Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bases for pseudovarieties closed under bideterministic product   We show that if $\mathsf V$ is a semigroup pseudovariety containing the
finite semilattices and contained in $\mathsf {DS}$, then it has a basis of
pseudoidentities between finite products of regular pseudowords if, and only
if, the corresponding variety of languages is closed under bideterministic
product. The key to this equivalence is a weak generalization of the existence
and uniqueness of $\mathsf J$-reduced factorizations. This equational approach
is used to address the locality of some pseudovarieties. In particular, it is
shown that $\mathsf {DH}\cap\mathsf {ECom}$ is local, for any group
pseudovariety $\mathsf H$.

28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th