Show that if P = NP, then "if the language A on the alphabet 2 is not NP-hard, then A=Φ or A= Σ holds.

Q: Find all the finite languages A (over the alphabet {a, b}) such that C = C ◦ C, and prove that they…

A: Given: Finite languages A where C = C ◦ C prove that they are the only such languages

Q: language L = {a i b j c k | i 6= j, j 6= k, i 6= k}; it is not a context- free language. Show that…

A: Given : L = {a i b j c k | i == j, j== k, i == k};

Q: Let L be the language L={ 0n1m | n≠(m-7) } over the alphabet Σ={0,1}. Prove that L is not regular…

A: Given: Let L be the language L={ 0n1m | n≠(m-7) } over the alphabet Σ={0,1}. Prove that L is not…

Q: L+Ø, and L2022 L2023 and Lº + L - your answer. hat for every non-empty language L over an alphabet…

A:

Q: Extra Credit: Given any language A, let A₁ = {x | for some y, |x| = |y| and xy = A}. Prove that the…

A: Closure Properties• Recall that we can carry out operations on one or more languages to obtain a new…

Q: A language L over an alphabet Σ is co-finite, if Σ∗ \L is empty or finite. Let COFNFA = {〈N 〉|N is a…

A: given A language L over an alphabet Σ is co-finite, if Σ∗ \L is empty or finite. LetCOFNFA = {〈N 〉|N…

Q: Each case below defines a language over {a, b}. In each case, decide whether the language can be…

A: The answer to the Following Question:-

Q: Question 3. Consider the language L = {w€ {0, 1}* | the strings 01 and 10 occur the same number of…

A: Given language is, L={w ∈{0,1}* | the strings 01 and 10 occur same number of times in w} Pumping…

Q: Prove that the language containing strings of the form 0k where k is multiple of n is a regular…

A: A language is regular language if and only if a DFA/NFA accepts it. Or if and only if a regular…

Q: For a Turing machine M, (M) refers to the binary representation of M. For a Turing machine M, L(M)…

A: ForL is unrecognizable, condition is that  there is no Turing machine that can take decisions  in L.…

Q: We know that for Σ = {0, 1}, there are uncountably many languages over Σ. Is this also true for the…

A: by using Kleen closer of regular language we can generate uncountable infinite language Kleen…

Q: Q3. E={0,1} and L={ 0"12"0" | n20 } is given. Using pumping lemma, prove that language L is…

A: ANSWER:-

Q: Please provide handwritten answer only Let L be the language L={ On1m | n#(m-7) } over the alphabet…

A: Introduction:

Q: A = {d'b?"\n > 0}. п

A: Pumping lemma is used to show that certain languages are not regular. It should never be used to…

Q: B: Is the following language decidable? If yes, give the outline of the Turing machine to solve it?…

A: ANSWER:- FOR SOLUTION SEE STEP NO. 2

Q: Show that the language L {w e {a,b}*: n(w) n(w) + 2} is not linear. %3D

A: Answer is given below:-

Q: Question 2 Let L be the language L-(anbmen | (3n+n)>m) over the alphabet Z-(a.b.c). Prove that Lis…

A: Given Language : L = {a3nbmcn  |  3n+n>m} Alphabet Set = {a,b,c} String of Language : The…

Q: Show how the Structured Programming Theorem reduces spaghetti code and GOTO uncertainty. Write an…

A: Structured Programming Theorem, or the Böhm–Jacopini Theorem, revolutionized how programmers…

Q: Build a PM that accepts the language of all words that have an a as the middle letter: (These words…

A: 1)The Language that accepts all the words that have an a as the middle letter is: waw' where w and…

Q: Suppose I is a non empty regular language, over Σ, such that every w E L satisfies [w] = k, for some…

A: Given that, non-empty regular language L over the alphabet Σ such that every string w in L satisfies…

Q: Consider the language L = {a'b'c* | i # j,j # k, i # k}; it is not a context- free language. Show…

A: Pumping lemma for CFL is used to prove the language is not cfl using some valid string s.  Never use…

Q: Let Z={a,b,c}. Show that (b) The set of all languages over Σ is uncountable

A: We need to prove the set of all languages over sigma is uncountable.

Q: Please classify the following languages as 1. in P         2. In P but not in NP         3.…

A: Hi there, Please find your solution below, I hope you would find my solution useful and helpful.…

Q: Let L be the language L={ 0n1m | n≠(m-7) } over the alphabet Σ={0,1}. Prove that L is not regular…

A: Let L be the language L={ 0n1m | n≠(m-7) } over the alphabet Σ={0,1}. Prove that L is not regular…

Q: A: Is the following language decidable? If yes, give the outline of the Turing machine to solve it?…

A: ANSWER:- FOR SOLUTION SEE STEP NO. 2

Q: The alphabet of the language is (a, b, c): Use pumping lemma to prove that the language (abc n>0} is…

A: Given grammar:

Q: P is the class of language that are decidable in polynomial time

A: ANSWER : Union: Let Li (i = 1, 2) be two languages in P and let Mi be a DTM that accepts Li in…

Q: F(L) = {0¹¹ a0¹ |a € A, n >0} Consider the condition that A is the language over {0, 1}. Using the…

A: Given language is, F(L)= {0na0n | a∈ A, n>=0} In this language, set of input alphabets are {0, a}

Q: Prove that the language {1®0"1k |k> 0, n > 0} is not regular. DO NOT use pumping lemma.

A: Closure Property of regular language: Regular languages are closed under concatenation. It means…

Q: Show that language is not regular using pumping lemma. Proof

A: I have explained your problem handwritten answer. see below steps.

Q: 2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r E RE, let L(r) be…

A: Regular Expressions Just as finite automata are used to recognize patterns of strings, regular…

Q: Let L be a language. It is clear from the definition that LL". Under what circumstances are they…

A:

Q: Prove that the below two definitions of NP languages are equivalent. 1. Define Verifier NP = {L|L…

A: The definition of NP in terms of verification can be formally stated as follows: A language L is in…

Q: 2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r€ RB, let L(r) be the…

A: Regular Expressions Just as finite automata are used to recognize patterns of strings, regular…

Q: Consider the language L = { 3x such that x = L(M₁) L(M₂)}. Show that L is not decidable.

A: To prove that the language L is not decidable, we need to show that there is no Turing machine that…

Q: 2. Let A be a Turing-recognizable language consisting of descriptions of Turing machines, i.e., A =…

A: Since A is Turing recognized, there will be existence of enumerator E. Mi be the ith output of E, Mi…

Q: 5. Let A, B, and C be languages over E. Prove or disprove the following. (а) If A <T B and B <т C,…

A: Answer: I have given answered in the handwritten format in brief explanation