Let L = {aibj | i ≠ j; i, j ≥ 0}. Design a CFG and...

Let L = {aⁱb^j | i ≠ j; i, j ≥ 0}.

Design a CFG and a PDA for this language. Provide a direct design for both CFG and PDA (no conversions from one form to another allowed).

Expert Solution

Colby Messinger answered 1 year ago

int f2 (int n) j = 0; while (j <n) {for (int i = 0; i...

int f2 (int n) j = 0; while (j <n) {for (int i = 0; i <n; ++ i) {cout << "j =" + j; j = j + 5; }}

3. Let S3 act on the set A={(i,j) : 1≤i,j≤3} by σ((i, j)) = (σ(i), σ(j))....

3. Let S3 act on the set A={(i,j) : 1≤i,j≤3} by σ((i, j)) = (σ(i), σ(j)). (a) Describe the orbits of this action. (b) Show this is a faithful action, i.e. that the permutation represen- tation φ:S3 →SA =S9 (c) For each σ ∈ S3, find the cycle decomposition of φ(σ) in S9.

def longest(string): start=0;end=1;i=0; while i<len(string): j=i+1 while j<len(string) and string[j]>string[j-1]: j+=1 if end-start<j-i: #update if current...

def longest(string): start=0;end=1;i=0; while i<len(string): j=i+1 while j<len(string) and string[j]>string[j-1]: j+=1 if end-start<j-i: #update if current string has greater length than #max start and end end=j start=i i=j; avg=0 for i in string[start:end]: avg+=int(i) print('The longest string in ascending order is',string[start:end]) print('Teh average is',avg/(end-start)) s=input('Enter a string') longest(s) i need a definition and explanation of this code that how it works?

Give turing Machine for L= ai b2j ai b2j where i,j>=0. Also provide the logic, show...

Give turing Machine for L= a*i b*2j a*i b*2j where i,j>=0. Also provide the logic, show 1 or 2 strings for accept, reject .

6.1.5. Problem. Let J be the open unit interval (0, 1). For each a let Ua...

6.1.5. Problem. Let J be the open unit interval (0, 1). For each a let Ua = ?a, a + 1 ?, and let U = {Ua : 0 ≤ a ≤ 34 }. Then certainly U covers J . (a) Find a finite subfamily of U which covers J. (b) Explain why a solution to (a) does not suffice to show that J is compact. (c) Show that J is not compact.

Let L be the set of all languages over alphabet {0}. Show that L is uncountable,...

Let L be the set of all languages over alphabet {0}. Show that L is uncountable, using a proof by diagonalization.

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

Let L = {b2k aab2k | k ≥ 0}. Use Myhill-Nerode to prove that L is not regular

Show that L = { (a2)^i | i ≥ 0} is not accepted by a finite...

Show that L = { (a2)^i | i ≥ 0} is not accepted by a finite automata.

The Chinese Remainder Theorem for Rings. Let R be a ring and I and J be...

The Chinese Remainder Theorem for Rings. Let R be a ring and I and J be ideals in R such that I + J = R. (a) Show that for any r and s in R, the system of equations x ≡ r (mod I) x ≡ s (mod J) has a solution. (b) In addition, prove that any two solutions of the system are congruent modulo I ∩J. (c) Let I and J be ideals in a ring R...

Suppose we toss two fair dice. Let X = i+j, where i is the outcome of...

Suppose we toss two fair dice. Let X = i+j, where i is the outcome of the first die, and j is the outcome of the second die, with i, j ∈ {1, 2, 3, 4, 5, 6}. Let p(x) = P(X=x) be the probability mass function of X. Round all answers to 4 decimal places. p(2) = Tries 0/5 p(3) = Tries 0/5 p(4) = Tries 0/5 p(5) = Tries 0/5 p(6) = Tries 0/5 p(7) = Tries 0/5...

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