We study the problem of streaming regular expression parsing: Given a regular expression and an input stream of symbols, how to output a serialized syntax tree representation as an output stream during input stream processing. We show that optimally streaming regular expression parsing, outputting bits of the output as early as is semantically possible for any regular expression of size m and a...

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...

We say that a monic polynomial with integer coefficients is polygomial if its each zero obtained by squaring the edge or diagonal of regular n-gon unit circumradius. find connections certain polygomials Morgan-Voyce polynomials and further Chebyshev second kind.

The aim of this note is to investigate isoperimetric-type problems for $3$-dimensional parallelohedra; that is, convex polyhedra whose translates tile the Euclidean space. Our main result states among parallelohedra with unit volume one minimal mean width regular truncated octahedron.

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

Functional MSO transductions, deterministic two-way transducers, as well streaming string transducers are all equivalent models for regular functions. In this paper, we show that every function, either on finite words or infinite words, captured by a transducer, can be described with transducer expression (RTE ). For the uses Muller acceptance and ω-regular look-ahead. RTEs constructed from con...