Lecture 14 PDAs and CFGs

Lecture 14 PDAs and CFGs - Ling 726 Mathematical...

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Unformatted text preview: Ling 726: Mathematical Linguistics, Lecture 14 PDAs and CFGs V. Borschev and B. Partee, November 4, 2004 p. 1 Lecture 14. Push-Down Storage Automata and Context-Free Grammars 1. Pushdown automata .............................................................................................................................................1 2. Context-free grammars and languages.................................................................................................................3 3. Pumping theorem for context-free languages.......................................................................................................3 4. Closure properties of context free languages. ......................................................................................................3 5. Decidability properties of context free languages...............................................................................................4 6. Are natural languages context-free?.....................................................................................................................5 7. Issues concerning the difficulty of processing nested and serial dependencies...................................................6 References................................................................................................................................................................7 Reading: Chapter 18, “Pushdown Automata, Context Free Grammars and Languages” of PtMW, pp. 485- 504. See also References . 1. Pushdown automata A pushdown automaton , or pda , is essentially a finite state automaton augmented with an auxiliary tape on which it can read, write, and erase symbols. Its transitions from state to state can depend not only on what state it is in and what it sees on the input tape but also on what it sees on the auxiliary state, and its actions can include not only change of state but also operations on the auxiliary tape. The auxiliary tape works as a pushdown store , “last in, first out”, like a stack of plates in some cafeterias. You can’t ‘see’ below the top item on the stack without first removing (erasing) that top item. States: as in a fsa, a pda has a finite number of states, including a designated initial state and a set of “final” or “accepting” states. Transitions: ( q i , a, A ) → ( q j , γ ), where q i , q j are states, a is a symbol of the input alphabet, A is either the empty string e or a symbol of the stack alphabet (which need not be the same as the input alphabet), and γ is a string of stack symbols, possibly the empty string. Interpretation: When in state q i , reading a on the input tape, and reading A at the top of the stack, go to state q j , and replace A by the string γ . The elements of the string γ go onto the stack one at a time, so the last symbol of γ ends up as the top symbol on the stack. In case γ is the empty string e , the effect is to erase γ , that is to remove it (“pop” it) from the stack. (“Push” down and “pop” , that is to remove it (“pop” it) from the stack....
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Lecture 14 PDAs and CFGs - Ling 726 Mathematical...

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