1st Question: One-way vs. Two-way. We wish to construct a Turing Machine = M (Q,E,F, 8, 8, Jaccept, reject) that decides the language L = {w = {0, 1}* ||w|≥ 2 and w ends in 00 or in 01} S 1 1 0 S 0 R S S 1 R S L 91 L L 91 0 92 0 L 91 92 1 L 91 92 0 92 1 Ireject Jaccept 0 R greject 1 R R L 92 L Ireject R L For which, if any, of the following machine models does M decide L? Explain your answers. (a) M is a standard machine with a one-way infinite tape. (b) M has a two-way infinite tape.
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- We are given two automatons for the following problem: Left automaton = {w E {a, b}" : w is empty or ends with a b} Right automaton = {w E {a, b}" : w either consists of an even number of a's and no b's, or has at least one b and an even number of a's after the last b} a a,b Construct a DFA/Cartesian product to design a finite automaton that recognizes the union of the two languages given.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∆aaabaaaExample 9.7 For E = {a,b}, design a Turing machine that accepts L= {a,b„:n21}. Intuitively, we solve the problem in the following fashion. Starting at the leftmost a, we check it off by replacing it with some symbol, say x. We then let the read-write head travel right to find the leftmost b, which in turn is checked off by replacing it with another symbol, say y. After that, we go left again to the leftmost a, replace it with an x, then move to the leftmost band replace it with y, and so on. Traveling back and forth this way, we match each a with a corresponding b. If after some time no a's or b's remain, then the string must be in L. Working out the details, we arrive at a complete solution for which Q= {qo91;9293,94},F= {q4}, E= {a,b},T={a,b, x, y,¤}. The transitions can be broken into several parts. The set
- create a 2 tape Turing machine (use JFLAP) that has on tape 1 the alphabet of a,b,null, on tape 2 the alphabet is 0,1,2,3, null. Tape 1 has initial content of (a+b)*, Tape 2 has initial content of (0+1)* Begin by processing tape 1, if the substring aa is found on tape 1, search tape 2 for the first 00 substring and replace it with 22 if the substring bb is found on tape 1, search tape 2 for the first 11 substring and replace it with 33. If at anytime aa does not have a matching 00 reject if at anytime bb does not have a matching 11 reject else accept after all of tape 1 has been processed.Here is a description of a Turing machine. The input alphabet is (a, b). The state set is: {90, 91, 92, 93, 94, 9acc, grej} The transition function is given in the table below: 9⁰ (9₁, a, R) b (92, b, R) (grej, *, R) 93 94 (qacc. a, R) (qrej, a, R) (arej, b, R) (qacc, b, R) (arej,*, R) (qrej, *, R) (a) Draw the configuration of the Turing machine after 3 steps on input "aabba". When the Turing machine is in the initial configuration, it has executed zero steps. a 91 (9₁, a, R) * 92 (92, a, R) (9₁, b, R) (93, *, L) (92, b, R) (94*, L) (b) For how many steps does the Turing machine run on input string "a" before the Turing machine halts? Does the Turing machine accept the string "a"? (c) Simulate the Turing machine on input "aaba". Does it accept? Draw the final two configurations of the Turing machine computation. In the last configuration, the Turing machine is either in the accept or reject state. (d) Simulate the Turing machine on input "aabb". Does it accept? Draw the final two…9. The Turing Machine M below accepts L = { a"b": n>= 1}. y:y,R а; а, R y;y, L a;a, L q1 biy.L a;x,R q0 X;X, R q2 Yiy.R y; y,R q4 0:0,L q3 Give instantaneous description traces of M on inputs w = ab; w = aab; w = aabbb, Use the instantaneous description trace format. Type your answer. Make conclusions whether or not the tested inputs are accepted or rejected by М. %%3D
- Construct a TM that accepts the following languages.a. L12={a2nbn | n ≥1}b. L5 = {02^n | n ≥1 }. i.e., the occurrences of 0 is always powers of 2, means, every time, you can divide the resultant to 2, recursively.Show that the following function is Turing-computable. f(x)=x+1 . I want the drawingYou will disappoint me if you solve it without drawing I just want you to draw me the following question please: Turing machine that computes the function f(x,y) = x+2y, with both x and y strictly positive integers.
- Convert the following DFA to an equivalent regular expression: Deterministic finite automaton a 93 a b b b a q2 q1 b a 44 Grafstate® M 1. Create an initial GNFA GO that is equivalent to M. Here are suggested steps: a. Choose a state in Q. Modify GO to create an equivalent GNFA called G1 that contains all states in GO except for the state you chose. b. Choose another state in Q. Modify G1 to create an equivalent GNFA called G2 that contains all states in G1 except for the state you chose. c. Choose another state in Q. Modify G2 to create an equivalent GNFA called G3 that contains all states in G2 except for the state you chose. d. Choose another state in Q. Modify G3 to create an equivalent GNFA called G4 that contains all states in G3 except for the state you chose.The Knapsack Problem is a famous computer science problem that is defined as follows: imagine you are carrying a knapsack with capacity to hold a total of weight C. You are selecting among n items with values A={a_1, a_2, ... , a_n} and associated weights W={w_1, w_2, ... , w_n}. Here the weights and values are all positive (but not necessarily unique). You wish to maximize the total value of the items you select not exceeding the given weight capacity, i.e. maximize sum_{a in A} such that sum_{w in W} <= C. Please note that you can only select your items once. a) We can reformulate this as a 2D bottom-up dynamic programming problem as follows. Define T_{i,j} as the highest possible value sum considering items 1 through i and total weight capacity j (j <= C). What is the base case i.e. T_{0,j} for all j and T_{i,0} for all i?, and What is the loop statement?Correct answer will be upvoted else downvoted. Computer science. Michael is blamed for disregarding the social removing rules and making a danger of spreading Covid. He is currently shipped off jail. Fortunately, Michael knows precisely what the jail resembles from within, particularly since it's actual straightforward. The jail can be addressed as a square shape a×b which is separated into stomach muscle cells, each addressing a jail cell, normal sides being the dividers among cells, and sides on the border being the dividers prompting opportunity. Prior to condemning, Michael can ask his companions among the jail representatives to make (all around stowed away) openings in a portion of the dividers (counting dividers among cells and the furthest dividers). Michael needs to have the option to escape the jail after this, regardless of which cell he is set in. Be that as it may, he likewise needs to break as couple of dividers as could be expected. Your assignment is to…