Related papers: A Bisimulation-Invariance-Based Approach to the Se…
Invariants allow to classify images up to the action of a group of transformations. In this paper we introduce notions of the algebras of simultaneous polynomial and rational 2D moment invariants and prove that they are isomorphic to the…
The split involution quantization scheme, proposed previously for pure second--class constraints only, is extended to cover the case of the presence of irreducible first--class constraints. The explicit Sp(2)--symmetry property of the…
Misestimates of $\sigma_{P_o}$, the \emph{uncertainty} in $P_o$ from a 2-state Bayes equation used for binary classification, apparently arose from $\hat{\sigma}_{p_i}$, the uncertainty in underlying pdfs estimated from experimental $b$-bin…
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…
Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic…
We prove exact complexity dichotomies for two quantum invariants of closed oriented three-manifolds, with the categorical data fixed. For a modular category $\mathcal{C}$, computing the Reshetikhin--Turaev invariant $Z_{\mathcal{C}}(M)$…
The traditional Pi-theorem tells us that for any dimensionally invariant relation there exists a full set of independent dimensionless "Pi groups" which can be used to nondimensionalise the relation. In this paper, we seek to understand…
We study bisimulations for useful description logics. The simplest among the considered logics is $\mathcal{ALC}_{reg}$ (a variant of PDL). The others extend that logic with inverse roles, nominals, quantified number restrictions, the…
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…
The P versus NP problem is studied under the relational model of E. F. Codd. I found that the term "complete configuration" is unnecessary and harmful in computational complexity theory because of excessive symbol redundancy. For an input,…
We investigate the computational problem of determining whether a bivariate polynomial with non-negative coefficients and no constant term can attain a prime value. While classical conjectures such as Bouniakowsky's provide necessary…
We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…
It was recently shown \cite{STV} that satisfiability is polynomially solvable when the incidence graph is an interval bipartite graph (an interval graph turned into a bipartite graph by omitting all edges within each partite set). Here we…
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the…
For a given monic polynomial $p(t)$ of degree $n$ over a commutative ring $k$, the splitting algebra is the universal $k$-algebra in which $p(t)$ has $n$ roots, or, more precisely, over which $p(t)$ factors, $p(t)=(t-\xi_1)...(t-\xi_n)$.…
The omega-regular separability problem for B\"uchi VASS coverability languages has recently been shown to be decidable, but with an EXPSPACE lower and a non-primitive recursive upper bound -- the exact complexity remained open. We close…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…