Related papers: Further Formalization of the Process Algebra CCS i…

We continue analysis of \cite{Parsa:2018kys} and study rigidity and stability of the BMS4 algebra and its centrally extended version. We construct and classify the family of algebras which appear as deformations of BMS4 and in general find…

We prove a complexity dichotomy theorem for symmetric complex-weighted Boolean #CSP when the constraint graph of the input must be planar. The problems that are #P-hard over general graphs but tractable over planar graphs are precisely…

The ABC conjecture implies many conjectures and theorems in number theory, including the celebrated Fermat's Last Theorem. Mason-Stothers Theorem is a function field analogue of the ABC conjecture that admits a much more elementary proof…

Conjugate partial-symmetric (CPS) tensor is a generalization of Hermitian matrices. For the CPS tensor decomposition some properties are presented. For real CPS tensors in particular, we note the subtle difference from the complex case of…

Bergstra and Klop have shown that bisimilarity has a finite equational axiomatisation over ACP/CCS extended with the binary left and communication merge operators. Moller proved that auxiliary operators are necessary to obtain a finite…

Approximate methods to full N-body simulations provide a fast and accurate solution to the development of mock catalogues for the modeling of galaxy clustering observables. In this paper we extend ICE-COLA (Izard et al. 2016), based on an…

We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an…

The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials…

We generalize the notion of an exact category and introduce weakly exact categories. A proof of the snake lemma in this general setting is given. Some applications are given to illustrate how one can do homological algebra in a weakly exact…

In this paper, we describe the formalization of the axiom of choice and several of its famous equivalent theorems in Morse-Kelley set theory. These theorems include Tukey's lemma, the Hausdorff maximal principle, the maximal principle,…

Hybrid games model cyber-physical systems (CPS), like cars, trains, and airplanes, where discrete control decisions interact with continuous physical dynamics. We use Large Language Models (LLMs) to scale formal verification and synthesis…

This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…

We study a special class of weakly associative algebras: the symmetric Leibniz algebras. We describe the structure of the commutative and skew symmetric algebras associated with the polarization-depolarization principle. We also give a…

High-accuracy composite wavefunction methods like Weizmann-4 (W4) theory, high-accuracy extrapolated \textit{ab initio} thermochemistry (HEAT), and Feller-Peterson-Dixon (FPD) enable sub-kJ/mol accuracy in gas-phase thermochemical…

A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…

The paper describes a deep reinforcement learning framework based on self-supervised learning within the proof assistant HOL4. A close interaction between the machine learning modules and the HOL4 library is achieved by the choice of tree…

A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…

This paper aims to study reducible and irreducible approximation in the set $\textsl{CSO}$ of all complex symmetric operators on a separable, complex Hilbert space $\mathcal H$. When ${\rm dim} \mathcal H=\infty$, it is proved that both…

We study operator algebraic and function theoretic aspects of algebras of bounded nc functions on subvarieties of the nc domain determined by all levels of the unit ball of an operator space (nc operator balls). Our main result is the…

Compensating CSP (cCSP) is a language defined to model long running business transactions within the framework of standard CSP process algebra. In earlier work, we have defined both traces and operational semantics of the language. We have…