PLT: Lecture 7

1
PLT Lecture 7

• Chomsky

2
Strings with Well-Formed Parenthesis

• Use Posts production rules to specify the
  generation of strings with well formed
  parenthesis
• WFP.L(,)
• WFP.VS, T,
• WFP.Axioms( )
• WFP.RulesS-gt(S), S-gtSS, S( )T-gtST

3
Chomskys Adaptation

• Post
• E.literals1
• E.VariablesS
• E.Axioms11
• E.ProductionsS-gtS11
• Chomsky
• E.Terminals1
• E.Non TerminalsS
• E.ProductionsS-gt11, S-gtS11
• Rewrite
• WFP(,), S,T, ( ), S-gt(S), S-gtSS,
  S( )T-gtST
• Pa,b,c, S, a,b,c,aa,bb,cc, S-gtaSa,
  S-gtbSb, S-gtcSc

4
Chomskys thoughts

• Words classified into grammatical categories
  nouns verbs etc
• Can generate structurally well formed sentences
  from
• Template of grammatical categories
• Article noun verb article noun .
• Substitution
• The cat chased the mouse .
• The man hit the dog .
• A student passed the exam .

5
A Post Production System for Phrases

• If we have
• Dsome, a the
• Abig, black
• Ncat, rat, hat, mat
• Then
• Phrase.Tsome, a, the, big, black, cat, rat,
  hat, mat
• Phrase.NTD, A, N
• Phrase.Production
• D-gtsome, D-gta, D-gtthe
• A-gtbig, A-gtblack
• N-gtcat, N-gtrat, N-gthat, N-gtmat
• P-gtDAN

6
Sentences

• Examples
• the cat sat on the mat
• the cat on the mat sat (shakespearean)
• on the mat sat the cat (Dr Zeuss)
• on the mat the cat sat (unusual, but could be
  response to Dr Zeuss question)
• sat the cat on the mat? ( fairly shakespearean)
• sat on the mat the cat? (even more strange than
  Dr. Zeuss)

7
Write the production rules

• That allow
• The big cat
• The big black cat
• The big black friendly cat
• (One or more adjectives)
• That allow
• Big cat
• The cat
• The big black friendly cat
• (Zero or one article at the start)
• (Zero or more adjectives)

8
Solution 1 Recursion

• So how do we cope with (1M adjectives) strings
  like
• The black cat
• The big black cat
• The big black friendly cat
• Heres how
• D-gtsome, D-gta, D-gtthe
• A-gtbig, A-gtblack, A-gtfriendly
• N-gtcat, N-gtrat, N-gthat, N-gtmat
• P-gtDQN
• Q-gtAQ
• Q-gtA

9
Solution 2 Tweaking Solution 1

• So how do we cope with (1M adjectives) strings
  like
• The cat
• The big black cat
• The big black helpful cat
• Big cat
• Heres how
• D-gtsome, D-gta, D-gtthe
• A-gtbig, A-gtblack, A-gthelpful
• N-gtcat, N-gtrat, N-gthat, N-gtmat
• P-gtDQ
• Q-gtAQ
• Q-gtA
• Q-gtN

10
Solution 2

• So how do we cope with (1M adjectives) strings
  like
• The cat
• The big black cat
• The big black helpful cat
• Big cat
• Heres how
• D-gtsome, D-gta, D-gtthe
• A-gtbig, A-gtblack, A-gthelpful
• N-gtcat, N-gtrat, N-gthat, N-gtmat
• P-gtDQ
• P-gtQ
• Q-gtAQ
• Q-gtA
• Q-gtN

11
Overall Structure

• Instances
• The cat chased the big rat
• The big dog hit the helpful frog
• frog caught a big black helpful cat
• Productions
• D-gtsome, D-gta, D-gtthe
• A-gtbig, A-gtblack, A-gthelpful
• N-gtcat, N-gtrat, N-gtdog, N-gtfrog
• V-gt hit, V-gtchased, V-gtcaught
• P-gtDQ
• P-gtQ
• Q-gtAQ
• Q-gtA
• Q-gtN
• S-gt PVP

12
Phase Structure, Generative Grammars

• 4-tuple VT, VN, P, S
• VT
• VN
• VN U VT
• P binary relations called productions or re-write
  rules
• Domain V x VN X V
• Codomain V
• Eventually some rules of type
• Domain -gt VT
• S element of VN