AUTOMATA THEORY: Find a Turing machine that computes the remainder of its input when divided by 3 whileeach number is represented by 1’s.If the remainder is zero, output should be one zero on the tape.If the remainder is greater than zero, output should start with one zero following by theremainder.For example, an input tape containing the number 8:Input: B11111111B (B represents blank)executing should leave the number 2 on the tape, because 2 is the remainder of 8 whendivided by 3. Output: 011

5. Consider the algorithm that takes an input n and runs the following pseudocode: for i := 1 to 5 for j := 1 to n k := 7.i+1 next j k := k + 3 – 2 - i next i

Q1. Design a Turing machine to count number of l's in the tape and write the output at beginning of the tape. (Consider that tape has binary numbers only). Q2. Consider the TM defined by M = (Q. E,r, 8, q0, B, F) 8 ( qo, a ) = (q1, a , R) 8 ( qo , b ) = ( q1 , b, R) 8( qo, B) = (q1,B , R) 8(q1, a) = ( qo, a, L) 8(q1, b )= ( qo, b , L) 8 ( qı, B ) = ( qo, B, L) What is the state of TM on input 'ab'?

Computer science

Let X. Y and Z be binary strings of same length and X-Xo X1.. X Xa. Y- yo y. y... Ya- and Z- zo Z1... Z..z A bitwise operation on X and Y is defined as f (X. Y)-Z where z- x, & y. The operation is defined as follows. Design a Turing machine T to compute the function f(X. Y). Assume any two characters as separators among the strings X. Y and Z.

Computer Science Please answer the questions. It is either yes or no for the answers.

Design a Turing machine that computes the function S1 if w is even lo if w is odd Note that you need to use unary representation for w. For example, if w = 3, then representation f(w) = of w is 111.

Turing Machine theory of computation   Design a Turing Machine (M1) that takes any string as input (except the empty string), and shifts each character of the string one place into the right. For instance, if the tape initially contains the following [a|b|a|␣|␣], then it should contain the following after M1 halts [#|a|b|a|␣]. You may assume that M1 always halts and accepts except when the tape does not contain anything. Assume the input alphabet Σ is {a, b} and the tape alphabet Γ is Σ ∪ {#, a, b, ␣}.   a)(30 points) Draw the state diagram for M1.     b)(20 points) Provide the formal definition for M1.   C)(25 points) Describe what M1 does in numbered stages (as an algorithm).       d) (25 points) Modify M1 to make it shift the tape content by two characters instead of one (e.g., the tape content in the previous example should be [#|#|a|b|a|␣]). Redraw the new version of M1.

E3

The unary numeral system is a numeral system to represent natural numbers as sequences of ones, that is, to represent a number ?, a symbol representing “1” is repeated ? times. For example, the number 4 is represented by 1111. The number 0 would be represented by the empty string. Create a Turing machine which adds 3 to a natural number, that is, writes three times a 1 after the given unary number. Afterwards move the head to the left-most position of input.