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Alternative natural models characterizing aux-k-sna behavior

Develop and identify natural computational models, fundamentally different from semi-unbounded fan-in cascading circuits, that precisely characterize the languages recognized by auxiliary depth-k nondeterministic storage automata under polynomial time and logarithmic work space.

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Background

The paper introduces semi-unbounded fan-in cascading circuits to capture the behavior of auxiliary depth-bounded nondeterministic storage automata and proves an exact characterization for even depths.

This open question seeks other, preferably more canonical or widely used, computational models that match the power of these automata without relying on the bespoke cascading-block circuit construction.

References

For future research, we wish to list eight key open questions associated with aux-$k$-sna's and $k$-cascading circuits. The computational model of cascading circuits is a simple modification of the standard circuit model by supplementing cascading blocks. We dare to ask whether or not there are any "natural" computational models, completely different from cascading circuits, which precisely capture the behaviors of aux-$k$-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 2