Related papers: A Step-Indexing Approach to Partial Functions
Unintended failures during a computation are painful but frequent during software development. Failures due to external reasons (e.g., missing files, no permissions) can be caught by exception handlers. Programming failures, such as calling…
We introduce the lcm-filtration and stepwise filtration, comparing their performance across various scenarios in terms of computational complexity, efficiency, and redundancy. The lcm-filtration often involves identical steps or ideals,…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
Recently, small models with latent recursion have obtained promising results on complex reasoning tasks. These results are typically explained by the theory that such recursion increases a networks depth, allowing it to compactly emulate…
We describe an effort to soundly use off-the-shelf incremental SAT solvers within ACL2 by modeling the behavior of a SAT solver library as an abstract stobj. The interface allows ACL2 programs to use incremental SAT solvers, and the…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
Machine learning applications are increasingly deployed not only to serve predictions using static models, but also as tightly-integrated components of feedback loops involving dynamic, real-time decision making. These applications pose a…
In data exploration, users need to analyze large data files quickly, aiming to minimize data-to-analysis time. While recent adaptive indexing approaches address this need, they are cases where demonstrate poor performance. Particularly,…
In this work, we present an approach towards constructing executable specifications of existing filesystems and verifying their functional properties in a theorem proving environment. We detail an application of this approach to the FAT32…
Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying…
A fragment of second-order lambda calculus (System F) is defined that characterizes the elementary recursive functions. Type quantification is restricted to be non-interleaved and stratified, i.e., the types are assigned levels, and a…
Proving the correctness of programs written for multiple processors is a challenging problem, due in no small part to the weaker memory guarantees afforded by most modern architectures. In particular, the existence of store buffers means…
In engineering design, one often wishes to calculate the probability that the performance of a system is satisfactory under uncertainty. State of the art algorithms exist to solve this problem using active learning with Gaussian process…
Automated reasoning is critical in domains such as law and governance, where verifying claims against facts in documents requires both accuracy and interpretability. Recent work adopts structured reasoning pipelines that translate natural…
Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated…
Reinforcement learning~(RL) is a versatile framework for learning to solve complex real-world tasks. However, influences on the learning performance of RL algorithms are often poorly understood in practice. We discuss different analysis…
This paper is a concise and painless introduction to the $\lambda$-calculus. This formalism was developed by Alonzo Church as a tool for studying the mathematical properties of effectively computable functions. The formalism became popular…
In-Context Learning (ICL) is an emergent capability of Large Language Models (LLMs). Only a few demonstrations enable LLMs to be used as blackbox for new tasks. Previous studies have shown that using LLMs' outputs as labels is effective in…
This paper formalizes and proves correct a compilation scheme for mutually-recursive definitions in call-by-value functional languages. This scheme supports a wider range of recursive definitions than previous methods. We formalize our…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…