👉 Impossible computing refers to the theoretical concept that certain computational problems, due to their inherent complexity or the limitations of physical systems, cannot be solved by any computer, no matter how powerful. These problems often involve tasks that require an impractically large amount of time or resources to solve exactly, such as determining the exact number of ways to arrange a set of objects with certain constraints or solving the halting problem for all possible program-input pairs. The halting problem, in particular, is undecidable; it asks whether there exists an algorithm that can determine, given any program and input, whether the program will eventually halt or run forever. This means that for some problems, no algorithm can provide a definitive answer, rendering them "impossible" in the sense that they cannot be computed by any computer.
