05 Jul proof project !!
Proof Project
The pumping lemma for regular languages:
If a language L is regular, there exists a constant p ≥ 1 such that every sentence s L of length ≥p can
be written as xyz =s satisfying these three conditions: |y| > 0, |xy| ≤ p, and for all i≥ 0, xyiz L.
L4 = {ak bn cn | k, n > 0 } {bi c j | i, j ≥ 0 } ∑= {a,b,c}
Note that L4 satisfy the pumping lemma but are not regular.
Write a report and the report (proofs) must be well written grammatically and technically. The quality and
style of your writing is expected to be suitable for publication.
Problem:
a) Use the diagonalization argument to show that the set of functions from the set of natural numbers
to the set {true, false} is not countable. Show how self-refutation is used in the proof.
b) Use the pumping lemma to prove that a subset of L4 is not regular, and then use a closure property
of regular languages to prove that L4 is not regular.
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