Related papers: Symbolic Functional Decomposition: A Reconfigurati…
The introduction of separation logic has led to the development of symbolic execution techniques and tools that are (functionally) compositional with function specifications that can be used in broader calling contexts. Many of the…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose…
Prior works have demonstrated that implicit representations trained only for reconstruction tasks typically generate encodings that are not useful for semantic tasks. In this work, we propose a method that contextualises the encodings of…
Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…
We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
This paper intends to lay the theoretical foundation for the method of functional maps, first presented in 2012 by Ovsjanikov, Ben-Chen, Solomon, Butscher and Guibas in the field of the theory and numerics of maps between shapes. We show…
Humans can reason compositionally when presented with new tasks. Previous research shows that appropriate prompting techniques enable large language models (LLMs) to solve artificial compositional generalization tasks such as SCAN. In this…
We present a branch and bound method for maximizing an arbitrary set function h mapping 2^V to R. By decomposing h as f-g, where f is a submodular function and g is the cut function of a (simple, undirected) graph G with vertex set V, our…
Decomposition and abstraction is an essential component of computational thinking, yet it is not always emphasized in introductory programming courses. In addition, as generative AI further reduces the focus on syntax and increases the…
Although neural sequence-to-sequence models have been successfully applied to semantic parsing, they fail at compositional generalization, i.e., they are unable to systematically generalize to unseen compositions of seen components.…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
The ability to learn and compose functions is foundational to efficient learning and reasoning in humans, enabling flexible generalizations such as creating new dishes from known cooking processes. Beyond sequential chaining of functions,…
In this paper we propose and lay the foundations of a functorial framework for representing signals. By incorporating additional category-theoretic relative and generative perspective alongside the classic set-theoretic measure theory the…
Restructuring compilers use dependence analysis to prove that the meaning of a program is not changed by a transformation. A well-known limitation of dependence analysis is that it examines only the memory locations read and written by a…
The black box problem in machine learning has led to the introduction of an ever-increasing set of explanation methods for complex models. These explanations have different properties, which in turn has led to the problem of method…
Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true…