LING 388: Language and Computers

1. LING 388: Language and Computers Sandiway Fong Lecture 9: 9/22

2. Administrivia • Reminder • LING 388 Homework #2 went out on Monday • is due next Monday September 27th (by midnight) • need help? • submit homework to sandiway@email.arizona.edu • use plain text if possible (easier for the grader) • Homework #1 • everyone should have gotten email

3. Last Time • Exercises on • FSA • Regular Grammars • including fragments of natural language • the man that I saw that you heard that I met …

4. Today’s Topics • more on natural language cases … • Finite State Transducers (FST) • Context-Free Grammars (CFG)

5. Finite State Transducers (FST) • a Finite State Transducer (FST) • is just a finite state machine, like FSA, but • is not only an acceptor • can also produce an output sequence as well as accepting input sequences • Application: • We can use FST to map from one word form into another • e.g. a rule of pluralization • technology  technologies • Also easy to implement in Prolog …

6. s a b c y:i :e :s X:X Finite State Transducers (FST) • Example: (pluralization) • convert word ending in –y to word ending in –ies • technology  technologies, boundary  boundaries • spy  spies, fly  flies, study  studies • *happy  happies, *correctly  correctlies • Notes: • : = separator between input and output characters • is the empty character • variable X can match any character • Machine is non-deterministic

7. s a b c y:i :e :s X:X Finite State Transducers (FST) • In Prolog: (FSA) • s([X|L]) :- s(L). • s([y|L]) :- a(L). • a(L) :- b(L). • b(L) :- c(L). • c([]). • In Prolog: (FST) • s([X|L],[X|M]) :- s(L,M). • s([y|L],[i|M]) :- a(L,M). • a(L,[e|M]) :- b(L,M). • b(L,[s|M]) :- c(L,M). • c([],[]).

8. s a b c y:i :e :s X:X Finite State Transducers (FST) • Computation tree • ?- s([s,p,y],O). X=s L=[p,y] O=[X|M] • ?- s([p,y],M). X’=p L’=[y] M=[X’|M’] • ?- s([y],M’). X”=y L”=[] M’=[X”|M”] • ?-s([],M”).No • ?- s([y],M’). L”=[] M’=[i|M”] • ?- a([],M”). L”’=[] M”=[e|M”’] • ?- b([],M”). L””=[] M”’=[s|M””] • ?- c([],M””). Yes M””=[] • Answer • O = [s|[p|[i|[e|[s|[]]]]]] • O = [s,p,i,e,s] • s([X|L],[X|M]) :- s(L,M). • s([y|L],[i|M]) :- a(L,M). • a(L,[e|M]) :- b(L,M). • b(L,[s|M]) :- c(L,M). • c([],[]). redo

9. s a b c y:i :e :s X:X s c y:ies X:X Finite State Transducers (FST) • In Prolog: (FST) • s([X|L],[X|M]) :- s(L,M). • s([y|L],[i|M]) :- a(L,M). • a(L,[e|M]) :- b(L,M). • b(L,[s|M]) :- c(L,M). • c([],[]). • In Prolog: (FST simplified) • s([X|L],[X|M]) :- s(L,M). • s([y|L],[i,e,s|M]) :- c(L,M). • c([],[]).

10. s a b c y:i :e :s X:X Finite State Transducers (FST) • Example: (pluralization) • convert word ending in –y to word ending in –ies • technology  technologies, boundary  boundaries • spy  spies, fly  flies, study  studies • *happy  happies, *correctly  correctlies • Counterexamples to the rule: • boy  boies, key  keies • say  saies • Revised Rule: • convert word ending in –y to word ending in –ies in context C__ where C is a consonant

11. s a b c y:i :e :s s z a b c y:i :e :s C:C X:X X:X Finite State Transducers (FST) • Revised Rule: • convert word ending in –y to word ending in –ies in context C__ where C is a consonant character • boy  boies, key  keies • say  saies

12. s z c y:ies C:C X:X Finite State Transducers (FST) • Revised Rule: • convert word ending in –y to word ending in –ies in context C__ where C is a consonant character consonant(b). consonant(c). consonant(d). consonant(f). … consonant(z). • In Prolog: (simplified FST) • s([X|L],[X|M]) :- s(L,M). • s([y|L],[i,e,s|M]) :- c(L,M). • c([],[]). • In Prolog: (revised rule, simplified FST) • s([X|L],[X|M]) :- s(L,M). • s([C|L],[C|M]) :- consonant(C), z(L,M). • z([y|L],[i,e,s|M]) :- c(L,M). • c([],[]).

13. Context-Free Grammars • Regular Grammars • Definite Clause Grammar (DCG) rules that obey special restrictions: • x --> y, [t]. x --> [t]. (left recursive) • x --> [t],y. x --> [t]. (right recursive) • Context-Free Grammars (CFG) • have no restrictions on the number of symbols on the RHS • x --> RHS. • you can mix many terminal and non-terminal symbols as you want • Example of a Context-Free Grammar • non-regular grammar for language anbn • a --> [a], b. • b --> [b]. • b --> a, [b].

14. Context-Free Grammars • Regular Grammars • Definite Clause Grammar (DCG) rules that obey special restrictions: • x --> y, [t]. x --> [t]. (left recursive) • x --> [t],y. x --> [t]. (right recursive) • Context-Free Grammars (CFG) • have no restrictions on the number of symbols on the RHS • x --> RHS. • you can mix many terminal and non-terminal symbols as you want • Another example of a Context-Free Grammar • Sheeptalk ( baa! baaa! baaaa! …) - is a regular language • s --> [b], [a], a, [‘!’]. • a --> [a]. • a --> a, [a].

15. Context-Free Grammars • Where do CFGs fit in? • Chomsky Hierarchy: • Type-0 General rewrite rules • Type-1 Context-sensitive rules • anbncn • Type-2 Context-free rules • anbn Pushdown Automata (PDA) • Type-3 Regular grammar rules • Regular Expressionsa+b+ • Finite State Automata (FSA)

16. FSA Regular Expressions Regular Grammars Context-Free Grammars Type-1 Type-3 Type-2 DCG = Type-0

17. Context-Free Grammars • In Homework #2, we explored some natural language fragments using regular grammars • the man that I saw (that you heard that I met …) • (object relative clauses) • But regular grammars are quite limited • the man likes dogs • the man that the cat saw likes dogs • ?the man that the cat that the mouse hates saw likes dogs • (center-embedding) • CFGs are not only more powerful but are also more useful for writing natural language grammars • Continued next time …