Lower bounds on the size of sweeping automata

Abstract

Establishing good lower bounds on the complexity of languages is an important area of current research in the theory of computation. However, despite much effort, fundamental questions such as P =? NP and L =? NL remain open. To resolve these questions it may be necessary to develop a deep combinatorial understanding of polynomial time or log space computations, possibly a formidable task. One avenue for approaching these problems is to study weaker models of computation for which the analogous problems may be easier to settle, perhaps yielding insight into the original problems. Sakoda and Sipser [3] raise the following question about finite automata: Is there a polynomial p, such that every n-state 2nfa (two-way nondeterministic finite automaton) has an equivalent p(n)-state 2dfa? They conjecture a negative answer to this. In this paper we take a step toward proving this conjecture by showing that 2nfa are exponentially more succinct than 2dfa of a certain restricted form.