1. LING 388 Language and Computers Lecture 7 9/23/03 Sandiway FONG

2. Administrivia Reminder Reminder  Thursday  Computer Lab Class Part 2…

3. Exercise 1: Finite State Automata (FSA) sx y a a b b L = {a + b + }

4. Exercise 1 From Lecture 4… From Lecture 4…  A possible Prolog encoding strategy:  Define one predicate for each state Name of state = name of predicateName of state = name of predicate Arity of predicate = 1Arity of predicate = 1 –taking one argument (the input string)

5. Exercise 1 Basic Idea 1: Basic Idea 1:  Treat the input string as a list  Consume one input character corresponding to transition arc from state, and  Call next state with remaining input string Basic Idea 2: Basic Idea 2:  For end state(s), match empty input  i.e. we can stop only when all input has been consumed and we’re in an end state

6. Exercise 1 Machine for L = {a + b + }Machine for L = {a + b + }  State s:  s([a|L]) :- x(L). match input string beginning with a and call state x with remainder of input  State x:  x([a|L]) :- x(L).  x([b|L]) :- y(L).  State y: (end state)  y([]).  y([b|L]) :- y(L).

7. Exercise 1 Consult FSA Consult FSA Turn on tracing facility Turn on tracing facility  ?- trace. Run query step-by-step Run query step-by-step  ?- s([a,a,b,b]). Run query Run query  ?- s([a,b,a]). Run query Run query  ?- s([a,X]).

8. Exercise 1 Homework Question (A): Homework Question (A):  What and how many answers does the query ?- s([X,Y,Z]). return? Homework Question (B): Homework Question (B):  If the clause x([a|L]) :- x(L). is removed from the program, what language does the revised FSA accept?

9. Exercise 2: Finite State Automata (FSA) Also from Lecture 4… Also from Lecture 4…  Formally:  Set of states: {s,x,y}  Start state: s, end state: y  Alphabet: {a, b}  Transition function  with signature: character x state -> state  (a,s)=x  (a,x)=x  (b,x)=y  (b,y)=y

10. Exercise 2 Basic Idea: Basic Idea:  Implement details of FSA as database facts  Write a generic program to call database facts Note: Note:  Compare implementation with Exercise 1 …where FSA details such as the layout of the FSA and program control, e.g. in the sense of what state to call next, are merged

11. Exercise 2 Database Facts: Database Facts:  startState(s).  endState(y).  transition(s,a,x).  transition(x,a,x).  transition(x,b,y).  transition(y,b,y).

12. Exercise 2 Generic Program: Generic Program:  fsa(L) :- startState(S),fsa(S,L).  fsa(S,[C|L]) :- transition(S,C,T),fsa(T,L).  fsa(S,[]) :- endState(S).

13. Exercise 2 Consult FSA and turn on tracing facility Consult FSA and turn on tracing facility Re-run queries from Exercise 1: Re-run queries from Exercise 1:  ?- fsa([a,a,b,b]).  ?- fsa([a,b,a]).  ?- fsa([a,X]).

14. Exercise 2 Homework Question (A): Homework Question (A):  What happens when we run the following query?  ?- fsa(L). Homework Question (B): Homework Question (B):  Does the corresponding query for the program in Exercise 1  ?- s(L). do the same thing? Homework Question (C): Homework Question (C):  Explain the behavior of the programs

15. Exercise 3 We’re going to implement a Finite State Transducer We’re going to implement a Finite State Transducer  i.e. a FSA that not only accepts input but produces output as well Strategy: Strategy:  Modify an existing FSA acceptor to take one more parameter (the output list)

16. Exercise 3: Finite State Transducer ab y : ies X : X Notation: input : output Variable denotes any character Example: convert word ending in –y to word ending in –ies

17. Exercise 3 Acceptor Program: Acceptor Program:  a([y|L]) :- b(L).  a([X|L]) :- a(L).  b([]). Note: Note:  FSA is non-deterministic

18. Exercise 3 Run queries: Run queries:  ?- a([f,l,y]).  ?- a([b,a,b,y]).  ?- a([a,p,p,l,e]).

19. Exercise 3 Convert FSA into transducer: Convert FSA into transducer:  a([y|L],M) :- b(L,M).  a([X|L],[X|M]) :- a(L,M).  b([],[i,e,s]). Notes: Notes:  M represents the output list

20. Exercise 3 Re-do previous queries with the extra output parameter: Re-do previous queries with the extra output parameter:  ?- a([f,l,y],X).  ?- a([b,a,b,y],X).  ?- a([a,p,p,l,e],X).

21. Exercise 3 Homework Question: Homework Question:  How does the transducer handle more than one “y” in the input?  Example: a([y,u,c,k,y],X).  Hint: turn on tracing