Algorithms and algebra

The algebraic definition of an algorithm given above is wider than the classical one. It is an abstract definition based on a signature only, and allows interpretation by any computational structure of this signature. Even introducing a set of properties does not necessarily determine the interpretation completely. This freedom is an advantage, it allows to treat a number of related algorithms under one single roof. Moreover, even for a given monomorphic type algorithms can be non-deterministic. This freedom allows to go to special descendants which show increased efficiency, including deterministic ones.