# Is maximising (or minimising) something enough to say that I am solving a decision problem? [duplicate]

We know that every optimisation problem has an equivalent decision problem.

So say I keep going up a mountain (I.e. I am maximising my altitude) following a certain number of finite steps (similarly to a TM). Is that enough to assert that I am solving a decision problem?

If yes which one?

• Sep 4, 2016 at 10:20
• And not, stating a maximization problem and calling it decision problem doesn't make it one. Sep 4, 2016 at 10:21
• @Raphael Well let me give you my version. In my example I am maximising my altitude by synthetically checking where my next step can lead me. Once that's done I take the step which produces the largest positive change in altitude. That's a decision problem and it looks like I can generalise this process leading me to believe that indeed every optimisation problem can be seen as a decision problems like shown by CS theory. Anything wrong with my reasoning? Sep 4, 2016 at 15:04
• You are not using "decision problem" in the way we do in TCS. We don't mean "decide where to go" but "decide between yes and no". Sep 4, 2016 at 18:44
• @Raphael I am. I am searching for the maximum altitude using a yes/no method Sep 4, 2016 at 19:30