Introduction to the Theory of Computation

Theory of computation deals with developing mathematical models of computation. This area of research is divided into three subareas: complexity theory, computability theory and automata theory. We mostly review basic structures of automata theory which are languages and finite state automata in this chapter. A language is defined over a set of symbols called an alphabet. A finite state machine is a mathematical tool to model a computing system. Unlike a combinational circuit, a finite state machine has a memory and its behavior and output depends on its current input and its current state. A finite state automata is a finite state machine with no outputs; instead, it has final states called accepting states. A finite state automata can be used to recognize a language conveniently. We review languages, finite state machines, finite state automata, language recognition in this chapter and conclude the first part with the Turing machine named after Alan Turing, which is a more general type of a finite state machine. We then have a short review of complexity theory with the basic complexity classes.