PPT-Minimal DFA Among the many DFAs accepting the same regular language L, there is

exactly one up to renaming of states which has the smallest possible number of states Moreover it is possible to obtain that minimal DFA for L starting from any other by the State Minimization Algorithm. 1. . Theory of Computation Peer Instruction Lecture Slides by . Dr. Cynthia Lee, UCSD.  are licensed under a . Creative Commons Attribution-. NonCommercial. -. ShareAlike. 3.0 . Unported. License. CS 4705. Some . slides adapted . from Hirschberg, Dorr/. Monz. , . Jurafsky. Some simple problems: . How much is Google worth?. How much is the Empire State Building worth?. How much is Columbia University worth?. Definitions. Equivalence to Finite Automata. 2. RE. ’. s: Introduction. Regular expressions. describe languages by an algebra.. They describe exactly the regular languages.. If E is a regular expression, then L(E) is the language it defines.. Formal definition of a regular expression.. Languages associated with regular expressions.. Introduction regular grammars. . Regular language and homomorphism. . The Chomsky Hierarchy . Regular Expression. Reading: Chapter 2. 2. Finite Automaton (FA). Informally, a state diagram that comprehensively captures all possible states and transitions that a machine can take while responding to a stream or sequence of input symbols. Reading: Chapter 3. 2. Regular Expressions vs. Finite Automata. Offers a declarative way to express the pattern of any string we want to accept . E.g., . 01*+ 10*. Automata => more machine-like . < input: string , output: [accept/reject] >. Reading: Chapter 4. 2. Topics. How to prove whether a given language is regular or not?. Closure properties of regular languages. Minimization of DFAs. 3. Some languages are . not . regular. When is a language is regular? . Lexers. Example in . javacc. TOKEN. : {. <IDENTIFIER: <LETTER> (<LETTER> | <DIGIT> | "_")* >. | . <INTLITERAL: . <DIGIT> (<DIGIT>)* . >. | <LETTER: ["a"-"z"] | ["A"-"Z"]>. Regular Languages. Regular languages are the languages which are accepted by a Finite Automaton.. Not all languages are regular. Non-Regular Languages. L. 0. = {. a. k. b. k. : k≤0} = . {ε}. is a regular language. Fall 2017. http://cseweb.ucsd.edu/classes/fa17/cse105-a/. Today's learning goals . Sipser Ch 1.2, 1.3. Decide whether or not a string is described by a given regular expression. Design a regular expression to describe a given language. Chapter 3 REGULAR LANGUAGES AND REGULAR GRAMMARS Learning Objectives At the conclusion of the chapter, the student will be able to: Identify the language associated with a regular expression Find a regular expression to describe a given language Regular Languages Refresher. Roman . Manevich. Ben-Gurion University of the Negev. Regular languages refresher. 2. Regular languages refresher. Formal languages. Alphabet = finite set of letters. Word = sequence of letter. Learning . Objectives. At the conclusion of the chapter, the student will be able to:. State the closure properties applicable to regular languages. Prove that regular languages are closed under union, concatenation, star-closure, complementation, and intersection. 2. Regular Expressions vs. Finite Automata. Offers a declarative way to express the pattern of any string we want to accept . E.g., . 01*+ 10*. Automata => more machine-like . < input: string , output: [accept/reject] >.