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Effect of multiple counters on the power of k-sna’s

Determine whether augmenting nondeterministic depth-k storage automata (k-sna’s) with multiple counters increases their language recognition power, and characterize any resulting hierarchy or class separations.

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Background

Recent work has shown that adding counters can enhance pushdown automata. The paper asks whether similar augmentations increase the power of depth-bounded storage automata.

A positive or negative answer would illuminate the robustness of the k-sna model with respect to standard memory extensions.

References

For future research, we wish to list eight key open questions associated with aux-$k$-sna's and $k$-cascading circuits. An additional memory device of ``counter'' is appended to pushdown automata in to enhance the computational power of the pushdown automata. Does the use of multiple counters help increase the computational power of $k$-sna's?

— Nondeterministic Auxiliary Depth-Bounded Storage Automata and Semi-Unbounded Fan-in Cascading Circuits (2412.09186 - Yamakami, 12 Dec 2024) in Section 7 (Brief Discussions and Future Research Directions), Item 9