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.

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