Charles Paperman

A Circuit Complexity Approach to Transductions

Low circuit complexity classes and regular languages exhibit very tight interactions that shade light on their respective expressiveness. We propose to study these interactions at a functional level, by investigating the deterministic rational transductions computable by constant-depth, polysize circuits. To this end, a circuit framework of independent interest that allows variable output length is introduced. Relying on it, there is a general characterization of the set of transductions realizable by circuits. It is then decidable whether a transduction is definable in \(\mathrm{AC}^0\) and, assuming a well-established conjecture, the same for \(\mathrm{ACC}^0\).

Separability of Reachability Sets of Vector Addition Systems.

Given two families of sets

Monadic Second-Order Logic with Arbitrary Monadic Predicates

\mathcal{F}

Two-variable first order logic with modular predicates over words.

and

Classes of Languages Generated by the Kleene Star of a Word

\mathcal{G}

Alternation Hierarchies of First Order Logic with Regular Predicates

, the

Finite-Degree Predicates and Two-Variable First-Order Logic

\mathcal{F}

Classes of languages generated by the Kleene star of a word

separability problem for

Schema Validation via Streaming Circuits

\mathcal{G}

Continuity and Rational Functions.

asks whether for two given sets