1
$\begingroup$

I need help with this problem.

There are 2 versions of the satisfiability problem:

[1] decision version: determine whether an arbitrary formula f is satisfiable or not

[2] search version: if an arbitrary formula f is satisfiable, return an assignment of truth values to variables in the formula that makes f satisfiable. if f is unsatisfiable, return NIL.

Show that [2] is Turing reducible to [1].

I have to prove that the oracle algorithm of [1] entails that of [2] to say "[2] is Turing reducible to [1]".

I see that [2] is just the oracle algorithm of [1] since it discriminates the satisfiability of an arbitrary formula f.

Can this mean the oracle algorithm of [1] entails that of [2]? If can, what would be the reason?

$\endgroup$

1 Answer 1

1
$\begingroup$

Any algorithm that decides the satisfiability of a formula can also be used to find an assignment for a satisfiable formula:

While not all variables are assigned:

  • Pick a variable and choose value 0.

  • If formula is no longer satisfiable, replace value with 1.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.