On the Existence of Universal Finite or Pushdown Automata

TL;DR

This paper explores whether universal automata exist for classes like finite automata and pushdown automata, analyzing how encoding affects their existence and proposing an alternative transition system approach.

Contribution

It provides new insights into the (non)-existence of universal automata for certain classes and introduces an alternative transition system method.

Findings

Universal automata do not exist for some classes under certain encodings

Encoding influences the existence of universal automata

Transition systems offer a different perspective on automata universality

Abstract

We investigate the (non)-existence of universal automata for some classes of automata, such as finite automata and pushdown automata, and in particular the influence of the representation and encoding function. An alternative approach, using transition systems, is presented too.