Related papers: SymInfer: Inferring Program Invariants using Symbo…

Static analysers search for overapproximating proofs of safety commonly known as safety invariants. Fundamentally, such analysers summarise traces into sets of states, thus trading the ability to distinguish traces for computational…

All classifiers, including state-of-the-art vision models, possess invariants, partially rooted in the geometry of their linear mappings. These invariants, which reside in the null-space of the classifier, induce equivalent sets of inputs…

Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…

The automatic verification of programs that maintain unbounded low-level data structures is a critical and open problem. Analyzers and verifiers developed in previous work can synthesize invariants that only describe data structures of…

We present a new approach for performing predicate abstraction based on symbolic decision procedures. Intuitively, a symbolic decision procedure for a theory takes a set of predicates in the theory and symbolically executes a decision…

We consider concurrent systems consisting of a finite but unknown number of components, that are replicated instances of a given set of finite state automata. The components communicate by executing interactions which are simultaneous…

Large Language Models (LLMs) often struggle with complex mathematical reasoning, where prose-based generation leads to unverified and arithmetically unsound solutions. Current prompting strategies like Chain of Thought still operate within…

Recent years have seen the proposal of a number of neural architectures for the problem of Program Induction. Given a set of input-output examples, these architectures are able to learn mappings that generalize to new test inputs. While…

Generating effective test inputs for a software system requires that these inputs be valid, as they will otherwise be rejected without reaching actual functionality. In the absence of a specification for the input language, common test…

We propose a novel hierarchical approach for text-to-image synthesis by inferring semantic layout. Instead of learning a direct mapping from text to image, our algorithm decomposes the generation process into multiple steps, in which it…

Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically…

Function contract generation is a classical problem in program analysis that targets the automated analysis of functions in a program with multiple procedures. The problem is fundamental in inter-procedural analysis where properties of…

We introduce a novel learning and planning framework that replaces traditional reward-based optimisation with constructive logical inference. In our model, actions, transitions, and goals are represented as logical propositions, and…

In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…

Auto-active program verification rests on the ability to effectively the translation from annotated programs into verification conditions that are then discharged by automated theorem provers in the background. Characteristic such tools,…

Symbolic execution has always been plagued by the inability to handle programs that require highly structured inputs. Most often, the symbolic execution engine gets overwhelmed by the sheer number of infeasible paths and fails to explore…

People grasp flexible visual concepts from a few examples. We explore a neurosymbolic system that learns how to infer programs that capture visual concepts in a domain-general fashion. We introduce Template Programs: programmatic…

Formal program specifications in the form of preconditions, postconditions, and class invariants have several benefits for the construction and maintenance of programs. They not only aid in program understanding due to their unambiguous…

In this paper, we develop a method for computing controlled invariant sets using Semidefinite Programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets. The task is reduced to a…

While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachable sets, aka. the collecting semantics of the program. The…