If L is a formal language, we de ne A L n t o b e t h e n umber of states in the smallest deterministic nite automaton that accepts a language which agrees with L on all inputs of length no more than n. This measure is called automaticity. In this paper, we rst study the closure properties of the class DPA of languages of deterministic polynomial automaticity, i.e., those languages L for which there exists k such that A L n = O n k . Next, we discuss similar results for a nondeterministic analogue of automaticity, introducing the classes NPA languages of nondeterministic polynomial automaticity and NPLA languages of nondeterministic poly-log automaticity. We conclude by showing how to construct a context-free language of automaticity arbitrarily close to the maximum possible.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.