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Finite-state abstractions (a.k.a. symbolic models) present a promising avenue for the formal verification and synthesis of controllers in continuous-space control systems. These abstractions provide simplified models that capture the…

We present a new abstract interpretation framework for the precise over-approximation of numerical fixpoint iterators. Our key observation is that unlike in standard abstract interpretation (AI), typically used to over-approximate all…

Inferring inductive invariants is one of the main challenges of formal verification. The theory of abstract interpretation provides a rich framework to devise invariant inference algorithms. One of the latest breakthroughs in invariant…

Sound deductive reasoning -- the ability to derive new knowledge from existing facts and rules -- is an indisputably desirable aspect of general intelligence. Despite the major advances of AI systems in areas such as math and science,…

In this paper, our aim is to propose a model for code abstraction, based on abstract interpretation, allowing us to improve the precision of a recently proposed static analysis by abstract interpretation of dynamic languages. The problem we…

Generalized planning studies the computation of general solutions for a set of planning problems. Computing general solutions with correctness guarantee has long been a key issue in generalized planning. Abstractions are widely used to…

The points-to problem is the problem of determining the possible run-time targets of pointer variables and is usually considered part of the more general aliasing problem, which consists in establishing whether and when different…

Generalized planning is about finding plans that solve collections of planning instances, often infinite collections, rather than single instances. Recently it has been shown how to reduce the planning problem for generalized planning to…

The essential step of abstraction-based control synthesis for nonlinear systems to satisfy a given specification is to obtain a finite-state abstraction of the original systems. The complexity of the abstraction is usually the dominating…

We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…

Many modern solvers and program analyzers rely on non-monotone reasoning (e.g. negation-as-failure, speculative updates, backtracking) for which classical monotone fixed-point methods do not apply. The general problem of finding the fixed…

We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…

The advent of neural audio codecs has increased in popularity due to their potential for efficiently modeling audio with transformers. Such advanced codecs represent audio from a highly continuous waveform to low-sampled discrete units. In…

In the present paper we formally define the notion of abstract program slicing, a general form of program slicing where properties of data are considered instead of their exact value. This approach is applied to a language with numeric and…

We show that abstract interpretation-based static program analysis can be made efficient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement…

This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…

Podcasts have recently shown a rapid rise in popularity. Summarization of podcast transcripts is of practical benefit to both content providers and consumers. It helps consumers to quickly decide whether they will listen to the podcasts and…

Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We…

In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…

In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines…