3 research outputs found
Cellular Automata and Discrete Complex Systems: 25th IFIP WG 1.5 International Workshop, AUTOMATA 2019, Guadalajara, Mexico, June 26–28, 2019, Proceedings
International audienceBook Front Matter of LNCS 1152
Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata
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
and (uniform) . 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 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