Under the auspices of the Computational Complexity Foundation (CCF)
We propose a generalization of the traditional algorithmic space and
time complexities. Using the concept introduced, we derive an
unified proof for the deterministic time and space hierarchy
theorems, now stated in a much more general setting. This opens the
possibility for the unification and generalization of other results
that apply to both the time and space complexities. As an example,
we present a similar approach for the gap theorems.