Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial time algorithm for left [right] local testability   A right [left] locally testable language S is a language with the property
that for some non negative integer k two words u and v in alphabet S are equal
in the semi group if (1) the prefix and suffix of the words of length k
coincide, (2) the set of segments of length k of the words as well as 3) the
order of the first appearance of these segments in prefixes [suffixes]
coincide. We present necessary and sufficient condition for graph [semi group]
to be transition graph [semi group] of the deterministic finite automaton that
accepts right [left] locally testable language and necessary and sufficient
condition for transition graph of the deterministic finite automaton with
locally idempotent semi group. We introduced polynomial time algorithms for the
right [left] local testable problem for transition semi group and transition
graph of the deterministic finite automaton based on these conditions.
Polynomial time algorithm verifies transition graph of automaton with locally
idempotent transition semi group.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys