Jumping Finite Automata

Abstract

The present paper proposes a new investigation area in automata theory — jumping finite automata. These automata work like classical finite automata except that they read input words discontinuously — that is, after reading a symbol, they can jump over some symbols within the words and continue their computation from there. The paper establishes several results concerning jumping finite automata in terms of commonly investigated areas of automata theory, such as decidability and closure properties. Most importantly, it achieves several results that demonstrate differences between jumping finite automata and classical finite automata. In its conclusion, the paper formulates several open problems and suggests future investigation areas.

Problems on Finite Automata and the Exponential Time Hypothesis

“…We picked these two processing modes for the subsequent analysis, as they were introduced quite recently [35,36].…”

“…In other words, a JFA may first jump to an arbitrary position of the input and then apply the rule there. This model was introduced in [36] and further studied in [37]. It is relatively easy to see that the languages accepted by JFAs are just the inverses of the Parikh images of the regular languages, or, in other words, the commutative (or permutation) closure of the regular languages, or, yet in different terminology, the inverses of the Parikh images of semilinear sets.…”

Two-dimensional jumping finite automata

“…The motivation for this paper is based on Jumping Finite Automata [1] for string languages. Most of the classical computer science methods developed in the previous century is for continuous information processing and hence their formal models, such as finite automata work strictly continuously from left to right in a symbol-by-symbol way.…”

“…This gives rise to the idea of adapting classical formal models in a discontinuous way. In this way, the study in [1] introduces new versions of finite automata, referred to as jumping finite automata which have always had a central role in computer science as a whole presenting a new, attractive, significant and up-to-date topic of modern automata theory. This paper is a major improvement to and development of [7] that has recently been introduced in the literature.…”

“…This paper is a major improvement to and development of [7] that has recently been introduced in the literature. Here the concept of Jumping Finite Automata [1] is extended to two-dimensional languages. New computational models based on two-dimensional languages are always of great interest.…”