He received his Doctor of Philosophy from Moscow State Pedagogical Institute in 1959 under the advisorship of Pyotr Novikov. Muchnik"s most significant contribution was on the subject of relative computability. He and Richard Friedberg, independently introduced the priority method which gave an affirmative answer to Post"s Problem regarding the existence of re Turing degrees between 0 and 0".
This groundbreaking result, now known as the Friedberg-Muchnik Theorem, opened a wide study of the Turing degrees of the recursively enumerable sets which turned out to possess a very complicated and non-trivial structure.
He also has a significant contribution in the subject of mass problems where he introduced the generalisation of Turing degrees, called "Muchnik degrees" in his work On Strong and Weak Reducibilities of Algorithmic Problems published in 1963.