From complexity analysis we can adopt the concept of polynomial-time reducibility and might define a type of equivalence relation where two algorithms are equiv

From complexity analysis we can adopt the concept of polynomial-time reducibility and might define a type of equivalence relation where two algorithms are equivalent only if both are pt-reducible to each other. Intuitively it’s not a sufficient condition for "sameness" – otherwise, for example, all NP-complete problems are the "same" and solvable with the "same" algorithm – but it’s arguably a necessary one.