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September 15

# September 15 - CSCI 2670 Introduction to Theory of...

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CSCI 2670 Introduction to Theory of Computing September 15, 2005

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Agenda Yesterday Introduce context-free grammars Today No quiz! Quiz postponed until Monday Regular expressions, pumping lemma, CFG’s Build CFG’s
Context-free grammar definition A context-free grammar is a 4-tuple (V, Σ ,R,S),  where 1. V is a finite set called the  variables , 1. Σ  is a finite set, disjoint from V, called the  terminals , 1. R is a finite set of  rules , with each rule being a  variable and a string of variables and terminals, and 2.  V is the  start variable .

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More definitions If u, v, and w are strings of variables and  terminals, and A   w is a rule of the grammar, we  say uAv  yields  uwv Denoted uAv   uwv If a sequence of rules leads from u to v – i.e., u    u 1    u 2    …   v, we denote this  *  v   (I can’t do the actual notation in powerpoint – the * should  be over the double bars) The  language  of the grammar is  {w    Σ *  | s  *  w}
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