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Numerous computer systems use dynamic control and data structures of unbounded size. These data structures have often the character of trees or they can be encoded as trees with some additional pointers. This is exploited by some currently…
We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
Dealing with biased data samples is a common task across many statistical fields. In survey sampling, bias often occurs due to unrepresentative samples. In causal studies with observational data, the treated versus untreated group…
Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for…
LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates.…
This paper is an experimental exploration of the relationship between the runtimes of Turing machines and the length of proofs in formal axiomatic systems. We compare the number of halting Turing machines of a given size to the number of…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
Polynomial series approximations are a central theme in approximation theory due to their utility in an abundance of numerical applications. The two types of series, which are featured most prominently, are Taylor series expansions and…
Despite significant advances in Large Reasoning Models (LRMs) driven by reinforcement learning with verifiable rewards (RLVR), this paradigm is fundamentally limited in specialized or novel domains where such supervision is prohibitively…
Recent advancements in code completion models have primarily focused on local file contexts. However, these studies do not fully capture the complexity of real-world software development, which often requires the use of rapidly-evolving…
This paper describes the autofeat Python library, which provides scikit-learn style linear regression and classification models with automated feature engineering and selection capabilities. Complex non-linear machine learning models, such…
We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…
The Parallel C++ Statistical Library for the Quantification of Uncertainty for Estimation, Simulation and Optimization, Queso, is a collection of statistical algorithms and programming constructs supporting research into the quantification…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
We study why Tool-Integrated Reasoning (TIR) makes Large Language Models (LLMs) more capable. While LLMs integrated with tools like Python code interpreters show great promise, a principled theory explaining why this paradigm is effective…
Automated program verifiers are typically implemented using an intermediate verification language (IVL), such as Boogie or Why3. A verifier front-end translates the input program and specification into an IVL program, while the back-end…
We introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in [Gebser&Schaub, ICLP 2006], with an added extension rule. We investigate the power of Extended ASP Tableaux…
We introduce PyParSVD\footnote{https://github.com/Romit-Maulik/PyParSVD}, a Python library that implements a streaming, distributed and randomized algorithm for the singular value decomposition. To demonstrate its effectiveness, we extract…