Final answer:
The question is about identifying a decidable problem from given options. The correct answer is the graph coloring problem, as it is possible for an algorithm to determine a solution in a finite amount of time.
Step-by-step explanation:
The question asks which of the following is a decidable problem: a. Graph coloring problem b. Traveling salesman problem c. Post correspondence problem d. Halting problem. A decidable problem is one where a computer algorithm can determine, in a finite amount of time, a yes-or-no answer for every input.
The Traveling salesman problem is an NP-complete problem. The complexity of this problem means it is not known whether a quick, efficient solution exists for all possible inputs, but they are not known to be undecidable. The Post correspondence problem and the Halting problem are both undecidable problems; no algorithm can determine a yes-or-no answer for every input in finite time.
Graph coloring problem
The correct answer is a. Graph coloring problem. For a given graph G and a number of colors k, it's possible to decide whether the vertices of G can be colored with k colors in such a way that no two adjacent vertices share the same color. This problem is decidable because there exists an algorithm that can exhaustively check all possible combinations of vertices and colors and decide whether a solution exists for a given input.