Between SC and LOGDCFL: families of languages accepted by logarithmic-space deterministic auxiliary depth-k storage automata

The closure of deterministic context-free languages under logarithmic-space many-one reductions ( -m-reductions), known as LOGDCFL, has been studied in depth from an aspect of parallel computability because it is nicely situated between and . By replacing a memory device of pushdown automata with an access-controlled storage tape, we introduce a computational model of one-way deterministic depth-k storage automata (k-sda's) whose tape cells are freely modified during the first k accesses and then become blank forever. These k-sda's naturally induce the language family . Similarly to , we study the closure of all languages in under -m-reductions. We demonstrate that by significantly extending Cook's early result (1979) of . The entire hierarch of for all therefore lies between and . As an immediate consequence, we obtain the same simulation bounds for Hibbard's limited automata. We further characterize in terms of a new machine model, called logarithmic-space deterministic auxiliary depth-k storage automata that run in polynomial time. These machines are as powerful as a polynomial-time two-way multi-head deterministic depth-k storage automata. We also provide a ‘generic’ -complete language under -m-reductions by constructing a two-way universal simulator working for all k-sda's.