass linear discriminant analysis, with the aim of identifying not only the…
The problem of learning Boolean linear functions from quantum examples w.r.t. the uniform distribution can be solved on a quantum computer using the Bernstein-Vazirani algorithm. A similar strategy can be applied in the case of noisy…