Related papers: Diagrammatic Semantics for Digital Circuits

Applications of category theory often involve symmetric monoidal categories (SMCs), in which abstract processes or operations can be composed in series and parallel. However, in 2020 there remains a dearth of computational tools for working…

We present a process semantics for the purely additive fragment of linear logic in which formulas denote protocols and (equivalence classes of) proofs denote multi-channel concurrent processes. The polycategorical model induced by this…

Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify…

The logical parallelism of propositional connectives and type constructors extends beyond the static realm of predicates, to the dynamic realm of processes. Understanding the logical parallelism of process propositions and dynamic types was…

We present a formulation of quantum circuit diagrams based on the exponential map which provides a new way to calculate graphically with circuits. We present a sound list of rewrite rules for this formulation and demonstrate a variety of…

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to…

We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…

We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one…

Boolean circuits abstract away from physical details to focus on the logical structure and computational behaviour of digital components. Although such circuits have been studied for many decades, compositionality has been widely ignored or…

This paper introduces a brand-new phase definition called the segmental phase for multi-input multi-output linear time-invariant systems. The underpinning of the definition lies in the matrix segmental phase which, as its name implies, is…

Accurately predicting the possible behaviors of traffic participants is an essential capability for autonomous vehicles. Since autonomous vehicles need to navigate in dynamically changing environments, they are expected to make accurate…

Advances in quantum technologies are often limited by slow device characterization, complex tuning requirements, and scalability challenges. Spin qubits in electrostatically defined quantum dots provide a promising platform but are not…

The technique of \emph{equality saturation}, which equips graphs with an equivalence relation, has proven effective for program optimisation. We give a categorical semantics to these structures, called \emph{e-graphs}, in terms of Cartesian…

Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics. While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in…

Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world…

Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of Jones's planar algebras, in which one drops the planarity condition on "connection diagrams". They provide a useful language for the study of virtual…

We study properties of relational structures such as graphs that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus…

While the disciplines of physics and engineering sciences in many cases have taken advantage from accurate time-series prediction of system behaviour by applying ordinary differential equation systems upon precise basic physical laws such…

We introduce a new type of diagrams and prove the existence of a particular one, the "central tuned diagram", with some optimal features, for finitely generated modules of certain categories. This is achieved by getting to the idea of "the…