CSA3050: NLP Algorithms

1. CSA3050: NLP Algorithms Parsing Algorithms 2 Problems with DFTD Parser Earley Parsing Algorithm CSA3050: Parsing Algorithms 2

2. Left Recursion Ambiguity Inefficiency Problems withDFTD Parser CSA3050: Parsing Algorithms 2

3. Left Recursion • A grammar is left recursive if it contains at least one non-terminal A for whichA * A and  *  • Intuitive idea: derivation of that category includes itself along its leftmost branch. NP  NP PP NP  NP and NP NP  DetP Nominal DetP  NP ' s CSA3050: Parsing Algorithms 2

4. Infinite Search CSA3050: Parsing Algorithms 2

5. Dealing with Left Recursion • Reformulate the grammar • A  A | as • A  A' A'  A' |  • Disadvantage: different (and probably unnatural) parse trees. • Use a different parse algorithm CSA3050: Parsing Algorithms 2

6. Ambiguity • Coordination Ambiguity: different scope of conjunction:Black cats and dogs like to play • Attachment Ambiguity: a constituent can be added to the parse tree in different places:I shot an elephant in my pyjamas • VP → VP PPNP → NP PP CSA3050: Parsing Algorithms 2

7. Catalan Numbers The nth Catalan number counts the ways of dissecting a polygon with n+2 sides into triangles by drawing nonintersecting diagonals. CSA3050: Parsing Algorithms 2

8. Handling Disambiguation • Statistical disambiguation • Semantic knowledge. CSA3050: Parsing Algorithms 2

9. Repeated Parsing ofSubtrees CSA3050: Parsing Algorithms 2

10. Earley Algorithm • Dynamic Programming: solution involves filling in table of solutions to subproblems. • Parallel Top Down Search • Worst case complexity = O(N3) in length N of sentence. • Table, called a chart, contains N+1 entries ● book ● that ● flight ● 0 1 2 3 CSA3050: Parsing Algorithms 2

11. The Chart • Each table entry contains a list of states • Each state represents all partial parses that have been reached so far at that point in the sentence. • States are represented using dotted rules containing information about • Rule/subtree: which rule has been used • Progress: dot indicates how much of rule's RHS has been recognised. • Position: text segment to which this parse applies CSA3050: Parsing Algorithms 2

12. Examples of Dotted Rules • Initial S RuleS → ● VP, [0,0] • Partially recognised NPNP → Det ● Nominal, [1,2] • Fully recognised VPVP → V VP ● , [0,3] • These states can also be represented graphically CSA3050: Parsing Algorithms 2

13. The Chart CSA3050: Parsing Algorithms 2

14. Earley Algorithm • Main Algorithm: proceeds through each text position, applying one of the three operators below. • Predictor: Creates "initial states" (ie states whose RHS is completely unparsed). • Scanner: checks current input when next category to be recognised is pre-terminal. • Completer: when a state is "complete" (nothing after dot), advance all states to the left that are looking for the associated category. CSA3050: Parsing Algorithms 2

15. Early Algorithm – Main Function CSA3050: Parsing Algorithms 2

16. Early Algorithm – Sub Functions CSA3050: Parsing Algorithms 2

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19. fl CSA3050: Parsing Algorithms 2

20. Retrieving Trees • To turn recogniser into a parser, representation of each state must also include information about completed states that generated its constituents CSA3050: Parsing Algorithms 2

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22. Chart[3] ↑Extra Field CSA3050: Parsing Algorithms 2