Introduction

Computation is a concept common to all computing machines, regardless of the messy details associated with their hardware implementation. However, actual computing machines/computers are too complicated (due to the several constraints caused by physical reality) for a manageable mathematical theory to be ascribed to them. Therefore, in order to fully understand the power and limitation of real machines, idealised computers or computational models are designed and studied. These idealised computers may be accurate in some ways but perhaps not in others.

There are several computational models and the purpose of a computational model is to capture the computational aspects that are relevant to the particular problem under consideration while hiding the other unimportant aspects. Thus, a computational model can be thought of as a custom machine designed to suit particular needs. Some of the important computational models are – deterministic finite automaton (DFA), the non-deterministic finite automaton (NFA), the deterministic pushdown automaton (DPDA), the nondeterministic pushdown automation (NPDA), the deterministic Turing machine (DTM) and the nondeterministic Turing machine (NTM). Undoubtedly each of these models has a special significance in the theory of computation. The most basic computational model is the deterministic finite automaton (DFA).

Finite Automata

As discussed in chapter 1, finite automaton is a mathematical model of a system with discrete inputs and outputs. Such a system can be in any one of the finite number of internal configurations or ‘states’ and each state of the system provides sufficient information concerning the past inputs so that the behaviour of the system could be studied on the provision of subsequent inputs.