Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
Applying the pumping lemma is not fundamentally di?erent than applying (general) su?x substitution closure or the non-counting property. The pumping lemma is a little more complicated-rather than just the single universal quanti?er ("for all languages L") and single existential quanti?er ("there exists n"), we have a nest of alternating quanti?ers (denoting "for all" as ∀ and "there exists" as ∃):
(∀L)[L regular ⇒
(∃n)[
(∀x)[x ∈ L and |x| ≥ n ⇒
(∃u, v,w)[x = uvw and
|uv| ≤ n and
|v| ≥ 1 and
(∀i ≥ 0)[uviw ∈ L]]]]].
Just as with the lemmas for the local languages, we will approach this as an adversary game. Our proof will consist of a strategy for showing that L fails to satisfy the pumping lemma. Our choices are the "for all"s; the "there exists"s are our adversary's choices. There are just a few more rounds in this game than there were in the lemmas for the local languages. The key things are being clear about which are our choices and which are the adversary's and making sure that our strategy accounts for every legal choice the adversarymight make.
The game starts with our choice of the L we wish to prove to be non regular. Our adversary then chooses some n, we choose a string x ∈ L of length at least n, etc. We win if, at the end of this process, we can choose i such that uviw ∈ L. Of course, our strategy at each step will depend on the choices our adversary has made.
What we end up with is a proof by contradiction. For instance:
To show that Lab = {ajbj| j ≥ 0} is not regular.
Rubber shortnote
what is theory of computtion
Differentiate between DFA and NFA. Convert the following Regular Expression into DFA. (0+1)*(01*+10*)*(0+1)*. Also write a regular grammar for this DFA.
wwwwwwwwwwwwwwwwwwww
write grammer to produce all mathematical expressions in c.
For every regular language there is a constant n depending only on L such that, for all strings x ∈ L if |x| ≥ n then there are strings u, v and w such that 1. x = uvw, 2. |u
We have now de?ned classes of k-local languages for all k ≥ 2. Together, these classes form the Strictly Local Languages in general. De?nition (Strictly Local Languages) A langu
While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless
Our DFAs are required to have exactly one edge incident from each state for each input symbol so there is a unique next state for every current state and input symbol. Thus, the ne
Suppose A = (Σ, T) is an SL 2 automaton. Sketch an algorithm for recognizing L(A) by, in essence, implementing the automaton. Your algorithm should work with the particular automa
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!
whatsapp: +1-415-670-9521
Phone: +1-415-670-9521
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd