Regular Expressions Prof. Busch - LSU.

Slides:



Advertisements
Similar presentations
Lecture 8 From NFA to Regular Language. Induction on k= # of states other than initial and final states K=0 a a* b a c d c*a(d+bc*a)*
Advertisements

Regular expressions Regular languages Sipser 1.3 (pages 63-76)
Regular expressions Sipser 1.3 (pages 63-76). CS 311 Mount Holyoke College 2 Looks familiar…
Prof. Busch - LSU1 Properties of Context-Free languages.
Costas Busch - RPI1 Single Final State for NFAs. Costas Busch - RPI2 Any NFA can be converted to an equivalent NFA with a single final state.
Courtesy Costas Busch - RPI1 Non Deterministic Automata.
Fall 2006Costas Busch - RPI1 Regular Expressions.
1 Regular Expressions. 2 Regular expressions describe regular languages Example: describes the language.
Fall 2006Costas Busch - RPI1 Deterministic Finite Automata And Regular Languages.
Homework #2 Solutions.
Fall 2004COMP 3351 Single Final State for NFA. Fall 2004COMP 3352 Any NFA can be converted to an equivalent NFA with a single final state.
1 Single Final State for NFAs and DFAs. 2 Observation Any Finite Automaton (NFA or DFA) can be converted to an equivalent NFA with a single final state.
Lecture 7 Sept 22, 2011 Goals: closure properties regular expressions.
Fall 2006Costas Busch - RPI1 Properties of Regular Languages.
Regular expressions Sipser 1.3 (pages 63-76). CS 311 Fall Looks familiar…
Courtesy Costas Busch - RPI1 Non-regular languages.
Fall 2006Costas Busch - RPI1 Non-Deterministic Finite Automata.
1 Non-Deterministic Automata Regular Expressions.
Finite Automata Costas Busch - RPI.
Fall 2004COMP 3351 Another NFA Example. Fall 2004COMP 3352 Language accepted (redundant state)
Costas Busch - LSU1 Non-Deterministic Finite Automata.
Prof. Busch - LSU1 Linear Grammars Grammars with at most one variable at the right side of a production Examples:
Prof. Busch - LSU1 Non-regular languages (Pumping Lemma)
Prof. Busch - LSU1 More Applications of the Pumping Lemma.
Prof. Busch - LSU1 Turing Machines. Prof. Busch - LSU2 The Language Hierarchy Regular Languages Context-Free Languages ? ?
Prof. Busch - LSU1 Reductions. Prof. Busch - LSU2 Problem is reduced to problem If we can solve problem then we can solve problem.
1 A Single Final State for Finite Accepters. 2 Observation Any Finite Accepter (NFA or DFA) can be converted to an equivalent NFA with a single final.
Fall 2004COMP 3351 Regular Expressions. Fall 2004COMP 3352 Regular Expressions Regular expressions describe regular languages Example: describes the language.
Costas Busch - LSU1 Languages. Costas Busch - LSU2 Language: a set of strings String: a sequence of symbols from some alphabet Example: Strings: cat,
1 Regular Expressions. 2 Regular expressions describe regular languages Example: describes the language.
Fall 2006Costas Busch - RPI1 Deterministic Finite Automaton (DFA) Input Tape “Accept” or “Reject” String Finite Automaton Output.
Prof. Busch - LSU1 NFAs accept the Regular Languages.
Transition Diagrams Lecture 3 Wed, Jan 21, Building Transition Diagrams from Regular Expressions A regular expression consists of symbols a, b,
CSCI 2670 Introduction to Theory of Computing September 1, 2005.
CSCI 2670 Introduction to Theory of Computing October 12, 2005.
Regular Expressions Costas Busch - LSU.
1 Other Models of Computation Costas Busch - LSU.
Finite Automata Chapter 1. Automatic Door Example Top View.
1 Language Recognition (11.4) Longin Jan Latecki Temple University Based on slides by Costas Busch from the courseCostas Busch
Costas Busch - LSU1 Linear Grammars Grammars with at most one variable at the right side of a production Examples:
1 Some Properties of Regular Languages. 2 Properties Concatenation:Star: Union: Are regular Languages For regular languages and.
Costas Busch - LSU1 Deterministic Finite Automata And Regular Languages.
Formal Language & Automata Theory
Non-regular languages
Standard Representations of Regular Languages
Non Deterministic Automata
Busch Complexity Lectures: Turing Machines
Languages Prof. Busch - LSU.
Languages Costas Busch - LSU.
Properties of Regular Languages
Busch Complexity Lectures: Reductions
Reductions Costas Busch - LSU.
Formal Language & Automata Theory
Single Final State for NFA
Language Recognition (12.4)
REGULAR LANGUAGES AND REGULAR GRAMMARS
Deterministic Finite Automata And Regular Languages Prof. Busch - LSU.
Non-Deterministic Finite Automata
Properties of Regular Languages
Non-Deterministic Finite Automata
Decidable Languages Costas Busch - LSU.
Transition Diagrams Lecture 3 Fri, Jan 21, 2005.
Elementary Questions about Regular Languages
CSCI 2670 Introduction to Theory of Computing
Decidable Problems of Regular Languages
Undecidable problems:
Chapter 1 Regular Language - 02
More Applications of the Pumping Lemma
Language Recognition (12.4)
Chapter 1 Regular Language
Presentation transcript:

Regular Expressions Prof. Busch - LSU

Regular Expressions Regular expressions describe regular languages Example: describes the language Prof. Busch - LSU

Recursive Definition Primitive regular expressions: Given regular expressions and Are regular expressions Prof. Busch - LSU

Examples A regular expression: Not a regular expression: Prof. Busch - LSU

Languages of Regular Expressions : language of regular expression Example Prof. Busch - LSU

Definition For primitive regular expressions: Prof. Busch - LSU

Definition (continued) For regular expressions and Prof. Busch - LSU

Example Regular expression: Prof. Busch - LSU

Example Regular expression Prof. Busch - LSU

Example Regular expression Prof. Busch - LSU

Example Regular expression = { all strings containing substring 00 } Prof. Busch - LSU

Example Regular expression = { all strings without substring 00 } Prof. Busch - LSU

Equivalent Regular Expressions Definition: Regular expressions and are equivalent if Prof. Busch - LSU

Example = { all strings without substring 00 } and are equivalent regular expressions Prof. Busch - LSU

Regular Expressions and Regular Languages Prof. Busch - LSU

Theorem Languages Generated by Regular Languages Regular Expressions Prof. Busch - LSU

Standard Representations of Regular Languages DFAs Regular Expressions NFAs Prof. Busch - LSU

Language is in a standard representation When we say: We are given a Regular Language We mean: Language is in a standard representation (DFA, NFA, or Regular Expression) Prof. Busch - LSU