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Generic programming (GP) is an increasingly important trend in programming languages. Well-known GP mechanisms, such as type classes and the C++0x concepts proposal, usually combine two features: 1) a special type of interfaces; and 2)…

Model checking has found a role in the engineering of reactive systems. However, model checkers are still strongly limited by the size of the system description they can check. Here we present a technique in which a system is simplified…

Images usually convey richer detail than text, but often include redundant information, which potentially downgrades multimodal reasoning performance. When faced with lengthy or complex messages, humans tend to employ abstract thinking to…

Bounded model checking is among the most efficient techniques for the automatic verification of concurrent programs. However, encoding all possible interleavings often requires a huge and complex formula, which significantly limits the…

Making a Prolog program more efficient by transforming its source code, without changing its operational semantics, is not an obvious task. It requires the user to have a clear understanding of how the Prolog compiler works, and in…

The traditional abstract domain framework for imperative programs suffers from several shortcomings; in particular it does not allow precise symbolic abstractions. To solve these problems, we propose a new abstract interpretation framework,…

Simulation-based compositional abstraction effectively mitigates state space explosion in model checking, particularly for timed systems. However, existing approaches do not support broadcast synchronization, an important mechanism for…

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…

The concept of causal abstraction got recently popularised to demystify the opaque decision-making processes of machine learning models; in short, a neural network can be abstracted as a higher-level algorithm if there exists a function…

Mechanistic interpretability aims to reverse engineer neural networks by uncovering which high-level algorithms they implement. Causal abstraction provides a precise notion of when a network implements an algorithm, i.e., a causal model of…

We give thread-modular non-relational value analyses as abstractions of a local trace semantics. The semantics as well as the analyses are formulated by means of global invariants and side-effecting constraint systems. We show that a…

In-context Learning (ICL) is an emerging few-shot learning paradigm on Language Models (LMs) with inner mechanisms un-explored. There are already existing works describing the inner processing of ICL, while they struggle to capture all the…

This paper provides a gentle introduction to problem solving with the IDP3 system. The core of IDP3 is a finite model generator that supports first order logic enriched with types, inductive definitions, aggregates and partial functions. It…

We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables. More specifically, we study the problem of performing static analysis by abstract interpretation using…

This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously…

Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…

In-context learning (ICL) refers to the ability of a model to learn new tasks from examples in its input without any parameter updates. In contrast to previous theories of ICL relying on toy models and data settings, recently it has been…

An abstraction can be used to relate two structural causal models representing the same system at different levels of resolution. Learning abstractions which guarantee consistency with respect to interventional distributions would allow one…

Any act of problem-solving combines prior knowledge, local search, and a third element that is less often discussed: the extraction of information from search to update understanding. I propose a model of mathematical problem-solving as a…

We introduce an efficient algorithm for the computation of the $W_3$ invariant of general unitary maps, which converges rapidly even on coarse discretization grids. The algorithm does not require extensive manipulation of the unitary maps,…