Show that the set of palindromes over {0, 1} is not regular using the pumping lemma given in Exercise 22. [Hint: Consider strings of form 0N10N]
*22. One important technique used to prove that certain sets not regular is the pumping lemma. The pumping lemma states that if
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Chapter 13 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
- Show that Lˆ is a linear operator, i.e., that is satisfies the necessary requirement for linearoperators.b) Find Lˆ† and using this find the conditions on k that make Lˆ self-adjoint.c) Find two sets of boundary conditions under which Lˆ is Hermitianarrow_forwardShow that the families defined in Examples 5.3.1, 5.3.2, 5.3.3, and 5.3.4 are in fact uniformities. Example 5.3.1. Given a prime number p, the p-adic uniformity on Z is generated by the entourages of the form:Dn = {(x, y) ∈ Z × Z : x ≡ y mod pn}, n ∈ N \ {0}. Example 5.3.2. The additive uniformity on a topological vector space E, has a basis formed by entourages of the form: {(x, y) ∈ E × E : x − y ∈ V }, where V is a neighborhood of the zero vector of E. Example 5.3.3. The left uniformity UL(G) on a topological group G, has a basis formed by entourages of the form: {(x, y) ∈ G × G : x−1y ∈ V },where V is a neighborhood of the identity element of G. Analogously, the right uniformity UR(G) is generated by the entourages of the form: {(x,y)∈G×G:xy−1 ∈V}, where V is a neighborhood of the identity element of G. Obviously, if G is an Abelian group, UL(G) and UR(G) coincide. Example 5.3.4. The (pseudo)metric uniformity on a (pseudo)metric space (X, d) is generated by the entourages Vεd :=…arrow_forwardLet p be a prime. Suppose that |Gal(E/F)| = p2. Draw all possiblesubfield lattices for fields between E and F.arrow_forward
- Consider the following language over the alphabet Σ = {a, b} L = {w : nb(w) is even, na(w) is odd, and w does not contain the substring ba} 1. Design the minimal deterministic finite automata which recognizes L. You do not need to prove correctness nor minimality. 2. Provide regular expressions for each of the equivalence classes of ≡L. [Hint: Use your answer from 1. A conversion algorithm is not necessary.]arrow_forwardHow can I show that T:ℂ2 -> ℂ2, defined by T((w,z)) = (iw, z-w) is 1-1 and onto?arrow_forwardFor the set of numbers 1 Less than or equal to x less than or equal to 9, list the ones that have reflection symmetry. Then list the ones that have rotational symmetry. Draw, for both symmetries, them to the right.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,