Optimal Proof Systems
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Recursive Jump Operators and Optimal Proof Systems
Announce Type: new Abstract: We study the relationship between the existence of optimal proof systems and recursive jump operators, two central open problems in proof complexity. For a set L, an optimal proof system is a strongest proof system in terms of proof length, whereas a recursive jump operator uniformly transforms any proof system for L into a stronger one with respect to proof length, thereby witnessing non-optimality. It is clear that the existence of a recursive jump operator for...
Optimizing Proof-Search via Linearization for G\"odel-L\"ob Logic with Tree-Hypersequents
Announce Type: new Abstract: We answer a question posed by Poggiolesi concerning a syntactic decidability proof for GL in the tree-hypersequent system CSGL, and resolve a challenge identified by Maggesi and Perini Brogi, who sought a PSPACE proof-search algorithm for GL in expressive sequent-based formalisms. We work with a notational variant of CSGL formulated in terms of (labeled) tree sequents. Our answer is complexity-optimal: we present a proof-search algorithm that decides the...
Hardness as an Information Constraint: A Unifying Meta-Complexity Assumption
Announce Type: new Abstract: Monroe (2026) shows that the nonexistence of an optimal proof system can be read as an information constraint regarding canonical hard instances: no sound arithmetic theory simulates the extensions adjoining sufficiently large, unprovable Busy Beaver values. Furthermore, if the best-known route to simulation is also necessary -- that is, if simulation requires a relative-consistency explanation over a weak base theory -- then the same constraint holds for...
Don't Gamble, GAMBLe: An Analytical Framework for AI-Driven Research Systems
arXiv:2606.02863v1 Announce Type: new Abstract: AI-Driven Research Systems (ADRS) -- systems coupling LLMs with automated evaluation to discover algorithms, proofs, and designs -- are being optimized and adopted across domains, but the tools to analyze them have not kept pace. ADRS performance depends on component interactions that are poorly understood, expensive to explore, and (as we show) not well captured by standard convergence guarantees. These guarantees rely on structural...
Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions
arXiv:2502.03847v2 Announce Type: replace Abstract: A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy...
Learning to Reason with Insight for Informal Theorem Proving
arXiv:2604.16278v2 Announce Type: replace Abstract: Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems.
Retrieval-Augmented Generation Must Move Beyond Factual Grounding to Represent Diverse Opinions
Announce Type: replace Abstract: This position paper argues that Retrieval-Augmented Generation systems exhibit a systematic factual bias-optimizing for epistemic uncertainty reduction while ignoring the aleatoric uncertainty inherent in opinion-rich content - and that this misalignment demands a paradigm shift in retrieval system design. A survey of 35 major RAG benchmarks reveals that only one addresses opinion synthesis, confirming that the bias is structural: embedded in datasets,...
Optimal Wiener-Filter Solutions for Denoising of Graph Signals on Directed Graphs
Electrical Engineering and Systems Science > Signal Processing [Submitted on 5 Jun 2026] Title:Optimal Wiener-Filter Solutions for Denoising of Graph Signals on Directed Graphs View PDF HTML (experimental)Abstract:Graph signal processing has opened new avenues to the canonical denoising problem in interesting settings.
Closed-Form Pose Estimation of Endoluminal Medical Devices via Gradiometer-Based Electromagnetic Localization System
arXiv:2606.01946v1 Announce Type: new Abstract: Embedded magnetic tracking holds highly attractive prospects for remote navigation of endoluminal medical devices. However, existing six-degree-of-freedom pose recovery approaches often require pre-calibrated workspace field maps or iterative nonlinear optimization. This letter presents a Gradiometer-Based Electromagnetic Localization System (GELS), a closed-form tracking framework that uses a compact magnetometer array as an embedded...
How I Get Free Traffic from ChatGPT in 2025 (AIO vs SEO)
Three weeks ago, I tested something that completely changed how I think about organic traffic. I opened ChatGPT and asked a simple question: "What's the best course on building SaaS with WordPress?" The answer that appeared stopped me cold.