Related papers: On the reconstructibility of totally symmetric fun…
We shed some new light to the problem of characterizing those functions of several arguments that have a unique identification minor. The 2-set-transitive functions are known to have this property. We describe another class of functions…
A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of…
A reconstruction problem is formulated for Sperner systems, and infinite families of nonreconstructible Sperner systems are presented. This has an application to a reconstruction problem for functions of several arguments and identification…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
An $n$-ary associative function is called reducible if it can be written as a composition of a binary associative function. We summarize known results when the function is defined on a chain and is nondecreasing. Our main result shows that…
The clones of Boolean functions are classified in regard to set-reconstructibility via a strong dichotomy result: the clones containing only affine functions, conjunctions, disjunctions or constant functions are set-reconstructible, whereas…
Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…
A new class of functions with a unique identification minor is introduced: functions determined by content and singletons. Relationships between this class with other known classes of functions with a unique identification minor are…
The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…
Let X and Y be separable metrizable spaces, and f:X-->Y be a function. We want to recover f from its values on a small set via a simple algorithm. We show that this is possible if f is Baire class one, and in fact we get a characterization.…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
We consider the inverse problem of finding a magnitude-symmetric matrix (matrix with opposing off-diagonal entries equal in magnitude) with a prescribed set of principal minors. This problem is closely related to the theory of recognizing…
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…
The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values…
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of…
There is a well-known correspondence between coherent theories (and their interpretations) and coherent categories (resp. functors), hence the (2,1)-category $\mathbf{Coh_{\sim}}$ (of small coherent categories, coherent functors and all…
Given an $n$-ary $k-$valued function $f$, $gap(f)$ denotes the essential arity gap of $f$ which is the minimal number of essential variables in $f$ which become fictive when identifying any two distinct essential variables in $f$. In the…