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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.
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.
Show that the language F = {a^i b^j c^k | i, j, k greater than or equal to 0 and if i = 1 then j = k} is not regular. Show, however, that it satisfies the statement of the pumping lemma
We know by rice's theorem that none of the following problems are decidable. However,are they recursively enumerable,or non-RE? IS L(M) infinite?
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.
Write some examples of declarative knowledge. Write some examples of procedural knowledge. Then, compare examples, highlighting the similarities & differences.
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?
Create a finite-state machine design to turn your FPGA development board into a simple programmable music box.
Dynamic programming algorithm to compute a shortest superstring.
Redundant sequence identi cation
Create a standard 1-tape Turing machine M to calculate the function sub3. Specifically, calculate sub3 of a natural number represented in binary.
Write down a structural induction principle for the PlayTree free type
What does the term solvable mean to you? What does it mean to say that "you solved a problem"? Determine examples of problems for which you believe there are no solutions.
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