Poly‑slicewise‑unambiguity or negation‑free tractable circuits for PAL^2 and primitive words

Ascertain whether the language of primitive words and the language PAL^2 (concatenations of two palindromes) are poly‑slicewise‑unambiguous and whether, for each, there exist tractable ×,⊎‑circuits without complementation that capture their length‑n slices.

Background

The authors introduce tractable circuits with complementation and use them to obtain polynomial‑time probabilistic membership for both primitive words and PAL^2. They remark that neither language is unambiguous, so earlier uCFG‑based results do not apply.

They explicitly state uncertainty about whether these languages fall into their earlier poly‑slicewise‑unambiguous framework, or whether complementation is necessary in their circuit constructions.