  Historically, the notion of effective algorithm is closely related to the
Church-Turing thesis. But effectivity imposes no restriction on computation
time or any other resource; in that sense, it is incompatible with engineering
or physics. We propose a natural generalization of it, means-fitting
effectivity, which is effectivity relative to the (physical or abstract)
underlying machinery of the algorithm. This machinery varies from one class of
algorithms to another. Think for example of ruler-and-compass algorithms,
arithmetical algorithms, and Blum-Shub-Smale algorithms. We believe that
means-fitting effectivity is meaningful and useful independently of the
Church-Turing thesis. Means-fitting effectivity is definable, at least in the
theory of abstract state machines (ASMs). The definition elucidates original
effectivity as well. Familiarity with the ASM theory is not assumed. We tried
to make the paper self-contained.
