Let L = {b2k aab2k | k ≥ 0}. Use Myhill-Nerode to prove that L is...

Let L = {b^2k aab^2k | k ≥ 0}. Use Myhill-Nerode to prove that L is not regular

Expert Solution

if you have any doubts please comment !!!!

venereology answered 2 months ago

1) a) Let k ≥ 2 and let G be a k-regular bipartite graph. Prove that G...

1) a) Let k ≥ 2 and let G be a k-regular bipartite graph. Prove that G has no cut-edge. (Hint: Use the bipartite version of handshaking.) b) Construct a simple, connected, nonbipartite 3-regular graph with a cut-edge. (This shows that the condition “bipartite” really is necessary in (a).) 2) Let F_n be a fan graph and Let a_n = τ(F_n) where τ(F_n) is the number of spanning trees in F_n. Use deletion/contraction to prove that a_n = 3a_n-1 - a_n-2...

Let G, H, K be groups. Prove that if G ≅ H and H ≅ K...

Let G, H, K be groups. Prove that if G ≅ H and H ≅ K then G ≅ K.

Suppose k is any natural number, k >= 0. Prove that the number of nodes in...

Suppose k is any natural number, k >= 0. Prove that the number of nodes in any binomial tree of height k is exactly 2^k.

Let (?,?,?) be a probability space and suppose that ?∈? is an event with ?(?)>0. Prove...

Let (?,?,?) be a probability space and suppose that ?∈? is an event with ?(?)>0. Prove that the function ?:?→[0,1] defined by ?(?)=?(?|?) is a probability on (?,?).

1. Let G be a k-regular bipartite graph. Use Corollary 3.1.13 to prove that G can...

1. Let G be a k-regular bipartite graph. Use Corollary 3.1.13 to prove that G can be decomposed into r-factors iff r divides k.

Let (E,d) be a metric space and K, K' disjoint compact subsets of E. Prove the...

Let (E,d) be a metric space and K, K' disjoint compact subsets of E. Prove the existence of disjoint open sets U and U' containing K and K' respectively.

Let G be a group and H and K be normal subgroups of G. Prove that...

Let G be a group and H and K be normal subgroups of G. Prove that H ∩ K is a normal subgroup of G.

Let Bt be a 1-dimensional Brownian motion and let c > 0 be a constant. Prove...

Let Bt be a 1-dimensional Brownian motion and let c > 0 be a constant. Prove that is also a Brownian motion.

Let S={1,2,3,6} and define the relation ~ on S2 by (m,n) ~ (k,l) for m+l=n+k Show...

Let S={1,2,3,6} and define the relation ~ on S2 by (m,n) ~ (k,l) for m+l=n+k Show that it is an equivalent relation Find the number of different equivalent classes and write all of them

Prove the following statements! 1. Let S = {0, 1, . . . , 23} and...

Prove the following statements! 1. Let S = {0, 1, . . . , 23} and define f : Z→S by f(k) = r when 24|(k−r). If g : S→S is defined by (a) g(m) = f(7m) then g is injective and (b) g(m) = f(15m) then g is not injective. 2. Let f : A→B and g : B→C be injective. Then g ◦f : A→C is injective. 3. Let f : A→B and g : B→C be surjective....

Question