Chapter 17 Jumping Finite Automata

Abstract

The present chapter introduces and studies jumping finite automata. In essence, these automata work just like classical finite automata except that they do not read their input strings in a symbol-by-symbol left-to-right way. Instead, after reading a symbol, they can jump in either direction within their input tapes and continue making moves from there. Once an occurrence of a symbol is read, it cannot be re-read again later on. Otherwise, their definition coincides with the definition of standard finite automata. Organized into eight sections, this chapter gives a systematic body of knowledge concerning jumping finite automata. First, it formalizes them (Sect. 17.1). Then, it demonstrates their fundamental properties (Sect. 17.2), after which it compares their power with the power of well-known language-defining formal devices (Sect. 17.3). Naturally, this chapter also establishes several results concerning jumping finite automata with respect to commonly studied areas of formal language theory, such as closure properties (Sect. 17.4) and decidability (Sect. 17.5). In addition, it establishes an infinite hierarchy of language families resulting from these automata (Sect. 17.6). Finally, it studies some special topics and features, such as one-directional jumps (Sect. 17.7) and various start configurations (Sect. 17.8). Throughout its discussion, this chapter points out several open questions regarding these automata, which may represent a new investigation area of automata theory in the future.