If L is a regular language, then there is an integer n > 0 with the property that: (*) for any string x ∈ L where x ≥ n, there are strings u, v, w such that (i) x = uvw,
pumping
2 Show that each of the following is or is not a regular language The decimal ( c) L = {w : w is the unary notation for a natural number n such that there exists a
Home Pumping
Thus, F is a fooling set for L Because F is infinite, L cannot be regular □ Solution (concise): For all non-negative integers i = j
lab bis sol
28 oct 2010 · Prove that the following languages are not regular using the pumping lemma a L = {0n1m0n m, n ≥ 0} Answer To prove that L is not a
hw solutions
2 Proof of the Pumping Lemma Theorem: Let L be a regular language n b n : n ≥ 0} Suppose a DFA M1 accepts L1 Let m be the number of states in M1
y = ϵ 2 xy ≤ n 3 for all k ∈ N we have xykz ∈ L Proof: For a regular language L there
notes x
2 Use the procedure described in Lemma 1 60 to convert the following DFA M to a regular Prove that the following languages are not regular Suppose that language A is recognized by an NFA N, and language B is the collection
hwsoln
Add new start state and final state Make original final state non-final S 1 2 F a a λ b b We want to prove the language A1 is non-regular In order to use the pump- If we set n ≥ p, the entire string xy must consist entirely of 0's since xy
hwSol
(b) {0n n is a perfect cube} We'll play the “adversarial game” version of the Pumping Lemma (1) We have already “picked” the language L to be
2 y > 0 Pumping Lemma Example 0} n n L = { 0 1 n is not regular Suppose L were regular Then let p be the pumping length given by the pumping lemma
lec seq
Thus F is a fooling set for L. Because F is infinite
2. Show that each of the following is or is not a regular language. (c) L = {w : w is the unary notation for a natural number n such that there exists a ...
If L is a regular language then there is an integer n > 0 with the property that: (*) for any string x ? L where
The following is a common exercise in a course in formal language theory. 1. Show that X1 = {anbn : n ? N} is not regular. 2. Show that X2 = {w :
Suppose that language A is recognized by an NFA N and language B is the collection of strings not accepted by some DFA M. Prove that A ? B is a regular
2. A non regular language must thus include an infinite number of words. n. 2 is not regular. Indeed the pumping lemma (second version) is.
Con- versely with two such sets of vectors
sets of two-factor interactions while it is not justified to assume A regular fraction in N = 2k = 2n?p level combinations can be obtained.
that no generalized (2n?1)-gon n ? 3
Prove that each of the following languages is not regular. . 02n n