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We want to remove ambiguity. Ambiguity is bad for programming languages. 63 ... Inherent Ambiguity. Some context free languages. have only ambiguous grammars. Example: ...
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Ambiguity. A context-free grammar G is said to be ambiguous if ... Ambiguity. If L is a context-free language for which there exists an ...
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A context-free grammar is ambiguous. if some string has: two or more derivation trees ... is non-ambiguous: Every string has. a unique derivation tree. Costas ...
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B Bb | ba B ba | baY. Y b | bY. 6. Removing Useless Productions. S aSb | | A. A aA ... Let G = (V, T, S, P) be a context-free grammar. ...
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Fall 2003. Costas Buch - RPI. 8. Unit-Productions. Unit Production: ... Fall 2003. Costas Buch - RPI. 18. A production is useless. if any of its variables is useless ...
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A grammar G = (V, T, S, P) is said to be context-free if all production rules in ... This grammar is linear (that is, there is at most a single variable on the right ...
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with length. We will show: in the derivation of. a variable of ... with lengths and. 30. Pumping Lemma says: for all. 31. We examine all the possible locations ...
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... convert any context-free grammar. Such that: Simulates leftmost ... Example of a NPDA in correct form: Fall 2004. COMP 335. 32. The Grammar Construction ...
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... grammars recognize exactly the same class of languages as non-deterministic pushdown automata. ... a, X, XB. a, X, B. b, Y, YA. b, Y, A. a, A, ?. b, B, ? ...
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v shot. shot. No more rules, but input is not ... shot. det n. an. elephant ... point, we are looking for a v, and shot fits the bill; the n reading never comes ...
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Step 2: Remove Unit-Productions. Step 3: Remove Useless Variables. This sequence guarantees that ... Conversion to Chomsky Normal Form. Example: Not Chomsky ...
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Context-Free and. Noncontext-Free Languages. Chapter 13. Languages ... The need for nondeterminism is the key. Deterministic PDAs. A PDA M is deterministic iff: ...
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A aAb | Ab | Exercise 5.1.7(f) S aS | aSb | SS | {aibjcjdie3: i, j 0} ... Leftmost: S AB bAB bbAB bbaB bbaaB... Rightmost: S AB AaB AabA ... But SAME derivation tree ...
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TOP-DOWN AND BOTTOM-UP SEARCH STRATEGIES ... BOTTOM-UP search: the parse tree must be an analysis of the input ... A hybrid of top-down and bottom-up parsing ...
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... number of adjectives, including, preceding ... 3' noun phrase adjective-list proper-noun 4' noun phrase determiner adjective-list common noun ...
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(1) A book was given to the professor. ... So, the extensions of x are the infinite values that x takes on at each time point t. ...
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Time complexity of exhaustive search. Suppose there are no productions of the form ... There exists a parsing algorithm. that parses a string. in time. The CYK parser ...
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Is the family of CFLs closed under a certain operation? 2. Pumping Lemma. Let L be an infinite CFL. ... Pumping Lemma for Linear CFLs. Let L be an infinite linear CFL. ...
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Context-Free and. Noncontext-Free Languages. Chapter 13. Languages That Are and. Are Not Context-Free ... AnBnCn = {anbncn : n 0} is not context-free. Languages ...
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Parse trees and abstract syntax. Ambiguous grammars ... In example grammar, left-most and right-most derivations produced identical parse trees ...
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Department of Math and Computer Science. Bennett College. Goals ... G is the finite collection of stack symbols. T is a finite collection of transitions. ...
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Introduce the new symbol to denote. the bottom of the stack. Fall 2003. Costas Busch - RPI ... if and only if. the NPDA goes from to. by reading string and. the ...
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Are natural languages context-free languages? ... det noun rel-pron verb det noun. NP. NP. NP. VP. Srel. NP. Martin Volk. 20. 11/8/09 ...
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7.1 Normal Forms for CFG's. 7.2 The Pumping Lemma for CFL's. 7.3 Closure ... Omitting useless symbols obviously will not change the language generated by the ...
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Approximating ContextFree Grammar Ambiguity
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word(girl,n). word(slept,vi). in the S network, there is. an ... girl slept NP2 S2 Recognize N. slept NP3 S2 Pop to S-network. slept S2 --- Push to VP-network ...
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Each level of languages in the Chomsky hierarchy has a computing model associated with it. ... Palindromes read the same forward and backward: Madam, I'm Adam. ...
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The class of context-free languages generalizes the class of regular languages, ... common-noun car (6) common-noun hamburger (7) determiner a (8) ...
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Depending on what sk 1...sn is, there might be a subtree formed from production ... ( When creating a parse tree, the A in this new item will have have children , as ...
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A number consists of one digit or many digits. For a one digit number, it could ... Definition 2: The set generated by a regular grammar G = (V, T, P, S) is { T ...
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Synchronous context-free grammars as translation models. Analysis of membership problem ... of the art machine translation systems based on statistical models ...
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Only searches for trees that can be answers ... Use one kind as the control and the other as a filter ... Combine the two to avoid over-generation: Top-Down ...
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A AAA | bA | Ab | a. Parse Trees for the word bbaaaab. S ... X ab | b. S. bX. aXX. aa. aabX. abX. aXab. aXb. aabb. abab. aabab. abb. abab. aabb. aabab. abb. bab ...
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Corollary: Let G be a CFG in CNF, and let w be a string in L(G) ... Since no non-terminal derives the empty string (in CNF), either V1 or V2 must ...
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The old woman gave a big red book to the small boy. ... British Left Waffles on Falkland Islands. Red Tape Holds Up New Bridges ...
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BA AB, CA AC and CB BC ... Exercise: What language is generated by the following type 0 grammar? S ABS AB BA BA AB A a B b ... AB BA. bB bb. bA ba. aA aa ...
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Refers to the way words are arranged together, and the relationship between them. ... Prescriptive: 'prescriptive linguistics' is an oxymoron ...
Title: Chapter 1 Author: mark temelko Last modified by: Joey Paquet Created Date: 5/6/2005 9:09:49 AM Document presentation format: On-screen Show (4:3)
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Syntax: the way words are arranged together. Main ideas of syntax: Constituency ... a high-class spot such as Mindy's attracts. the Broadway coppers love. They ...
