CONSIDERABLE UNCERTAINTY existed regarding the magnitude of pulmonary dead space in the immediate post-World War II era. The dead space concept was originated by Bohr (2), who viewed total ventilation as composed of two distinct, but homogeneous, components—alveolar ventilation that participated fully in gas exchange and dead space ventilation in which no respiratory exchange occurred. With kno...

We analyse the space complexity of specific formula structures constructed using the core language of the LogicGuard framework. Unlike previous analysis which focused on the local space complex around a single quantifier, in this work we fix the global structure of the formula enough to allow analysis as a whole. Though we end up with precise results for two very specific cases, we show that th...

A machine solves a problem using space s(·) if, for every input x, the machine outputs the correct answer and uses only the first s(|x|) cells of the tape. For a standard Turing machine, we can’t do better than linear space since x itself must be on the tape. So we will often consider a machine with multiple tapes: a read-only “input” tape, a read/write “work” or “memory” tape, and possibly a w...

We propose logical characterizations of problems solvable in deterministic polylogarithmic time (PolylogTime) and space (PolylogSpace). introduce a novel two-sorted logic that separates the elements input domain from bit positions needed to address these elements. prove inflationary partial fixed point variants this capture PolylogTime PolylogSpace, respectively. In course proving our indeed ca...

We develop a theory of LOGSPACE structures and apply it to construct a number of examples of Abelian Groups which have LOGSPACE presentations. We show that all computable torsion Abelian groups have LOGSPACE presentations and we show that the groups Z, Z(p∞), and the additive group of the rationals have LOGSPACE presentations over a standard universe such as the tally representation and the bin...