Validate string given Context Free Grammar in Java

Question

How can someone validate if a string is part of a context free Grammar? Not just virtually, but build an algorithm for it?

Given a context free grammar with rules such as

• V-> v1v2
• v1->1 | 1v1
• v2-> 2 | 2v2

It is obvious that this is the language 1^n 2^n. But how would you go about with an algorithm to verify if it actually is. I am trying to accomplish this in java.

Answer 1

You might want to look into Earley's algorithm or the CYK algorithm, which are two algorithms for deciding whether a string is generated by a context-free grammar. Earley's algorithm runs in time O(n³) for any string of length n regardless of the production rules in the grammar (though the constant term in the big-O notation depends on the grammar), while the CYK algorithm requires that the grammar first be converted to Chomsky normal form to guarantee O(n³) runtime.

Hope this helps!