Related papers: FORM version 4.0
Most Formal Languages and Automata Theory courses explore the duality between computation models to recognize words in a language and computation models to generate words in a language. For students unaccustomed to formal statements, these…
An operator formalism for bosonic $\beta-\gamma$ systems on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra…
This note continues the theoretical development of deterministic integer factorization algorithms based on systems of polynomials equations. The main result establishes a new deterministic time complexity bench mark in integer…
Previous studies have shown that automated text-mining tools are becoming increasingly important for successfully unlocking variant information in scientific literature at large scale. Despite multiple attempts in the past, existing tools…
Foundation models (FMs), including large language models, have become increasingly popular due to their wide-ranging applicability and ability to understand human-like semantics. While previous research has explored the use of FMs in…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
These notes originate from a reading course held by the authors in the spring of 2024 at the Universit\`a di Genova. They provide a hands-on introduction to the F4 and FGLM algorithms. In addition to the notes, we present two…
Functional reactive programming (FRP) is a declarative programming paradigm for implementing reactive programs at a high level of abstraction. It applies functional programming principles to construct and manipulate time-varying values,…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
Data compression techniques are characterized by four key performance indices which are (i) associated accuracy, (ii) compression ratio, (iii) computational work, and (iv) degree of freedom. The method of data compression developed in this…
In this paper we present a formal computational framework for modeling manipulation actions. The introduced formalism leads to semantics of manipulation action and has applications to both observing and understanding human manipulation…
This note is a complete library of symbolic parametrized expressions for both real and complexified configuration spaces of a planar 4-bar linkage. Building upon the previous work from Izmestiev (2015), this library expands on the…
The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the history and recent developments for several fields in which the…
Autoformalization serves a crucial role in connecting natural language and formal reasoning. This paper presents MASA, a novel framework for building multi-agent systems for autoformalization driven by Large Language Models (LLMs). MASA…
It is important to enable reasoning about the meaning and possible effects of updates to ensure that the updated system operates correctly. A formal, mathematical model of dynamic update should be developed, in order to understand by both…
While the state-of-the-art for frame semantic parsing has progressed dramatically in recent years, it is still difficult for end-users to apply state-of-the-art models in practice. To address this, we present Frame Semantic Transformer, an…
$\mathcal{H}\Phi$ [$aitch$-$phi$] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented…
Modal synthesis is an important area of physical modeling whose exploration in the past has been held back by a large number of control parameters, the scarcity of general-purpose design tools and the difficulty of obtaining the…
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…
This paper introduces the FermiFab toolbox for many-particle quantum systems. It is mainly concerned with the representation of (symbolic) fermionic wavefunctions and the calculation of corresponding reduced density matrices (RDMs). The…