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Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Software vulnerabilities, caused by unintentional flaws in source code, are a primary root cause of cyberattacks. Static analysis of source code has been widely used to detect these unintentional defects introduced by software developers.…

The iterative conditional branchings appear in various sensitive algorithms, like the modular exponentiation in the RSA cryptosystem or the scalar multiplication in ellipticcurve cryptography. In this paper, we abstract away the desirable…

In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms. This paper explores whether using…

The goal of neural-symbolic computation is to integrate the connectionist and symbolist paradigms. Prior methods learn the neural-symbolic models using reinforcement learning (RL) approaches, which ignore the error propagation in the…

We focus on the problem of inducing logic programs that explain models learned by the support vector machine (SVM) algorithm. The top-down sequential covering inductive logic programming (ILP) algorithms (e.g., FOIL) apply hill-climbing…

Textual Large Language Models (LLMs) provide a simple and familiar interface: a string of text is used for both input and output. However, the information conveyed to an LLM often has a richer structure and semantics, which is not conveyed…

Recent frontier large language models (LLMs) have shown strong performance in identifying security vulnerabilities in large, mature open-source systems. As LLM-generated code becomes increasingly common, a natural goal is to prevent such…

Compilers transform code into action. They convert high-level programs into executable hardware instructions - a crucial step in enabling reliable and scalable quantum computation. However, quantum compilation is still in its infancy, and…

Failure detection protocols---a fundamental building block for crafting fault-tolerant distributed systems---are in many cases described by their authors making use of informal pseudo-codes of their conception. Often these pseudo-codes use…

Traditional software fault injection methods, while foundational, face limitations in adequately representing real-world faults, offering customization, and requiring significant manual effort and expertise. This paper introduces a novel…

We explore the capabilities of LVLMs and LLMs in deciphering rare scripts not encoded in Unicode. We introduce a novel approach to construct a multimodal dataset of linguistic puzzles involving such scripts, utilizing a tokenization method…

There is growing excitement about building software verifiers, synthesizers, and other Automated Reasoning (AR) tools by combining traditional symbolic algorithms and Large Language Models (LLMs). Unfortunately, the current practice for…

Inherently interpretable machine learning (IML) models offer valuable support for clinical decision-making but face challenges when features contain missing values. Traditional approaches, such as imputation or discarding incomplete…

State-of-the-art approaches for integrating symbolic knowledge with deep learning architectures have demonstrated promising results in static domains. However, methods to handle temporal logic specifications remain underexplored. The only…

We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of…

Recently deep reinforcement learning has achieved tremendous success in wide ranges of applications. However, it notoriously lacks data-efficiency and interpretability. Data-efficiency is important as interacting with the environment is…

A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…

Reducing application runtime, scaling parallel applications to higher numbers of processes/threads, and porting applications to new hardware architectures are tasks necessary in the software development process. Therefore, developers have…

We propose a symbolic execution method for programs that can draw random samples. In contrast to existing work, our method can verify randomized programs with unknown inputs and can prove probabilistic properties that universally quantify…