A TURING MACHINE IS JUST A FINITE AUTOMATON WITH TWO STACKS: A COMMENT ON TEACHING THEORY OF COMPUTATION

Abstract

Traditionally, when we teach Theory of Computations we start with finite automata, we show that they are not sufficient, then we switch to pushdown automata (i.e., automata-with-stacks). Automata-with-stacks are also not sufficient, so we introduce Turing machines. The problem is that while the transition from finite automata to automata-with-stacks is reasonably natural, Turing machine are drastically different, and as a result, transition to Turing machines is difficult for some students. In this paper, we propose to solve this pedagogical problem by emphasizing that a Turing machine is, in effect, nothing else but a finite automaton with two stacks. This representation make transition to Turing machines much more natural and thus, easier to understand and to learn.