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This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
Marx (STOC~2010, J.~ACM 2013) introduced the notion of submodular width of a conjunctive query (CQ) and showed that for any class $\Phi$ of Boolean CQs of bounded submodular width, the model-checking problem for $\Phi$ on the class of all…
Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We…
Recent work has shown that integrating large language models (LLMs) with theorem provers (TPs) in neuro-symbolic pipelines helps with entailment verification and proof-guided refinement of explanations for natural language inference (NLI).…
This paper presents composable attestation as a generalized cryptographic framework for Continuous and Incremental Trust in Distributed Systems,such as Artificial Intelligence (AI) computation, and Open Source Software (OSS) supply chain…
Side-channel attacks are a major threat to the security of cryptosystems. Masking is a widely used countermeasure against such attacks, but proving the security of masked algorithms is error-prone without formal verification. In this work,…
Modern lattice-based cryptography, particularly the learning with errors paradigm, relies on injecting artificial noise to secure data against quantum adversaries. This study systematically examines the theoretical and physical boundaries…
This paper presents a comprehensive cryptographic analysis of the security parameters of the LINEture post-quantum digital signature scheme, which is constructed using matrix algebra over elementary abelian 2-groups. We investigate the…
NIST is standardizing Post Quantum Cryptography (PQC) algorithms that are resilient to the computational capability of quantum computers. Past works show malicious subversion with cryptographic software (algorithm subversion attacks) that…
Topological quantum computing holding global anti-interference ability is realized by braiding some anyons, such as well-known Fibonacci anyons. Here, based on $SO(3)_2 $ theory we obtain a total of 6 anyon models utilizing…
We propose and validate on real quantum computing hardware a new method for extended two-qubit gate set design, replacing iterative, fine calibration with fast characterization of a small number of gate parameters which are then tracked and…
Quantum error correction assumes that all syndrome activations represent errors requiring correction. We present evidence from 756 QEC runs across three IBM Eagle r3 processors that this assumption is wrong. The hardware exhibits…
To bridge the ever increasing gap between deep neural networks' complexity and hardware capability, network quantization has attracted more and more research attention. The latest trend of mixed precision quantization takes advantage of…
Automated malware analysis increasingly relies on machine learning, yet most existing methods remain task-specific and depend on handcrafted features or narrowly scoped models. Recent developments in binary-level foundation models suggest a…
Realizing large-scale quantum advantage is expected to require quantum error correction (QEC), making the compilation and optimization of logical operations a critical area of research. Logical computation imposes distinct constraints and…
It is argued that 4-valued paraconsistent truth values (called here "p-bits") can serve as a conceptual, mathematical and practical foundation for highly AI-relevant forms of probabilistic logic and probabilistic programming and concept…
This paper focuses on a fundamental problem on information security of bounded labeled Petri nets: non-interference analysis. As in hierarchical control, we assume that a system is observed by users at different levels, namely high-level…
The April 2026 Claude Mythos sandbox escape exposed a critical weakness in frontier AI containment: the infrastructure surrounding advanced models remains susceptible to formally characterizable arithmetic vulnerabilities. Anthropic has not…
We study deterministic polynomial identity testing (PIT) and reconstruction algorithms for depth-$4$ arithmetic circuits of the form \[ \Sigma^{[r]}\!\wedge^{[d]}\!\Sigma^{[s]}\!\Pi^{[\delta]}. \] This model generalizes Waring…
We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…