Expert answer:Computer Science

Expert answer:Using the C++-implementation of (possibly nondeterministic)Turing machines, create a deterministic Turing machine (transducer) thatdoes the following: If the input is a finite string over the alphabet {0, 1}, then the inputcan be interpreted as a binary number. The Turing machine assumes that the input is a binary number withmost significant digit first, and increases this number by one.
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CS Track Core Theory, Programming Exercise
Deadline: Monday 04.12.2017
The tasks must be made individually. Code must be submitted to Moodle by
Monday 04.12.2017, not later than 23.59. Hand drawn Turing machines with
explanations must be handed in to me (HdN) in room 7.222 not later than 18.00.
1. (5 pts.) Using the C ++ -implementation of (possibly nondeterministic)
Turing machines, create a deterministic Turing machine (transducer) that
does the following:
• If the input is a finite string over the alphabet {0, 1}, then the input
can be interpreted as a binary number.
• The Turing machine assumes that the input is a binary number with
most significant digit first, and increases this number by one.
Here are some examples:
101
results in
1011 results in
11111 results in
110
1100
100000
There is no need to modify the C ++ code for the Turing machine. You
can follow the example in turing.cpp. You are free to add states and
symbols to the files state.h and symbol.h.
2. Let us write a nondeterministic Turing machine that solves the SATproblem for CNF.
For simplicity, we encode atoms as single letters. Assume an alphabet
Σ = { a, b, c, d, e, ′ |′ , ′ −′ , ′ +′ }. We will use ′ |′ as separator between
clauses, ′ −′ for building negative literals, and ′ +′ for building positive
literals.
|-a+b|+a+b|-c|
// In the language.
|-a+b|+a+b|-b|
// Not in the language.
|+a+b|-a+b|-a-b|+a-b| // Not in the language.
1
(a) (5 pts.) Write a deterministic Turing machine that checks whether
an input represents a well-formed representation of a SAT problem.
It should accept all inputs above, but it should reject for example
|+a-b|++a| and |+ab|.
(b) (5 pts.) Write a nondeterministic Turing machine (transducer) that
selects/guesses an atom from each clause in a set of clauses. For example, in the first example above, a possible output would be -a+b-c.
In the last example, a possible output would be +a+b-b+a.
(c) (5 pts.) Write a Deterministic Turing machine that takes a sequence
of literals and accepts this sequence if there is no complementary pair
in it (No pair of form +v and −v). It would accept -a+b-c, but reject
+a+b-b+a.
(d) (5 pts.) It should now be possible to combine the three Turing
machines of the previous tasks into a single, nondeterministic Turing
machine that recognizes the SAT-problem for CNF.
Please provide drawings for your Turing machines, and show that they
work by providing a few examples.
2
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