CSA305: Natural Language Algorithms

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CSA305 Natural Language Algorithms

• Deterministic and Non Deterministic Recognition

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Acknowledgement

• Material presented adapted fromJurafsky and
  Martin Ch 2

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Representation of Automata using Transition Tables
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Transition Table Representation in Prolog

• S a b !
• s(0,1,0,0).
• s(1,0,2,0).
• s(2,0,3,0).
• s(3,0,3,4).
• s(4,0,0,0).
• next(OldState,a,NewState) -
• s(OldState,NewState,_,_).
• next(OldState,b,NewState) -
• s(OldState,_,NewState,_).
• next(OldState,!,NewState) -
• s(OldState,_,_,NewState).

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A Better Representation

• s(0,b,1).
• s(1,a,2).
• s(2,a,3).
• s(3,a,3).
• s(3,!,4).
• next(OldState,Sym,NewState) -
• s(OldState,Sym,NewState).

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The Process of Recognition 1

• Start in the initial state and at the first
  symbol of the word.
• If there is an arc labelled with that symbol, the
  machine transitions to the next state, and the
  symbol is consumed.
• The process continues with successive symbols
  until ....

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The Process of Recognition 2

• One or more of these conditions holds
• A. All symbols in the input are consumed
• IF current state is final, succeed, else fail
• B. There are no transitions out of a state for
  the current symbol.
• fail

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Deterministic Recognition

• A deterministic algorithm is one that has no
  choice points
• The following algorithm takes as input a tape and
  an automaton.
• returns accept else reject

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DETERMINISTIC FSA RECOGNITION
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Skeleton of Prolog Implementation

• drec(Tape,Machine,State,Result).
• drec( , M, S, yes) -
• final(S).
• drec(HT, M, S, Result) -
• tran(M,S,H,N),
• drec(T,M,N,Result).
• drec(_,_,_,no).

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Failure States

• We can regard failure as a special state.
• That state is reached by adding supplementary
  arcs that represent invalid input.

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Adding a Failure State
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Deterministic versus Non Deterministic
Recognition.

• The behaviour of the automata we have considered
  is fully determined by the current state, and the
  input symbol.
• The recognition process is said to be
  deterministic
• This is not necessarily the case.
• Several arcs with the same label.
• ?-Transitions. Arcs with no label.
• Automata like this are called non-determinstic

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Non Deterministic FAs
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Non Deterministic Recognition

• There are three ways of dealing with
  non-deterministic recognition
• Backtracking at every choice point, record the
  state and as yet unexplored choices.
• Lookahead peek ahead n symbols in the input in
  order to decide which path to take.
• Parallel search look at every path in parallel.

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ND-RECOGNISE
function ND-RECOGNISE(tape,machine) returns
accept or reject agenda ? (q0(machine),0)
search_state ? NEXT(agenda) loop if
ACCEPT-STATE?(search_state) true then return
accept else agenda ? agenda ? GENERATE-NEW-STATES(
search_state) if agenda is empty then return
reject else current_state ? NEXT(agenda) end
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ACCEPT-STATE?
function ACCEPT-STATES?(search_state) mstate ?
first(search_state) tape_pos ? second(search_state
) if tapetape_pos end_input and
IS-FINAL?(mstate) then return true else return
false
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GENERATE-NEW-STATES
function GENERATE-NEW-STATES(search_state) mstate
? first(search_state) tape_pos ?
second(search_state) return (x,tape_pos)
xtrantablemstate,? ? (x, tape_pos 1)
trantablemstate, tapetape_pos
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Recognition as Search

• Recognition can be regarded as a search problem
• Initial state, Goal State
• Rules
• Strategy
• Different search behaviours (depth first, breadth
  first) can be evoked by managing the agenda in
  different ways.
• See Jurafsky Martin sect 2.2

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Deterministic and Non Deterministic FSAs

• The class of languages recognisable by NDFSA is
  identical to that recognised by DFSA.
• For every NDFSA ND there is an equivalent FSA D.
• The states of D correspond to sets of states in
  ND
• If N is the number of states in ND, the number of
  states in D is 2N