2. a. Describe carefully the relationships between the languages below using the ¶ operator. That is, your answer should look like A≤ B ≤C or A ≤ B, A ≤ C etc. TD = set of Turing Decidable (recursive) decision problems TA = set of Turing Acceptable (recognizable, recursively enumerable) decision problems NP = set of decision problems that have nondeterministic polynomial Turing Machines NPC = set of NP-complete decision problems P = set of decision problems with polynomial solvers

Q: one NP-complete language

A: Given :- The statements are given in above mention question as, 1. P = NP 2. At least one NP -…

Q: Show that the language K = {(M) | M is a TM and does not accept (M)} is not Turing-recognizable.…

A:

Q: Define the problem SDFA: SDFA = { M1 and M2 are DFAs and L(M1) is a subset of L(M2)} In other…

A: DFA stands for - Deterministic Finite Automata Anatomy of a Deterministic Finite Automation  ---…

Q: Please use the pumping lemma to prove, thank you every much. Points Consider the following language,…

A: Pumping Lemma states that if the infinite language has to be accepted by finite automata, then there…

Q: 3. True or false? And justify your answer. (a) 0* U 1* = {0, 1}* (b) 0*n1* = Ø

A: 3. (a)False 0* U 1* do not have stings 0101...combinations so this language won't be equivalent to…

Q: Q. The formal description of a NFA (Nondeterministic finite automaton) is: ({qı, q2}, {0,1}, 8, qı,…

A: Regular expressions are patterns used to match character combinations in strings. A regular…

Q: Question 5. Recall that EQCFG = {(G, H) | G, H are CFGs and L(G) = L(H)}. Show that EQCFG is…

A: If and only if its complement (EQCFG)' is a Turing-recognizable language, EQCFG is a…

Q: The correct statements are: P versus NP is one of the seven million-dollar Millennium Problems. | If…

A: P is the class of choice problems for which a deterministic Turing machine may find a solution (or…

Q: (b) Argue that the language {a"b"|n = 0,1,...}U{b"a"|n = 0,1,...} over the alphabet {a,b} belongs to…

A: 1) Binary strings of even length is as follows:   L = {0011,01,0000,11,1100}…

Q: Let Γ be a set of sentences of L1 (the language of propositional logic) and let φ be a sentence of…

A: Let Γ be a set of sentences of L1 and φ a sentence of L1. The argument with all sentences in Γ as…

Q: (1) State the pumping lemma with all its conditions and indicate how you go about proving that a…

A: the pumping lemma with all its conditions and indicate  you go about proving that a language is not…

Q: Prove that the language L over {a,b,c}",given by L= {wcv: |w\a = [vl6} is recursive. You must…

A: The language Lover (a,b,c} *, given by L = {wev: [wla = [vlo} is recursive. A Turing machine that…

Q: Prove the following statement using padding: NSPACE(n) = SPACE(n) ⇒ NSPACE(n2 ) = SPACE(n2 ). Hint:…

A: According to the question ,we have to Prove the statement using padding: NSPACE(n) = SPACE(n) ⇒…

Q: Problem 3 over the alphabet E= {a,6,c, 9} that contains ex- actly those strings whose form is: Let L…

A:

Q: Let L be a language defined over {a,b}* and recognizable by a finite automaton. The language Reverse…

A: Hello Student, hope you are doing well, I will be trying my best to explain and fulfill your query.…

Q: LetΣ ={a, b}. LetL={aibai|i≥0}.Give a Turing machine (TM) that accepts the languageL.Assume (as in…

A:

Q: the language F which contains all natural numbers which are not prime. The numbers in F are called…

A: According to the question, we have to  i. Prove that F is in NP by writing (in pseudo-code) the…

Q: in b), as shown below. us the algorithm of Kleene' theorem to construct a FA3 for the Union language…

A: Kleene's Theorem :-   Part 1:- Every language that can be defined by a finite automaton can also be…

Q: Statically-typed languages with type inference often share syntactic similarities with dynamically-…

A: The answer is

Q: (a) L = {all words with exactly one b}. (b) L = {all words with at least one a}. (c) L = {all words…

A: For the alphabet Σ ={a, b}, construct an FA that accepts the following languages.(a) L = {all words…

Q: Consider the alphabet is Σ = {a,b,c}. For each of the following languages, specify if the language…

A: We are given three different languages and asked whether they are regular languages or not.Regular…

Q: Q2. Determine whether each of these statements is true or false. x ∈ {x} {x} ⊆ {x} {x} ∈ {x} ∅…

A: Here is the answer to each of these statements whether true or false with an Explanation.

Q: Grammar A -> aB B -> bB, B -> aX CaX X →>bX X ->2 (111) AaA, A → cB. A -> bX BbB. BaX. A -> 2 X -> 2…

A: Grammar: Grammar is a finite set of formal rules that generate syntactically correct sentences. The…

Q: One of the following questions is decidable and the other is undecidable. For the undecidable…

A: Answer: I have given answer in the handwritten format

Q: Define the problem SDFA: SDFA = { M1 and M2 are DFAS and L(M1) is a subset of L(M2)} In other words,…

A:

Q: Let L={ | G is a CFG, M is a TM, and L(M) is a subset of L(G)}. Classify L as (a) decidable (b)…

A: Answer is given below-

Q: For problems 3-5, use the pumping lemma for context-free languages to prove that L is not a CFL. 3.…

A: The pumping Lemma for Context free languages is, If L be a CFL and w∈L such that |w|>=n for some…

Q: 1. Given the following definition of a Turing machine M = (Q, E, I, 6, 9₁, 9accept, Greject):…

A: A Turing machine which refers to an abstract computational model  which are that used to performs…

Q: replace each production of form Ai ⟹Aj? with Ai ⟹ X1? | X2? | X3? |…| ?

A: A grammar is left recursive if it has a non-terminal A such that there is a derivation A⇒Aα  for…

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: Problem 2. Proving Undecidability with Reducibility Consider the following language, L5 = {(M)| M is…

A: The question is to Showing that deciding whether a given TM accepts a word of length 5 is…

Q: Trace the computation of M₂ on input string aabcc. Give TWO (2) other strings that will be accepted…

A: Given:

Q: 5. A set of formulas Mo is an axiom system for a set of formulas M if {A A is a model for Mo} = {A |…

A: Answer is explained below in detail

Q: 2. Construct the state diagram for a nondeterministic Turing machine whose language is the set of…

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: The correct statements are: P versus NP is one of the seven million-dollar Millennium Problems. | If…

A: The P versus NP problem is a Millennium Prize math challenge. While widely believed that P (problems…

Q: Show that the language K = {(M) | M is a TM and does not accept (M)} is not Turing-recognizable.…

A: Given: Show that the language K={<M> | is a TM and does not accept <M>} is not…

Q: i need answer of all. if any answer will be skipped, your answer will be rejected. only complete…

A:

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

Q: Fill out the table for executing the polynomial-time dynamic programming algorithm for deciding…

A: A → BC | CC B → BA | 0 C → AB | BB | 1 Grammar is given below we are using CYK algorithm to find…

Q: Let Mx be a Turing machine that decides the language X and let My be a Turing machine that decides…

A: A Turing machine is a state machine, similar to the ones we have seen until now, but with…

Q: We are given two automatons for the following problem: Left automaton = {w E {a, b}" : w is empty or…

A: SUMMARY: - hence we discussed all the points.