Generalized Linear One-Way Jumping Finite Automata

TL;DR

This paper introduces a generalized linear one-way jumping finite automaton model that enhances computational power by allowing substring deletions and directional jumps, and compares it with existing models and the Chomsky hierarchy.

Contribution

It defines and analyzes a new automaton model that extends previous jumping finite automata with generalized substring deletions and directional jumps, and explores its properties and hierarchy relations.

Findings

The new model is more powerful than the original jumping finite automata.

Variants of the model are defined and compared.

Closure properties are analyzed.

Abstract

A new discontinuous model of computation called one-way jumping finite automata was defined by H. Chigahara et. al. This model was a restricted version of the model jumping finite automata. These automata read an input symbol-by-symbol and jump only in one direction. A generalized linear one-way jumping finite automaton makes jumps after deleting a substring of an input string and then changes its state. These automata can make sequence of jumps in only one direction on an input string either from left to right or from right to left. We show that newly defined model is powerful than its original counterpart. We define and compare the variants, generalized right linear one-way jumping finite automata and generalized left linear one-way jumping finite automata. We also compare the newly defined models with Chomsky hierarchy. Finally, we explore closure properties of the model.