Computational power of one-way multihead finite automata

Abstract

In this paper we sketch our results concerning one-way multihead finite automata (1-MFA). The full version with complete proofs can be found in a series of papers ([3],[4],[5],[6]). 1-MFA belong to the weakest models of computational devices. Despite that, they recognize many interesting and important languages. They work in linear time, so the algorithms running on 1-MFA are in some sense practical. Unfortunately, many important questions concerning 1-MFA have turned out to be hard to answer, despite the simplicity of the computational model. We get the results which answer some of such open questions. Before we proceed, we recall shortly the definition of 1-MFA. A 1-MFA consists of an input tape, some number of read-only heads and a control unit with finitely many internal states (see figure 1). Input words are placed on the input tape, each symbol occupying one cell. The heads are placed initially at the first from the left input symbol. During a computation the heads move independently on the tape (no moves to the left are allowed) and read different symbols of the input word. The computation consists of several steps, during which the internal state can change and the heads can move to the right.