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Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata
Authors
A Rosenfeld
C Iwamoto
+20Â more
DA Mix Barrington
H Caussinus
H Straubing
H Vollmer
JA Brzozowski
M Kutrib
M Sudan
ML Furst
N Immerman
OH Ibarra
R McNaughton
R McNaughton
R Rubinfeld
R Sommerhalder
S Arora
S Eilenberg
S Kim
SA Cook
V Terrier
WL Ruzzo
Publication date
13 March 2020
Publisher
'Springer Science and Business Media LLC'
Doi
Cite
View
on
arXiv
Abstract
After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors whose acceptance condition depends on the states of all cells in the automaton. We prove a time hierarchy theorem for sublinear-time ACA classes, analyze their intersection with the regular languages, and, finally, establish strict inclusions in the parallel computation classes
S
C
\mathsf{SC}
SC
and (uniform)
A
C
\mathsf{AC}
AC
. As an addendum, we introduce and investigate the concept of a decider ACA (DACA) as a candidate for a decider counterpart to (acceptor) ACAs. We show the class of languages decidable in constant time by DACAs equals the locally testable languages, and we also determine
Ω
(
n
)
\Omega(\sqrt{n})
Ω
(
n
​
)
as the (tight) time complexity threshold for DACAs up to which no advantage compared to constant time is possible.Comment: 16 pages, 2 figures, to appear at DLT 202
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Last time updated on 10/08/2021