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Unformatted text preview: 1 Equivalence of PDA, CFG Conversion of CFG to PDA Conversion of PDA to CFG 2 Overview ◆ When we talked about closure properties of regular languages, it was useful to be able to jump between RE and DFA representations. ◆ Similarly, CFG’s and PDA’s are both useful to deal with properties of the CFL’s. 3 Overview – (2) ◆ Also, PDA’s, being “algorithmic,” are often easier to use when arguing that a language is a CFL. ◆ Example : It is easy to see how a PDA can recognize balanced parentheses; not so easy as a grammar. ◆ But all depends on knowing that CFG’s and PDA’s both define the CFL’s. 4 Converting a CFG to a PDA ◆ Let L = L(G). ◆ Construct PDA P such that N(P) = L. ◆ P has: ◗ One state q. ◗ Input symbols = terminals of G. ◗ Stack symbols = all symbols of G. ◗ Start symbol = start symbol of G. 5 Intuition About P ◆ Given input w, P will step through a leftmost derivation of w from the start symbol S. ◆ Since P can’t know what this derivation is, or even what the end of w is, it uses nondeterminism to “guess” the production to use at each step. 6 Intuition – (2) ◆ At each step, P represents some leftsentential form (step of a leftmost derivation). ◆ If the stack of P is α , and P has so far consumed x from its input, then P represents leftsentential form x α ....
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This note was uploaded on 03/30/2012 for the course CS 154 taught by Professor Motwani,r during the Spring '08 term at Stanford.
 Spring '08
 Motwani,R

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