Prove that the following language L is decidable: L = {(M) : 3x = {0,1}*, 1000 € ReachCells(M,x)}.
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- For a Turing machine M, (M) refers to the binary representation of M. For a Turing machine M, L(M) contains the set of all strings accepted by M. For a Turing machine M and an input x € {0,1}*, Steps(M, x) refers to the number of steps taken by M to execute on x before it halts. Here, one step of execution of M on x = one movement (left or right) of the tape head. For a Turing machine M and an input x = {0,1}*, we define the following: ReachCells(M,x) = {i : M reaches ith tape cell when M is executed on x} Informally, it contains all locations on the tape that are visited when M is ecuted on x. The leftmost location on the tape is the first tape cell, the location next to it is the second tape cell, and so on. A string w₁ is an anagram of w2 if w₁ can be obtained by rearranging the alphabets of w2. Formally, if w₁ is an n length string, wê is called an anagram of w₁ if there exists a permutation à on n elements such that π(w₁) = W2.4. LetΣ ={a, b}. LetL={aibai|i≥0}.Give a Turing machine (TM) that accepts the languageL.Assume (as in the examples done in our course videos) that, when theTM starts, the head is on a blank symbol,∆, and the input string isimmediately after that blank symbol on the tape. For example, if theinput string wereaaabaaa, then the inital tape configuration would be∆aaabaaaes remaining 8. Consider the function f:NxN-N defined recursively by: 1) Base case: Let meN and define (0,m) = 0 2) Recursive case: For any x,meN, x>0, define f(x,m) = (x-1,m) + (m+m) Prove the following theorem holds using proof by induction: Thereom: For any n,meN, m>0 we have (n.m) I m = n+n Fill in your answer here 9 Help BIU X, x L - ɔE =N E X Format
- A problem called S reduces to a problem called T if a T solver can be used as a subroutine to solve S. In pseudocode: Solves(...): ... SolveT(...) ... Assuming that this reduction is correct, answer the following questions regarding what the reduction tells us. If we know that an algorithm exists for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm cannot exist for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm exists for solving Problem T, what does that tell us about Problem S? [ Select ] [ Select ] An algorithm cannot exist for solving Problem S,r solving Problem T, what does that tell us about Nothing An algorithm exists for solving Problem SLet p be a proposition and P be a propositional function. Identify if the following statement is always true, never true, or only sometimes true/false: T→p⇒T^p Always True O Never True O Sometimes True Suppose there is a robot that builds a copy of itself in 2 hours. The copy then starts to build copies of itself as well. Let be the total number of fully functional robots after n hours. Suppose ro = 1. Recursive Case, 'n = 'n = [(n-2) +2 In = [(n-2) *2 In = [(n-1) +1 O None. Function description: g: Z→R g(x) = (x − 2)(x+2)x Identify if g is: 1. One-to-One II. Onto III. One-to-One Correspondence O IV. NoneComputer Science 1. Let Σ = {0, 1} be an alphabet.(a) Let w = 101 be a word over Σ. Compute |w|, the length of w.(b) List all of the words in Σ32. Let {a, b, c} be an alphabet. List all of the words in Σ23. Let Σ = {a, b} be an alphabet and let · denote concatenation. Compute (ba · ε) · abb,where ε is the empty word.4. Let Σ = {0, 1} be an alphabet and let L ⊆ {0, 1} ∗ be the language defined as L = {w ∈ {0, 1} ∗ |w = x10y, x, y ∈ {0, 1}∗}. (a) Determine whether 01 ∈ L.(b) Determine whether 0101 ∈ L. 5. Let Σ = {0, 1} be an alphabet and let L ⊆ Σ ∗ be the language consisting of all wordsover Σ that contain the substring 10. Construct a DFA that accepts L. Thank you in advance
- A common problem that arises in software maintenance is identifying (and then removing) dead code, code that will never be executed no matter what input the program is given. The analogous problem for TMs would be to determine if a state is never entered, no matter what input the TM is given. Prove by reduction that Ldead, the set of pairs (T,s) where T is a Turing machine and s is a dead state, is not recursive.Show that the following function is Turing-computable. f(x)=x+1 . I want the drawingThe reverse function maps a string w to wR. Draw a multi-tape Turing machine that computes the reverse of a binary string. That is, given a binary string w as input, your Turing machine should compute wR, write the result to tape 1, and halt.
- Correct answer will be upvoted else downvoted. Computer science. You are given a grid a comprising of positive integers. It has n lines and m segments. Develop a framework b comprising of positive integers. It ought to have a similar size as a, and the accompanying conditions ought to be met: 1≤bi,j≤106; bi,j is a various of ai,j; the outright worth of the contrast between numbers in any nearby pair of cells (two cells that share a similar side) in b is equivalent to k4 for some integer k≥1 (k isn't really something similar for all sets, it is own for each pair). We can show that the appropriate response consistently exists. Input The primary line contains two integers n and m (2≤n,m≤500). Every one of the accompanying n lines contains m integers. The j-th integer in the I-th line is ai,j (1≤ai,j≤16). Output The output ought to contain n lines each containing m integers. The j-th integer in the I-th line ought to be bi,j.In-Class Assignment Consider an (8,4) binary linear block code with minimum distance of 4. • How many valid codewords are there? • What is the code rate? • What is the minimum weight of the code? • If the code is used for error detection only, how many errors can it detect? • If the code is used for error correction, how many errors can it correct?Must be new solution and run on GNU Common Lisp! Using Lisp, write a program that solves the Missionaries and Cannibals problem that uses a DFS( depth first search). It should use (mac start end). Start is the current state (which can be (3 3 l) and End is the goal state (which can be (0 0 r). This should output the sequences of moves needed to reach the end state from the start state. This should print nil if there is no solution. For example, the call should be something like this! Call: (mac '(3 3 l) '(0 0 r)) Output: ((3 3 l) (2 2 r) (3 2 l) (3 0 r) (3 1 l) (1 1 r) (2 2 l) (0 2 r) (0 3 l) (0 1 r) (1 1 l) (0 0 r))