相关论文: Mace4 Reference Manual and Guide

In this paper, we identify a fragment of second-order logic with restricted quantification that is expressive enough to capture numerous static analysis problems (e.g. safety proving, bug finding, termination and non-termination proving,…

This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…

In this paper, we compare two alternative mechanisms for deciding the validity of first-order formulas over finite domains supported by the mathematical model checker RISCAL: first, the original approach of semantic evaluation (based on an…

This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…

Differential equations are fundamental to modeling dynamic systems in physics, engineering, biology, and economics. While analytical solutions are ideal, most real-world problems necessitate numerical approaches. This study conducts a…

Completeness is one of the most important attributes of software requirement specifications. Unfortunately, incompleteness is meanwhile one of the most difficult problems to detect. Some approaches have been proposed to detect missing…

In this paper we deal with verification of safety properties of term-rewriting systems. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which further resolved by…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…

We design and analyze an algorithm for computing solutions with coefficients in a finite field $\mathbb{F}_q$ of underdetermined systems defined over $\mathbb{F}_q$. The algorithm is based on reductions to zero-dimensional searches. The…

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…

Large language models (LLMs) have recently demonstrated remarkable progress in formal theorem proving. Yet their ability to serve as practical assistants for mathematicians, filling in missing steps within complex proofs, remains…

Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model inference have been based on a maximum likelihood objective. Efficient algorithms exist…

While it is trivial to multiply two C-finite sequences (just like integers), it is not quite so trivial to "factorize" them, or to decide whether they are "prime". The former is plain linear algebra, while the latter is heavy-duty…

The availability of shared software models provides opportunities for reusing, adapting and learning from them. Public models are typically stored in a variety of locations, including model repositories, regular source code repositories,…

We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…

Automated compilation error repair, the problem of suggesting fixes to buggy programs that fail to compile, has generated significant interest in recent years. Apart from being a tool of general convenience, automated code repair has…

The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…

In Earth System Modeling (ESM), meshes of different models usually do not match, requiring data mapping algorithms implemented in coupling software. Valcke et al. recently introduced a benchmark to evaluate such algorithms and compared…

In recent years, language models (LMs), such as GPT-4, have been widely used in multiple domains, including natural language processing, visualization, and so on. However, applying them for analyzing and optimizing high-performance…