Formal Language Theory

Homework Read documentation on Graphviz – – Use graphviz to generate figures like these (more or less):

Back to Regular Expressions import re myString="I have red shoes and blue pants and a green shirt. My phone number is and my friend's phone number is (800) and my cell number is You could also call me at if you'd like.” phoneNumbersRegEx=re.compile(''1?-?\(?\d{3}\)?-?\d{3}-?\d{4}'') print phoneNumbersRegEx.findall(myString) 10. A more interesting example Answer is here, but let’s derive it together

Formal Definition of Regular Expressions  character  ( ) Concatenation:  Union:  + Kleene Star:  ( ) * Characters: – lower case: a-z – upper case: A-Z – digits: 0-9 – special cases: \t \n – octal codes: \000 – any single character:.

An Equivalence Relation (= R ) A Partition of S ≡ Set of Subsets of S –Mutually Exclusive & Exhaustive Equivalence Classes ≡ A Partition such that –All the elements in a class are equivalent (with respect to = R ) –No element from one class is equivalent to an element from another Example: Partition integers into evens & odds Even integers: 2,4,6… Odd integers: 1,3,5… –x = R y  x has the same parity as y Three Properties –Reflexive: a = R a –Symmetric: a = R b  b = R a –Transitive: a = R b & b = R c  a = R c

>>> for s in wn.synsets('car'): print s.lemma_names ['car', 'auto', 'automobile', 'machine', 'motorcar'] ['car', 'railcar', 'railway_car', 'railroad_car'] ['car', 'gondola'] ['car', 'elevator_car'] ['cable_car', 'car'] >>> for s in wn.synsets('car'): print flatten(s.lemma_names) + ': ' + s.definition car auto automobile machine motorcar: a motor vehicle with four wheels; usually propelled by an internal combustion engine car railcar railway_car railroad_car: a wheeled vehicle adapted to the rails of railroad car gondola: the compartment that is suspended from an airship and that carries personnel and the cargo and the power plant car elevator_car: where passengers ride up and down cable_car car: a conveyance for passengers or freight on a cable railway Word Net (Ch2): An Equivalence Relation

Synonymy: An Equivalence Relation?

Comments

A Partial Order (≤ R ) Powerset({x,y,z}) – Subsets ordered by inclusion – a≤ R b  a  b Three properties – Reflexive: a≤a – Antisymmetric: a≤b & b≤a  a=b – Transitivity: a≤b & b≤c  a≤c

Wordnet: A Partial Order >>> for h in wn.synsets('car')[0].hypernym_paths()[0]: print h.lemma_names ['entity'] ['physical_entity'] ['object', 'physical_object'] ['whole', 'unit'] ['artifact', 'artefact'] ['instrumentality', 'instrumentation'] ['container'] ['wheeled_vehicle'] ['self-propelled_vehicle'] ['motor_vehicle', 'automotive_vehicle'] ['car', 'auto', 'automobile', 'machine', 'motorcar']

Help s = wn.synsets('car')[0] >>> s.name 'car.n.01' >>> s.pos 'n' >>> s.lemmas [Lemma('car.n.01.car'), Lemma('car.n.01.auto'), Lemma('car.n.01.automobile'), Lemma('car.n.01.machine'), Lemma('car.n.01.motorcar')] >>> s.examples ['he needs a car to get to work'] >>> s.definition 'a motor vehicle with four wheels; usually propelled by an internal combustion engine' >>> s.hyponyms()[0:3] [Synset('stanley_steamer.n.01'), Synset('hardtop.n.01'), Synset('loaner.n.02')] >>> s.hypernyms() [Synset('motor_vehicle.n.01')]

CFGs: Context Free Grammars (Ch8)

Ambiguity

The Chomsky Hierarchy – Type 0 > Type 1 > Type 2 > Type 3 – Recursively Enumerable > CS > CF > Regular Examples – Type 3: Regular (Finite State): Grep & Regular Expressions Right-Branching: A  a A Left-Branching: B  B b – Type 2: Context-Free (CF): Center-Embedding: C  …  x C y Parenthesis Grammars:  ( ) w w R – Type 1: Context-Sensitive (CS): w w – Type 0: Recursively Enumerable – Beyond Type 0: Halting Problem

Syntax & Semantics Syntax: Symbol pushing / Parsing – Parsing: use context-free grammar to map string  tree Semantics: Meaning (making sense of trees) – Is synonymy an equivalence relation? Dichotomy is important both for – Natural Languages (English, FIGS, CJK, etc.) FIGS: French, Italian, German & Spanish CJK: Chinese, Japanese & Korean – as well as Artificial Languages Python, HTML, Javascript, SQL, C

Summary Chapter 1 NLTK (Natural Lang Toolkit) – Unix for Poets without Unix – Unix  Python Object-Oriented – Polymorphism: “len” applies to lists, sets, etc. Ditto for: +, help, print, etc. Types & Tokens – “to be or not to be” – 6 types & 4 tokens FreqDist: sort | uniq –c Concordances Chapters 2-8 Chapter 3: URLs Chapter 2 – Equivalence Relations: Parity Synonymy (?) – Partial Orders: Wordnet Ontology Chapter 8: CF Parsing – Chomsky Hierarchy CS > CF > Regular