arXiv:2606. 11171v4 Announce Type: replace Abstract: We develop Bellman-sufficient information complexity, a formal representation-level framework for sequential decision making.
arXiv:2606. 11171v2 Announce Type: replace Abstract: We develop indexed Bellman information complexity, a representation-level theory of interactive decision making centered on information indices and reference histories.
arXiv:2608. 02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$.
We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $Ω(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity.
arXiv:2606. 24074v1 Announce Type: cross Abstract: Wang~\cite{Wang2026} introduced the Stochastic-Oracle Turing Machine (SOTM) framework and defined token complexity as the minimum expected cost of interacting with a stochastic oracle needed to attain a specified solution quality for a task.
arXiv:2608. 16438v1 Announce Type: new Abstract: In a world where valuable artifacts are increasingly created, completed, or processed by LLMs, the central economic question is not only what the LLM can produce, but what \emph{value} remains in the inputs (i.
arXiv:2509. 11208v3 Announce Type: replace-cross Abstract: Transformers used for evidence-grounded binary adjudication (e.
arXiv:2606. 12211v1 Announce Type: cross Abstract: A central principle in quantum machine learning is that an ansatz should be expressive enough to represent the quantum data of interest.
arXiv:2607. 15459v1 Announce Type: new Abstract: A trained deep reinforcement learning policy is a black box, and we ask whether it can be made explainable by rewriting it as an executable logic program that reproduces its behaviour and that a person can read, a logic engine can run, and an optimizer can edit.
arXiv:2507. 05972v3 Announce Type: replace-cross Abstract: Pseudoentropy characterizations give quantitatively precise formulations of the relationship between computational hardness and computational randomness.
arXiv:2609.06036v1 Announce Type: new Abstract: Proposal-based controllers---learned policies, language-model planners, and other black-box \emph{generators}---are increasingly deployed behind runtim...
The paper introduces the concept of task‑conditioned active observability, defining the minimal interaction cost needed for an autonomous agent to identify task‑relevant states while guaranteeing safe abstention. It formalizes this complexity, proving that task‑predictive equivalence yields a unique minimal sufficient quotient that preserves complexity and eliminates unnecessary distinctions. The authors present theoretical characterizations for deterministic and noisy regimes, and demonstrate a certified observer that reduces sensor usage and model steps while maintaining zero false acceptances in extensive high‑dimensional trials.
arXiv:2608. 10650v1 Announce Type: new Abstract: Reducing the number of focal elements of a mass function is classically driven by an intrinsic distance, such as Jaccard or Jousselme, that keeps the approximation close to the original as a body of evidence.