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An Algebraic View of the Expressivity of Recurrent Language Models

cs.FL · 2026-06-01 · unverdicted · novelty 7.0

A unified algebraic account reduces RNN expressivity to syntactic monoid division in wreath products and shows diagonal state-space models realize every even-modulus counter under unsigned-integer quantization but none under floating-point recurrences.

Hallucination, abstention, and computable inseparability

math.LO · 2026-04-30 · accept · novelty 7.0 · 2 refs

Abstaining AI systems cannot guarantee both large coverage of correct answers and zero hallucination in sufficiently expressive domains, as shown by the existence of inseparable pairs in the arithmetical hierarchy.

Remarks on Primitive Regulation

math.LO · 2026-05-18 · unverdicted · novelty 6.0 · 2 refs

An obstruction theorem establishes that Eval(C), MP(C), Cons(C), and LEM(C) are jointly incompatible for any closure predicate C on formulas built from bottom and implication.

Experiments, Computability, and the Existence of Physical Functions

physics.hist-ph · 2026-04-23 · unverdicted · novelty 5.0

Reproducible experiments compute physical functions via a Church-Turing bridge, compatible with finite precision through computable analysis, while separating existence, computability, and protocol-independence questions.

Turing or Cantor: That is the Question

cs.CL · 2026-04-12 · unverdicted · novelty 3.0

Turing's work relies on Cantor's contributions; a new undecidability measure and U-complete, D-complete, H-complete classes are defined, with a negative answer to a P-vs-NP analog for undecidable problems.

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  • Hallucination, abstention, and computable inseparability math.LO · 2026-04-30 · accept · none · ref 6 · 2 links

    Abstaining AI systems cannot guarantee both large coverage of correct answers and zero hallucination in sufficiently expressive domains, as shown by the existence of inseparable pairs in the arithmetical hierarchy.

  • Remarks on Primitive Regulation math.LO · 2026-05-18 · unverdicted · full · ref 16 · 2 links

    An obstruction theorem establishes that Eval(C), MP(C), Cons(C), and LEM(C) are jointly incompatible for any closure predicate C on formulas built from bottom and implication.