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Expressivity bounds for finite-state deterministic transducers with a meta-vertex

Ascertain bounds on the expressive power of finite-state deterministic string machines that incorporate the meta-vertex by characterizing the class of languages they can decide (e.g., determine whether these languages coincide with or are a strict subset of the context-free languages).

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Background

The meta-vertex allows string machines to output and execute other string machines at runtime, increasing expressivity; for example, the authors construct a meta-level-1 machine that recognizes palindromes.

Despite this increased power, the authors have not established formal bounds on the class of languages these machines can decide, though they speculate it may be some subset of the context-free languages. Precisely characterizing this class remains open.

References

We have not yet established bounds on the expressivity of finite-state deterministic transducers which incorporate the meta-vertex, but, due to the bounding on levels of meta, it is likely that the languages they decide are some subset of context-free languages.

— Time complexity for deterministic string machines (2405.06043 - Cataltepe et al., 9 May 2024) in Further work: Characterizing the expressivity of transducers with a meta-vertex and monadic transducers