Prove that if a language is not recursively enumerable, then its complement cannot be recursive. In...

Prove that if a language is not recursively enumerable, then its complement cannot be recursive. In this problem, you can use diagrams (black boxes with inputs and outputs to represent procedures and algorithms) as we used in class, in your proof. What can the complement be?

Expert Solution

Let us assume for contradiction that the language L's complement is recursive. Then according to the definition of recursive languages, there is a

venereology answered 1 year ago

Prove or disprove with a counterexample the next claims: (a) The complement of a decidable language...

Prove or disprove with a counterexample the next claims: (a) The complement of a decidable language is decidable. (b) The Kleene star of a Turing-recognizable language is Turing-recognizable.

Prove that string concatenation cannot be checked by finite automata by showing that the following language...

Prove that string concatenation cannot be checked by finite automata by showing that the following language over Σ = {0, 1} is not regular: L3 = {w1#w2#w1w2 : w1, w2 ∈ Σ ∗ }

Write a recursive method that takes a String argument and recursively prints out each word in...

Write a recursive method that takes a String argument and recursively prints out each word in the String on a different line. Note: You will need to use methods such as indexOf() and substring() within the String class to identify each word and the remaining string. For example, if the input was “the cat purred”, then the method would print the following to the Java console: the cat purred Challenge Problem Write a recursive method that takes a string as...

Implement and complement the recursive code to compute the product of two positive integers, x and...

Implement and complement the recursive code to compute the product of two positive integers, x and y, using only addition and/or subtraction. The function will take as its arguments two integers to multiply together ( x x y ) and will return the product. Hint: consider the following: 6 x 1 = 6 6 x 2 = 6 + (6 x 1) 6 x 3 = 6 + (6 x 2) = 6 + [6 + (6 x 1)] =...

Is the following language a regular language? ( Prove with pumping Lenma ) L = {...

Is the following language a regular language? ( Prove with pumping Lenma ) L = { o^n 1^n 2^n | n => 0} Define CFL pumping lemma

2)Prove, using Boolean Algebra theorems, that the complement of XOR gate is XNOR gate(Hint : Prove...

2)Prove, using Boolean Algebra theorems, that the complement of XOR gate is XNOR gate(Hint : Prove that AB + AB = AB + ABby using De-Morgan’s theorem)3)Draw the K-Map for the following Boolean function. Obtain the simplified Sum of Products (SOP) expression, using the K-Map minimization procedure .?(????)=∑?(1,2,3,5,7,9,11,13)

1.Prove the following statements: . (a) If bn is recursively defined by bn =bn−1+3 for all...

1.Prove the following statements: . (a) If bn is recursively defined by bn =bn−1+3 for all integers n≥1 and b0 =2, then bn =3n+2 for all n≥0. .(b) If cn is recursively defined by cn =3cn−1+1 for all integers n≥1 and c0 =0, then cn =(3n −1)/2 for all n≥0. .(c) If dn is recursively defined by d0 = 1, d1 = 4 and dn = 4dn−1 −4dn−2 for all integers n ≥ 2, then dn =(n+1)2n for all n≥0.

Prove by construction that the language An = { ai | i is a multiple of...

Prove by construction that the language An = { ai | i is a multiple of n } is regular. In other words the language An contains all strings composed of the letter a some multiple of n times

1. Using Induction on the length of derivations, prove that the set of all Primitive Recursive...

1. Using Induction on the length of derivations, prove that the set of all Primitive Recursive Functions (PR) is a subset of all Partial Computable Functions (P). 2. Using the preceding problem, conclude that the set of all Primitive Recursive Functions (PR) is a subset of all Computable Functions (R).

Suppose A and B are regular language. Prove that AB is regular

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