Related papers: Pebble Minimization of Polyregular Functions
Distributions of pebbles to the vertices of a graph are said to be solvable when a pebble may be moved to any specified vertex using a sequence of admissible pebbling rules. The optimal pebbling number is the least number of pebbles needed…
This paper proves that in Size Theory the comparison of multidimensional size functions can be reduced to the 1-dimensional case by a suitable change of variables. Indeed, we show that a foliation in half-planes can be given, such that the…
A language over an alphabet $B = A \cup \overline{A}$ of opening ($A$) and closing ($\overline{A}$) brackets, is balanced if it is a subset of the Dyck language $D_B$ over $B$, and it is well-formed if all words are prefixes of words in…
It is well known, due to Lindstr\"om, that the minors of a (real or complex) matrix can be expressed in terms of weights of flows in a planar directed graph. Another classical fact is that there are plenty of homogeneous quadratic relations…
Superregular matrices, i.e., matrices where all square submatrices are non-singular, have a wide range of applications in communications. A superregular block matrix is a broader concept where all full block submatrices, with the…
We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments…
We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps $W^{1,p}(\mathbb{R}) \times W^{1,q}(\mathbb{R}) \to W^{1,r}(\mathbb{R})$ with $1 <p,q < \infty$ and $r\geq 1$, boundedly and…
Finite-state transducers give efficient representations of many Natural Language phenomena. They allow to account for complex lexicon restrictions encountered, without involving the use of a large set of complex rules difficult to analyze.…
In this paper we propose a new, more appropriate definition of regular and indeterminate strings. A regular string is one that is "isomorphic" to a string whose entries all consist of a single letter, but which nevertheless may itself…
Regular polygons are characterized as area-constrained critical points of the perimeter functional with respect to particular families of perturbations in the class of polygons with a fixed number of sides. We also review recent results in…
A continous map $f: \mathbb{C}^n \rightarrow \mathbb{C}^N$ is $k$-regular if the image of any $k$ points spans a $k$-dimensional subspace. It is an important problem in topology and interpolation theory, going back to Borsuk and Chebyshev,…
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the…
We prove that if X is any 2-regular projective scheme (in the sense of Castelnuovo-Mumford) then X is "small". This means that if L is a linear space and Y:= L\cap X is finite, then Y is "linearly independent" in the sense that the…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…
We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modelled via an origin function which associates to any position of…
A coarse-grained multi-blob description of polymer solutions is presented, based on soft, transferable effective interactions between bonded and non-bonded blobs. The number of blobs is chosen such that the blob density does not exceed…
A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…
This paper examines the Balanced Submodular Flow Problem, that is the problem of finding a feasible submodular flow minimizing the difference between the flow values along the edges. A min-max formula is given to the problem and an…
We show that for any positive integer $d$, there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function…
This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a…