Question 3  Prove each language over {0,1} is undecidable using a reduction with A_TM = { < M, w > | w is an element of {0,1}*, M is a Turing machine, M accepts w }: a) L = { < M, k >, k > 2 | M visits at least k different states when given the empty string as input } b) L = { < M > | M halts on exactly 2 string inputs }

Q: Provide deterministic finite automata accepting the following languages over the alphabet Σ = {a,…

A: Deterministic Finite Automata (DFAs) are formal models of computation used in theoretical computer…

Q: Q4a. Let ETM = {(M)| M is a TM and L(M) = Ø}. Show that ETM', the complement of ETM, is…

A: Turing-recognizable In the fields of mathematics, logic, and computer science, a formal language is…

Q: Start Multiple Choice O O O 1 (4) (1) (0, 1) *n (0) (1) * {0} {0, 1) * [ n(0, 1)*n (1)*(0, 1) * (1)…

A: A Finite State Automaton (FSA), also known as a Finite State Machine (FSM), is a computational model…

Q: Show that the language {M: M is a Turing machine with L(M) to be a finite set} is undecidable. You…

A: The given language is as following- FTM = { M | M is a TM and L(M) is finite} The  Properties of the…

Q: Let Σ = {0, 1}, and let L10101 ⊆ Σ∗ be a language of exactly all the strings that contain the…

A: Approach to solving the question: To show that the language (L10101​) is undecidable, we can use a…

Q: Let KCOMMONTM = { | M and N are Turing machines and |L(M) ^Ł(N)| ≥ k}. Show that KCOMMONTM is…

A: Given input &lt;M,w&gt; of , create input &lt;M1,M2,1&gt; for where M1 and M2 are such that L(M1)…

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: 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: Exercise 7.3.2: Consider the following two languages: L₁ = {an2ncm | n, m≥ 0} L₂ = {anbmc²m|n, m≥ 0}…

A: The question asks for:a) Providing grammars for each of the given languages L1 and L2, showing that…

Q: Let L be the set of exactly those strings over the alphabet {a, b, c, g} whose last symbol is either…

A: Given NFA should accept all strings over {a,b,c,g} even length Accepting strings are aa ab abcg aabb…

Q: [Undecidability and Reductions] OVERLAPPING = {{M, D) : | M is a Turing Machine and D is a DFA such…

A: A reduction from ATM to Overlapping is : Input : &lt;M,w&gt; Create a DFA D which accepts only one…

Q: Prove the language L = { |M accepts w in less than 10 steps } is Turing decidable. Note: solution in…

A: A language is Turing decidable, if some Turing machine decides it. What does decides mean ? A…

Q: A Given Turing-Decidable languages A (decided by Turing machine MA) and B (decided by Turing machine…

A: The question asks for an implementation-level description of a single-tape deterministic Turing…

Q: Let Σ = {0, 1}. We define the language L5−8={⟨A⟩∣A is a deterministic finite automaton and…

A: In this problem, we are given a language L5-8, which is defined as the set of all deterministic…

Q: Let Σ = {0, 1}, and let L10101 ⊆ Σ∗ be a language of exactly all the strings that contain the…

A: The question is asking us to prove that the language J_10101, which is defined as the set of all…

Q: A palindrome is a string that reads the same backward as forward, i.e., w = wR. A palindromic…

A: Hey there, I am writing the required solution of the questin mentioned above. Please do find the…

Q: a b 1 2 a a 3 a b. b a b 4

A: The Answer is in Below Steps

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: Consider the given language L. Show that L is Turing-recognizable.

A: A language is turing recognizable if some turing machine recognizes it. What does recognize mean ?…

Q: Q4b. Show that ATM is not mapping reducible to ETM meaning that there is no computable function…

A: 4b solution: Suppose for a contradiction that ATM ≤m ETM via reduction f. This means that w ∈ ATM if…

Q: A finite automaton (FA) is an abstract machine that can be used to represent certain forms of…

A: Regular Expression is a pattern used to describe a set of strings that matches the pattern. It…

Q: Suppose L1, L2 are two regular languages over the alphabet Σ = {a, b}. Consider the following two…

A: Shuffle1(L1, L2) and shuffle2(L1, L2) are two new languages defined based on the shuffle operation…

Q: PDA with only six states over Σ = {a , b , c} for the language:

A: Given : Σ = {a , b , c} L = {a^n b^m c^k : n ≥ 0, m ≥ 0, k ≥ 0, (n=m ∨ n=k)}

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: Exercise 2.29 Describe an algorithm that, given finite automata accepting lan- guages L1 and L2,…

A: A branch of theoretical computer science, a deterministic finite automaton also known as…

Q: Let SINGLETM ={ | M is a TM and for all s e L(M), Is| - 1). Show that SINGLETM is undecidable by…

A: Solution: First of all we have to understand what is undecidable language in TM? There is no turing…

Q: A Consider the following deterministic finite automaton that accepts the language L2 = {w \w…

A: In the theoretical computer science, finite automata and Turing machines play pivotal roles in…

Q: 1. Give a state diagram for a deterministic finite automaton that recognizes the following language…

A: Below i have drawn the DFA

Problems on Turing Machines

In the computational world, the Turing machine is a powerful computation engine. The invention of the Turing Machine is done by Alan Turing in 1936. A Turing Machine (TM) is a diagrammatic model of a fictional computer. It determines an output from a set of input variables using a pre-defined set of rules. It is used to get around the limitations of finite automata and pushdown automata.