Related papers: Relatively Complete Counterexamples for Higher-Ord…

Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…

First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…

#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…

We present a framework for symbolically executing and model checking higher-order programs with external (open) methods. We focus on the client-library paradigm and in particular we aim to check libraries with respect to any definable…

Behavioral software contracts are a widely used mechanism for governing the flow of values between components. However, run-time monitoring and enforcement of contracts imposes significant overhead and delays discovery of faulty components…

Competitive programming, due to its high reasoning difficulty and precise correctness feedback, has become a key task for both training and evaluating the reasoning capabilities of large language models (LLMs). However, while a large amount…

Sequence generation applications require satisfying semantic constraints, such as ensuring that programs are correct, using certain keywords, or avoiding undesirable content. Language models, whether fine-tuned or prompted with few-shot…

The problem of synthesis of gate-level descriptions of digital circuits from behavioural specifications written in higher-level programming languages (hardware compilation) has been studied for a long time yet a definitive solution has not…

The Handbook of Combinatorial Designs catalogs many types of combinatorial designs, together with lists of open instances for which existence has not yet been determined. We develop a constructive protocol CPro1, which uses Large Language…

Automated Test Case Generation (ATCG) is crucial for evaluating software reliability, particularly in competitive programming where robust algorithm assessments depend on diverse and accurate test cases. However, existing ATCG methods often…

Thanks to the rapid progress and growing complexity of quantum algorithms, correctness of quantum programs has become a major concern. Pioneering research over the past years has proposed various approaches to formally verify quantum…

Reinforcement learning (RL) with unit test feedback has enhanced large language models' (LLMs) code generation, but relies on sparse rewards provided only after complete code evaluation, limiting learning efficiency and incremental…

In first-year programming courses it is often difficult to show students how an algorithm can be discovered. In this paper we present a program format that supports the development from specification to code in small and obvious steps; that…

We present an automated reasoning framework for synthesizing recursion-free programs using saturation-based theorem proving. Given a functional specification encoded as a first-order logical formula, we use a first-order theorem prover to…

Large Language Models (LLMs) have shown significant potential in automating code generation tasks offering new opportunities across software engineering domains. However, their practical application remains limited due to hallucinations -…

We consider the task of mapping pseudocode to long programs that are functionally correct. Given test cases as a mechanism to validate programs, we search over the space of possible translations of the pseudocode to find a program that…

Clause sets saturated by hierarchic ordered resolution do not offer a model representation that can be effectively queried, in general. They only offer the guarantee of the existence of a model. We present an effective symbolic model…

We present a method for generating training data for reinforcement learning with verifiable rewards to improve small open-weights language models on mathematical tasks. Existing data generation approaches rely on open-loop pipelines and…

In the field of large language model (LLM)-based proof generation, despite extensive training on large datasets such as ArXiv, LLMs still exhibit only modest performance on proving tasks of moderate difficulty. We believe that this is…

We give a language-parametric solution to the problem of total correctness, by automatically reducing it to the problem of partial correctness, under the assumption that an expression whose value decreases with each program step in a…