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

Union, Intuitively, closure of SL 2 under intersection is reasonably easy ...

Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a

Numerical integration, what problems are tackled under numerical integratio...

what problems are tackled under numerical integration

Tuning machine, design a tuning machine for penidrome

design a tuning machine for penidrome

Computation and languages, When we study computability we are studying prob...

When we study computability we are studying problems in an abstract sense. For example, addition is the problem of, having been given two numbers, returning a third number that is

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

What is pumping lemma for regular sets, State & prove pumping lemma for reg...

State & prove pumping lemma for regular set. Show that for the language L={ap |p is a prime} is not regular

Mealy machine, Construct a Mealy machine that can output EVEN or ODD Accord...

Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.

Exhaustive search, A problem is said to be unsolvable if no algorithm can s...

A problem is said to be unsolvable if no algorithm can solve it. The problem is said to be undecidable if it is a decision problem and no algorithm can decide it. It should be note

Closure properties to prove regularity, The fact that regular languages are...

The fact that regular languages are closed under Boolean operations simpli?es the process of establishing regularity of languages; in essence we can augment the regular operations

Distinguish between mealy and moore machine, Distinguish between Mealy and ...

Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1's encountered is even or odd.

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