Formal Statement
If a language L is context-free, then there exists some integer p ≥ 1 such that any string s in L with |s| ≥ p (where p is a "pumping length") can be written as
- s = uvxyz
with substrings u, v, x, y and z, such that
- 1. |vxy| ≤ p,
- 2. |vy| ≥ 1, and
- 3. uv nxy nz is in L for all n ≥ 0.
Read more about this topic: Pumping Lemma For Context-free Languages
Famous quotes containing the words formal and/or statement:
“The formal Washington dinner party has all the spontaneity of a Japanese imperial funeral.”
—Simon Hoggart (b. 1946)
“Eloquence must be grounded on the plainest narrative. Afterwards, it may warm itself until it exhales symbols of every kind and color, speaks only through the most poetic forms; but first and last, it must still be at bottom a biblical statement of fact.”
—Ralph Waldo Emerson (1803–1882)