Finite-state automata Day 12 LING Computational Linguistics Harry Howard Tulane University

21-Sept-2009LING , Prof. Howard, Tulane University2 Course organization   NLTK is installed on the computers in this room!  How would you like to use the Provost's $150?

SLP §2.2 Finite-state automata Sheeptalk

21-Sept-2009LING , Prof. Howard, Tulane University4 The sheep language  How would you recognize this language?  baa!  baaa!  baaaa!  baaaaa! ……  Regex in Python?  '^baa+!$'

21-Sept-2009LING , Prof. Howard, Tulane University5 q0q0 q1q1 q2q2 q3q3 q4q4 baa a ! State transitions  A directed graph of vertices/nodes connected by links/arcs.  Each node is labeled as a state, q 0 - q 4  q 0 is the start state;  q 4 is the final or accepting state.  Each transition from state to state is labeled with the character that it recognizes.

21-Sept-2009LING , Prof. Howard, Tulane University6 Equivalency to a tape  Start at the start state.  Check the next character of the input.  If it matches the symbol on the arc leaving the current state,  then cross the arc, and move to the next state.  Return to beginning.  If it is the final state, and there is no more input, the input has been recognized successfully.  If the final state is never reached, the input is rejected. baaa! q0q0

21-Sept-2009LING , Prof. Howard, Tulane University7 Input Stateba! :000 State-transition table  : marks final state.  0 = illegal or missing transition.  If in state 0 and see input b, go to state 1;  if in state 0 and see input a or !, fail.

21-Sept-2009LING , Prof. Howard, Tulane University8 Definition p. 28  The procedure is known as a finite(-state) automaton, which consists of five parameters:  Q a finite set of n states,   a finite input alphabet of symbols,  q 0 the start state,  Fthe set of final states,   (q,i)the transition function or matrix. For a state q and an input symbol i,  (q,i) returns a new state q'.

21-Sept-2009LING , Prof. Howard, Tulane University9 Algorithm Fig. 2.12, p. 29 function D-RECOGNIZE(tape, machine) returns accept or reject index  Beginning of tape current-state  Initial state of machine loop if End of input has been reached then if current-state is an accept state then return accept else return reject elseif transition-table[current-state,tape[index]] is empty then return reject else current-state  transition-table[current-state,tape[index]] index  index + 1 end

21-Sept-2009LING , Prof. Howard, Tulane University10 Python dictionaries  Use the Python data object known as a dictionary (hash table in other languages) your_dict = {key1: value1, key2: value2,...} >>> your_dict[key1] value1  Part of speech dictionary, see NLPP pp. 190ff pos = {'colorless': 'ADJ', 'ideas': 'N', 'furiously': 'ADV'} >>> pos['furiously'] 'ADV'

21-Sept-2009LING , Prof. Howard, Tulane University11 A state-transition table  Need compound keys your_dict = {(key1a, key1a): value1, (key2a, key2b): value2,...} >>> your_dict[(key2a, key2a)] value2  Sample first line for sheep language stt = {(0,'b'): 1, (0,'a'): 0, (0,'!'): 0, >>> stt[(0,'!')] 0  HINT: put dictionary at beginning of function

Next time Code up the algorithm and bring a printout of it to class on Wed. SLP §2.2.2-end