Related papers: Once and for all: how to compose modules -- The co…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
Making quantum mechanical equations and concepts come to life through interactive simulation and visualization are commonplace for augmenting learning and teaching. However, graphical visualizations nearly always exhibit a set of hard-coded…
In this thesis a comprehensive verification framework is proposed to contend with some important issues in composability verification and a verification process is suggested to verify composability of different kinds of systems models, such…
In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…
In several applications, including in synthetic biology, one often has input/output data on a system composed of many modules, and although the modules' input/output functions and signals may be unknown, knowledge of the composition…
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…
We present in this paper the preliminary design of a module system based on a notion of components such as they are found in COM. This module system is inspired from that of Standard ML, and features first-class instances of components,…
This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently…
The predominant knowledge-based approach to automated model construction, compositional modelling, employs a set of models of particular functional components. Its inference mechanism takes a scenario describing the constituent interacting…
We introduce a concept called a collective: an interface with a protocol for aggregating contributions and distributing returns. Through such a protocol, many members may participate in a mutual endeavor. We present a variety of real-world…
The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets.…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
A $\textit{covering system}$ is a collection of integer congruences such that every integer satisfies at least one congruence in the collection. A covering system is called $\textit{distinct}$ if all of its moduli are distinct. An expansive…
Compositional understanding is crucial for human intelligence, yet it remains unclear whether contemporary vision models exhibit it. The dominant machine learning paradigm is built on the premise that scaling data and model sizes will…
We define and study the problem of modular concept learning, that is, learning a concept that is a cross product of component concepts. If an element's membership in a concept depends solely on it's membership in the components, learning…
Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…
We introduce the notion of quantum computational webs: These are quantum states universal for measurement-based computation which can be built up from a collection of simple primitives. The primitive elements - reminiscent of building…
A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional…
In programming, protocols are everywhere. Protocols describe the pattern of interaction (or communication) between software systems, for example, between a user-space program and the kernel or between a local application and an online…