Teori Bahasa dan Automata Lecture 6: Regular Expression By: Nur Uddin, Ph.D

Finite Automata

Finite Automata

Finite Automata

Formal Definition of Computation Condition 1 says that the machine starts in the start state. Condition 2 says that the machine goes from state to state according to the transition function. Condition 3 says that the machine accepts its input if it ends up in an accept state.

Regular language

Example 1.13

Regular language

Designing Finite Automata Done

Regular operations We introduced and defined finite automata and regular languages. Both help develop a toolbox of techniques for designing automata to recognize particular languages. In arithmetic, the basic objects are numbers and the tools are operations for manipulating them, such as + and × . In the theory of computation, the objects are languages and the tools include operations specifically designed for manipulating them. We define three operations on languages, called the regular operations, and use them to study properties of the regular languages.

Regular operations The empty string ε is always a member of A*, no matter what A is.

Regular operations

Regular Expression

Regular Expression

Regular expression

Regular expression

Regular expression

Identity

Equivalence with finite automata Regular expressions and finite automata are equivalent in their descriptive power. This fact is surprising because finite automata and regular expressions superficially appear to be rather different. However, any regular expression can be converted into a finite automaton that recognizes the language it describes, and vice versa.

Converting regular expression into NFA Let’s convert R into an NFA N.

Converting regular expression into NFA Let’s convert R into an NFA N.

Converting regular expression into NFA

Converting regular expression into NFA