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Lecture Notes for CS 373 - Theory of Computation with Viswanathan at Illinois (UIUC)

Notes Information

Material Type:Class Note
Professor:Viswanathan
Class:CS 373 - Theory of Computation
Subject:Computer Science
University:University of Illinois - Urbana-Champaign
Term:Fall 2008
Keywords:
  • Buffer State
  • Either...or
  • Transitions
  • Immediately
  • Induction Step
  • Simple Solution
  • Language Definition
  • Proposition
  • Definitions
  • Normalization
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CS 373: Theory of Computation Manoj Prabhakaran Mahesh Viswanathan Fall 2008 Part I Lecture 12 1 Context Free Grammars 1 Introduction Parenthesis Matching Problem Describe the the set of arithmetic expressions with correctly matched parenthesis. Arithmetic expressions with correctly matched parenthesis cannot be described by a regular expression . Let L be the language of correct expressions . Suppose h maps number and variables to epsilon1, and opening parenthesis to 0 and closing paren- thesis to 1 then h(L)?{0,1}? . h(L)?0?1? ={0n1n|n?0}which is not regular. This is an example of a context-free language, that we study. Parenthesis Matching Inductive Definition Ignoring numbers and variables, and focussing only on parenthesis, correctly matched expressions can be defined as . The epsilon1 is a valid expression . A valid string (negationslash= epsilon1) must either be - The concatenation of two correctly matched expressions, or - It must begin with ( and end with ) and moreover, once...

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