Read-only-input work-space classes and constructibility

A read-only-input machine has one read-only input tape and finitely many work tapes. On an input $x$ of length $n$, the input is bracketed by endmarkers and the input head is confined to those $n+2$ positions. The input tape is never written and its cells are not charged.

$\mathrm{D}\mathrm{W}\mathrm{O}\mathrm{R}\mathrm{K}\mathrm{S}\mathrm{P}\mathrm{A}\mathrm{C}\mathrm{E}(s)$ contains the languages decided by such machines while visiting $O(s(n))$ work-tape cells. A bound $s$ is work-space constructible when a deterministic read-only-input machine, on input $1^n$, outputs the binary expansion of $s(n)$ while visiting $O(s(n))$ work cells. In hierarchy applications we require $\lceil {\log }_2(n+2)\rceil =O(s(n))$ so that an input-head address fits in the work bound. This model is distinct from all-tapes DSPACE.