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a. Draw a Turing machine (using Sipser notation) having at least 4 nontrivial (i.e., nonrejecting) states and at least six nontrivial (i.e., not to the rejecting state) transitions.
b. Use set notation to define the language this machine recognizes. The language must be nontrivial (i.e., it must not be either the empty language or Sigma^* for some alphabet Sigma^*).
c. Give the binary encoding of this Turing machine two input strings: one in the language and one not.
d. For both of the strings in part c, give the contents of the tape of your universal Turing machine (from homework 8) at the time it halts when given the strings from part c as input.
Create a standard 1-tape Turing machine M to calculate the function sub3. Specifically, calculate sub3 of a natural number represented in binary.
How the problem would be encountered in attempting to represent the following statements in Predicate logic. it should be possible to: John only likes to see French movies.
We showed to prove that if L can be identified by DFA then the language left half(L) = {x ∈ ∑*|∃y xy ∈ L and |x| = |y|} is also regular; here |x| means length of x.
Express the following set as a regular expression: The set of all strings of length at least three over {0,1} such that every three consecutive.
Dynamic programming algorithm to compute a shortest superstring.
Consider a logic function with three outputs, A , B , and C , and three inputs, D , E , and F . The function is defined as follows: A is true if at least one input is true, B is true
Consider the language L = L1 ∩ L2, where L1 = {ww^R : w ∈ {a, b}* and L2 = {a^n b*a^n: n ≥ 0}. Write the first four strings in the lexicographic enumeration of L?
Write a program would read two numbers and then print all numbers between the first and the second, inclusive. Design unambiguous grammar to parse expressions
Suppose f is a function that returns the result of reversing the string of symbols given as its input, and g. What ambiguity exists in the statement x?
Create a finite-state machine design to turn your FPGA development board into a simple programmable music box.
In this problem, we consider a very restricted subset of Boolean expressions. Define an operator to be one of the four symbols: ¬, ∧, ∨, and →. Define a variable to be one of the five symbols
Show that the following identities hold for regular expressions over any alphabet: epsilon + R*R = R*. These should be done by interpreting the regular expressions as languages.
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