Between SC and LOGDCFL: Families of Languages Accepted by Logarithmic-Space Deterministic Auxiliary Depth-k Storage Automata
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The closure of deterministic context-free languages under logarithmic-space many-one reductions (L-m-reductions), known as LOGDCFL, has been studied in depth from an aspect of parallel computability because it is nicely situated between L and AC^1∩SC^2. By changing a memory device from pushdown stacks to access-controlled storage tapes, 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 kSDA. Similarly to LOGDCFL, we study the closure LOGkSDA of all languages in kSDA under L-m-reductions. We first demonstrate that DCFL⊆ kSDA⊆SC^k by significantly extending Cook's early result (1979) of DCFL⊆SC^2. The entire hierarch of LOGkSDA for all k≥1 therefore lies between LOGDCFL and SC. As an immediate consequence, we obtain the same simulation bounds for Hibbard's limited automata. We further characterize the closure LOGkSDA 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 "generic" LOGkSDA-complete languages under L-m-reductions by constructing a universal simulator working for all two-way k-sda's.
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