Theory of Computation Automata Theory Dr. Ayman Srour

TOPIC 2: REGULAR LANGUAGES OUTLINE 2.1 Introduction 2.2 Finite Automata 2.3 Nondeterminism 2.4 Regular Expressions 2.5 Generalized Nondeterministic Finite Automaton

2.1 Finite Automata/Designing Finite Automata design is a creative process and it cannot be reduced to a simple recipe or formula. you might find a particular approach helpful when designing various types of automata. That is, put yourself in the place of the machine you are trying to design and then see how you would go about performing the machine's task. Suppose that you are given some language and want to design a finite automaton that recognizes it. Pretending to be the automaton, you receive an input string and must determine whether it is a member of the language the automaton is supposed to recognize. You get to see the symbols in the string one by one. After each symbol you must decide whether the string seen so far is in the language. For example, suppose that the alphabet is {O, 1} and that the language consists of all strings with an odd number of 1s.

2.1 Finite Automata/The Regular Operations Previously, we learned what is the FSA and regular languages, but not yet their prosperities. It can help, including ways of proving, to determine if a particular language is regular of not. In arithmetic, the basic objects are numbers and the tools are operations for manipulating them, such as + and x. In the theory of computation the objects are languages and the tools include operations specifically designed for manipulating them. regular operations We define three operations on languages, called the regular operations, and use them to study properties of the regular languages.

2.1 Finite Automata/The Regular Operations regular operations We define three operations on languages, called the regular operations, and use them to study properties of the regular languages.

2.2 Finite Automata/Example

2.1 Finite Automata/Theorem