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arXiv · 2412.09186

Nondeterministic Auxiliary Depth-Bounded Storage Automata and Semi-Unbounded Fan-in Cascading Circuits

Tomoyuki Yamakami
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Abstract

We discuss a nondeterministic variant of the recently introduced machine model of deterministic auxiliary depth-$k$ storage automata (or aux-$k$-sda's) by Yamakami. It was proven that all languages recognized by polynomial-time logarithmic-space aux-$k$-sda's are located between $\mathrm{LOGDCFL}$ and $\mathrm{SC}^k$ (the $k$th level of Steve's class SC). We further propose a new and simple computational model of semi-unbounded fan-in Boolean circuits composed partly of cascading blocks, in which the first few AND gates of unbounded fan-out (called AND$_{(ω)}$ gates) at each layer from the left (where all gates at each layer are indexed from left to right) are linked in a "cascading" manner to their right neighbors though specific AND and OR gates. We use this new circuit model to characterize a nondeterministic variant of the aux-$2k$-sda's (called aux-$2k$-sna's) that run in polynomial time using logarithmic work space. By relaxing the requirement for cascading circuits, we also demonstrate how such cascading circuit families characterize the complexity class $\mathrm{P}$. This yields an upper bound on the computational complexity of $\mathrm{LOG}k\mathrm{SNA}$ by $\mathrm{P}$.

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BibTeXRIS

Tomoyuki Yamakami. 2024-12-12. Nondeterministic Auxiliary Depth-Bounded Storage Automata and Semi-Unbounded Fan-in Cascading Circuits. https://arxiv.org/abs/2412.09186

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