Convert chomsky normal form into binary form, Theory of Computation

Assignment Help:

Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows:

1. Define maxrhs(G) to be the maximum length of the right hand side of  any  production.

2. While maxrhs 3 we convert G to an equivalent reduced grammar G' with smaller maxrhs.

3. a) Choose a production A → α where is of maximal length in G.

b) Rewrite α as α1α2 where |α1| = |α1|/2 (largest integer ≤ |α1|/2) and  |α2| = |α2|/2 (smallest integer ≥ |α2|/2)

c) Replace A -> α in P by A  -> α1B and B -> α2

If we repeat step 3 for all productions of maximal length we create a grammar G' all of whose productions are of smaller length than maxrhs.

We can then apply the algorithm to G' and continue until we reach a grammar that has maxrhs ≤ 2.


Related Discussions:- Convert chomsky normal form into binary form

Mapping reducibility, Can you say that B is decidable? If you somehow know...

Can you say that B is decidable? If you somehow know that A is decidable, what can you say about B?

Non-regular languages, Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = ...

Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = {q 0 , q 1 , . . . , q n-1 } includes n states. Thinking of the automaton in terms of its transition graph, a string x is recogn

what is a turing machine, A Turing machine is a theoretical computing mach...

A Turing machine is a theoretical computing machine made-up by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine having of a line of

TRANSPORTATION, DEGENERATE OF THE INITIAL SOLUTION

DEGENERATE OF THE INITIAL SOLUTION

Trees and graphs , Trees and Graphs Overview: The problems for this ...

Trees and Graphs Overview: The problems for this assignment should be written up in a Mircosoft Word document. A scanned hand written file for the diagrams is also fine. Be

Transition and path functions, When an FSA is deterministic the set of trip...

When an FSA is deterministic the set of triples encoding its edges represents a relation that is functional in its ?rst and third components: for every q and σ there is exactly one

Finite languages and strictly local languages, Theorem The class of ?nite l...

Theorem The class of ?nite languages is a proper subclass of SL. Note that the class of ?nite languages is closed under union and concatenation but SL is not closed under either. N

Kleene closure, So we have that every language that can be constructed from...

So we have that every language that can be constructed from SL languages using Boolean operations and concatenation (that is, every language in LTO) is recognizable but there are r

Reducibility among problems, A common approach in solving problems is to tr...

A common approach in solving problems is to transform them to different problems, solve the new ones, and derive the solutions for the original problems from those for the new ones

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd