1. A language L is Turing-recognizable if there exists a TM M such that given an input strir w over the alphabet of L, M a) Halts and accepts w b) Halts and rejects w c) Loops and returns no answer d) Both (a) and (b) e) All of (a), (b), and (c) 2. Which ones of the following languages are Turing-decidable: a) ADFA = {< D, w> | D is a DFA that accepts input string w} b) EQDFA = { | D1 & Dz are DFAS and L(D;) = L(D2) } c) Both (a) & (b) d) None of the above 3. Which ones of the following languages are Turing-recognizable, but not decidable: a) AREX = { | R is a regular expression that describes string w} b) EDFA = { | D is a DFA and L(D) = Ø } c) ECFG = { | G is a CFG and L(G) = Ø } d) None of the above

Q: Question 3  Prove each language over {0,1} is undecidable using a reduction with A_TM = { | w is…

A: a) L = { &lt; M, k &gt;, k &gt; 2 | M visits at least k different states when given the empty string…

Q: Let ATMR be the language consisting of words of the form (M, w) where M is a Turing machine whose…

A: According to the information given:- When we suppose ATMR language consist of words &lt;M,w&gt;…

Q: What is the language of the following Turing Machine? a → a, R b → b, R

A: Given:

Q: Construct a Turing machine for the given languages. (a) L = {w ∈ {0,1} * | w contains 101 }

A: We are going to draw turing machine for the language which contains strings containing 101 as…

Q: Show that a language is Turing-decidable if and only if some enumerator enumerates the language in…

A: We need to show that if we have a Turing Machine , let's say M then it will decide A , and then we…

Q: Define the following operation, called NOTIN, on languages: NOTIN(A) = {w | w & A}

A: Define the following operation, called NOTIN, on languages:NOTIN(A) = {w|w A}

Q: Given the Turing machine M with input alphabet {0, 1} in Figure 1 answer the following question

A: Trace the computation for the input string ???. • Trace the computation for the input string ???. •…

Q: Draw a 2-tape Turing machine that recognizes the language {w#w|w ∈ {0, 1} ∗ } b. Include a…

A: A Turing machine is a mathematical model of computation that defines an abstract machine that…

Q: Suppose L₁ and L2 are Turing decidable, prove that the language L3 is decidable, where L3 is de-…

A: If L1 and L2 are Turing decidable languages, we can construct a decider for L3, defined as the set…

Q: Construct an enumerating Turing machine that enumerates the language a∗b∗

A: I have answered the question in step 2.

Q: Problem 1 Design a Turing Machine recognizing each of the following languages and draw its state…

A: Solution: Given: The Turing Machine must be in the format of "a b, L/R", namely the machine reads…

Q: Suppose that both a language L and its complement are Turing-recognizable. Is L also necessarily…

A: Here, we are going to check whether language L is also necessary to be Turing decidable or not.…

Q: Show that given two Turing recognizable languages A and B, that the following languages are Turing…

A: Show that given two Turing recognizable languages A and B, that the following languages are Turing…

Q: 2 Context Free Let TRTM = { | M is a TM that recognizes a Turing Recognizable language} Prove…

A: ANSWER:-   Let TRTM = {&lt; M &gt; | M is a TM that recognizes a Turing Recognizable language} Prove…

Q: Define the following operation, called BOTH, on languages:

A: Given A and B are two regular languages. We define BOTH(A,B)={w | w ∈ A and w ∈ B } i.e w belongs to…

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: Multiple choice A language L is Turing-recognizable if there exists a TM M such that given an input…

A: Multiple choice A language L is Turing-recognizable if there exists a TM M such that given an input…

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.