Chomsky’s Hierarchy-Grammars and languages, Models of Computation

Grammars and languages: Chomsky’s hierarchy

N. Chomsky: Three models are there for the explanation of language.

Motivating illustration:

Sentence -> Noun Verb Noun, example: Bob loves Alice.

Sentence -> Sentence Conjunction Sentence, example: Bob loves Alice and Rome fights Carthage.

Grammar G(V, A, P, S). V: alphabet of the non-terminal symbols, variables and grammatical types;

A: alphabet of the terminal symbols, S ∈ V: start symbol, ‘sentence’;

P: unordered set of the productions of form L -> R, where L, R ∈ (V ∪ A)*

Rewriting step: for x, y, y’, z ∈ (V ∪ A)*, u -> v if u = xyz, v = xy’z and y -> y’ ∈ P

Derivation: “->*” is the transitive, reflexive closure of “->”, that is, u ->* v iff ∃ w0, w1 ... wj, with j ≥ 0, u = w0, w(i-1) -> wi,  wj = v

Language defined by G: L(G) = {w ∈ A* | S ->* w)

Different restrictions on the productions define various types of grammars and corresponding languages:

Type 0: Phrase structure grammar: No restrictions

Type 1: Context sensitive: |L| ≤ |R|, (exception: S -> ε is permitted when S never takes place on any right-hand side)

Type 2: context free: L ∈ V

Type 3: regular: L ∈ V, R = a or R = aX, where a ∈ A, X ∈ V

Exercise: Define a grammar for some very small subset of natural language, and exemplify it with illustrations. Try this for a subset of English and a semantically identical subset of the other language, and show that distinct natural languages encompass different grammars.

Latest technology based Theory of Computation Online Tutoring Assistance

Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Theory of Computation help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Theory of Computation, project ideas and tutorials. We provide email based Theory of Computation help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Theory of Computation. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Theory of Computation Homework help and assignment help services. They use their experience, as they have solved thousands of the Theory of Computation assignments, which may help you to solve your complex issues of Theory of Computation. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.