A regular equivalence on a relation induces matrix blocks that are either 0-blocks or regular-blocks, where a regular-block contains at least one positive entry in each row and column. The authors devise both a permutation test and an exact statistical test that separates these two aspects of regular equivalence, 0-blocks and regular-blocks. To test for the regular-block property, the natural t...

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 ...

The small subgraph conditioning method first appeared when Robinson and the second author showed the almost sure hamiltonicity of random d-regular graphs. Since then it has been used to study the almost sure existence of, and the asymptotic distribution of, regular spanning subgraphs of various types in random d-regular graphs and hypergraphs. In this paper, we use the method to prove the almos...

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...