Question

In: Computer Science

Prove whether the following are regular (include the file) or not regular (attach a proof). The...

Prove whether the following are regular (include the file) or not regular (attach a proof). The alphabet is {0, 1}.

1. The set of strings that start with N 0's which are directly followed by 2N 1's.

2. The set of strings start with two 0's, followed by N 1's, followed by N 1's and end with three 0's.

3. The set of strings where every substring of length 5 has more 0's than 1's. Strings less than length five are not included in the set.

4. The set of strings that start with N 1's, followed by a 0, followed by N 1's.

Solutions

Expert Solution

4)answer)


Related Solutions

Prove the following: theorem: every topological group is completely regular. Proof. Let V0 be a neighborhood...
Prove the following: theorem: every topological group is completely regular. Proof. Let V0 be a neighborhood of the identity elemetn e, in the topological group G. In general, coose Vn to be a neighborhood of e such that Vn.VncVn-1. Consider the set of all dyadic rationals p, that is all ratinal number of the form k/sn, with k and n inegers. FOr each dyadic rational p in (0,1], define an open set U(p) inductively as foloows: U(1)=V0 and
Prove that all regular languages are context free. Note: Proof must proceed by structural induction on...
Prove that all regular languages are context free. Note: Proof must proceed by structural induction on regular expressions Please prove by Structural Induction. Will Upvote for correct answer. Thanks
Prove the following using the method suggested: (a) Prove the following either by direct proof or...
Prove the following using the method suggested: (a) Prove the following either by direct proof or by contraposition: Let a ∈ Z, if a ≡ 3 (mod 5) and b ≡ 2 (mod 5), then ab ≡ 1 (mod 5). (b) Prove the following by contradiction: Suppose a, b ∈ Z. If a² + b² is odd, then (2|a) ⊕ (2|b), where ⊕ is the exclusive disjuntion, i.e. p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q). (d)...
Are the following languages over {a, b} regular? If they are then prove it. If they...
Are the following languages over {a, b} regular? If they are then prove it. If they are not prove it with the Pumping Lemma a) {ap | p is a prime number} b) {xax | x Î{a,b}*} (start by listing some strings in, not in, the language
Prove that the proof by mathematical induction and the proof by strong induction are equivalent
Prove that the proof by mathematical induction and the proof by strong induction are equivalent
Write a formal proof to prove the following conjecture to be true or false. If the...
Write a formal proof to prove the following conjecture to be true or false. If the statement is true, write a formal proof of it. If the statement is false, provide a counterexample and a slightly modified statement that is true and write a formal proof of your new statement. Conjecture: Let w, x, y, and z be single-digit numbers. The 4-digit number wxyz* is divisible by 9 if and only if 9 divides the sum w + x +...
Determine whether or not the following languages are regular. If the language is regular then give...
Determine whether or not the following languages are regular. If the language is regular then give an NFA or regular expression for the language. Otherwise, use the pumping lemma for regular languages or closure properties to prove the language is not regular. 1) L = { 0 n1 k : k ≤ n ≤ 2k} 2) L = { 0 n1 k : n > 0, k > 0 } È { 1 k0 n : k > 0, n...
Using Euclid's Propositions: 1. Prove that the regular octagon is constructible. 2. Prove that the regular...
Using Euclid's Propositions: 1. Prove that the regular octagon is constructible. 2. Prove that the regular decagon is constructible.
Regular => Context-Free Give a proof by induction on regular expressions that: For any language A,...
Regular => Context-Free Give a proof by induction on regular expressions that: For any language A, if A is regular, then A is also context-free. You may assume that the statements from the previous Closure under Context-Free Languages problem are proved. R is a regular expression if RR is: a for some a∈alphabet Σ, the empty string ε, the empty set ∅, R​1​​∪R​2​​, sometimes written R​1​​∣R​2​​, where R​1​​ and R​2​​ are regular expressions, R​1​​∘R​2​​, sometimes written R​1​​R​2​​, where R​1​​ and...
Create a mathematical proof to prove the following: Given an integer n, and a list of...
Create a mathematical proof to prove the following: Given an integer n, and a list of integers such that the numbers in the list sum up to n. Prove that the product of a list of numbers is maximized when all the numbers in that list are 3's, except for one of the numbers being either a 2 or 4, depending on the remainder of n when divided by 3.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT