Related papers: Non-Termination Proving: 100 Million LoC and Beyon…

An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so; it…

LLMs show strong performance in code generation, but their outputs lack correctness guarantees. Sample-based uncertainty estimators address this by generating multiple candidate programs and measuring their disagreement. However, existing…

Large language models (LLMs) are notorious for hallucinating, i.e., producing erroneous claims in their output. Such hallucinations can be dangerous, as occasional factual inaccuracies in the generated text might be obscured by the rest of…

Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…

Large Language Models (LLMs) have significantly advanced automated test generation, yet existing methods often rely on ground-truth code for verification, risking bug propagation and limiting applicability in test-driven development. We…

Probabilistic programming languages (PPLs) are an expressive means of representing and reasoning about probabilistic models. The computational challenge of probabilistic inference remains the primary roadblock for applying PPLs in practice.…

With the significant progress of large reasoning models in complex coding and reasoning tasks, existing benchmarks, like LiveCodeBench and CodeElo, are insufficient to evaluate the coding capabilities of large language models (LLMs) in real…

Large language models (LLMs) have demonstrated remarkable performance, yet their diverse strengths and weaknesses prevent any single LLM from achieving dominance across all tasks. Ensembling multiple LLMs is a promising approach to generate…

The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…

In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained…

Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…

The C Bounded Model Checker (CBMC) demonstrates the violation of assertions in C programs, or proves safety of the assertions under a given bound. CBMC implements a bit-precise translation of an input C program, annotated with assertions…

Commercial large language models are typically deployed as black-box API services, requiring users to trust providers to execute inference correctly and report token usage honestly. We present IMMACULATE, a practical auditing framework that…

Current evaluations of mathematical reasoning in large language models (LLMs) are dominated by static benchmarks, either derived from competition-style problems or curated through costly expert effort, resulting in limited coverage of…

Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…

We present an efficient approach to prove termination of monotone programs with integer variables, an expressive class of loops that is often encountered in computer programs. Our approach is based on a lightweight static analysis method…

We present a new kind of nontermination argument for linear lasso programs, called geometric nontermination argument. A geometric nontermination argument is a finite representation of an infinite execution of the form $(\vec{x} +…

There are many techniques and tools to prove termination of C programs, but up to now these tools were not very powerful for fully automated termination proofs of programs whose termination depends on recursive data structures like lists.…

Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…

We give a number of formal proofs of theorems from the field of computable analysis. Many of our results specify executable algorithms that work on infinite inputs by means of operating on finite approximations and are proven correct in the…