Input-Driven Double-Head Pushdown Automata

TL;DR

This paper introduces input-driven double-head pushdown automata, exploring their language recognition capabilities, closure properties, and decision problems, as a generalization of traditional pushdown automata with two input heads moving in opposite directions.

Contribution

It presents a novel automaton model with two input heads and input-driven control, analyzing its language families and theoretical properties compared to classical models.

Findings

Two variants of input-driven double-head pushdown automata are defined.

Language families recognized by these automata are characterized.

Closure properties and decision problems are studied for these models.

Abstract

We introduce and study input-driven deterministic and nondeterministic double-head pushdown automata. A double-head pushdown automaton is a slight generalization of an ordinary pushdown automaton working with two input heads that move in opposite directions on the common input tape. In every step one head is moved and the automaton decides on acceptance if the heads meet. Demanding the automaton to work input-driven it is required that every input symbol uniquely defines the action on the pushdown store (push, pop, state change). Normally this is modeled by a partition of the input alphabet and is called a signature. Since our automaton model works with two heads either both heads respect the same signature or each head owes its own signature. This results in two variants of input-driven double-head pushdown automata. The induced language families on input-driven double-head pushdown automata are studied from the perspectives of their language describing capability, their closure properties, and decision problems.