notes21 Pushdown Automata and CFGs

notes21 Pushdown Automata and CFGs - CS 373: Theory of...

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Unformatted text preview: CS 373: Theory of Computation Gul Agha Mahesh Viswanathan Fall 2010 1 1 Pushdown Automata 1.1 Computing Using a Stack Restricted Infinite Memory: The Stack • So far we considered automata with finite memory or machines with infinite memory • Today: automata with access to an infinite stack — infinite memory but restricted access • The stack can contain an unlimited number of characters. But – can read/erase only the top of the stack: pop – can add to only the top of the stack: push • On longer inputs, automaton may have more items in the stack Keeping Count Using the Stack • An automaton can use the stack to recognize { n 1 n } – On reading a 0, push it onto the stack – After the 0s, on reading each 1, pop a 0 – (If a 0 comes after a 1, reject) – If attempt to pop an empty stack, reject – If stack not empty at the end, reject – Else accept Matching Parenthesis Using the Stack • An automaton can use the stack to recognize balanced parenthesis • e.g. (())() is balanced, but ())() and (() are not – On seeing a ( push it on the stack – On seeing a ) pop a ( from the stack – If attempt to pop an empty stack, reject – If stack not empty at the end, reject – Else accept 2 1.2 Definition Pushdown Automata (PDA) a b...
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This note was uploaded on 10/04/2011 for the course CS 373 taught by Professor Viswanathan,m during the Fall '08 term at University of Illinois, Urbana Champaign.

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notes21 Pushdown Automata and CFGs - CS 373: Theory of...

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