Related papers: Foundations of Digital Circuits: Denotation, Opera…
High-dimensional quantum computation needs a native circuit-level equational theory for qudits. We give the first finite schematic equational theory that is sound and complete for exact unitary qudit circuits in every finite dimension at…
This work presents an abstract model for the computations performed by analytic column stores or columnar query processors. The model is based on circuits whose wires carry columns rather than scalar values, and whose nodes apply operators…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Sequence diagrams are a popular technique for describing interactions between software entities. However, because the OMG group's UML standard is not based on a rigorous mathematical structure, it is impossible to deduce a single…
I present a formal connection between algebraic effects and game semantics, two important lines of work in programming languages semantics with applications in compositional software verification. Specifically, the algebraic signature…
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular…
Formal semantics offers a complete and rigorous definition of a language. It is important to define different semantic models for a language and different models serve different purposes. Building equivalence between different semantic…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or discarded at will. In SMTs, traditional tree-like terms are…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
In software system design, one of the purposes of diagrammatic modeling is to explain something (e.g., data tables) to others. Very often, syntax of diagrams is specified while the intended meaning of diagrammatic constructs remains…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
We introduce the notion of combinatorial encoding of continuous dynamical systems and suggest the first examples, which are the most interesting and important, namely, the combinatorial encoding of a Bernoulli process with continuous state…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural…
Structural operational semantics (SOS) is a technique for defining operational semantics for programming and specification languages. Because of its intuitive appeal and flexibility, SOS has found considerable application in the study of…
We introduce a formal operational semantics that describes the fused execution of variable contraction problems, which compute indexed arithmetic over a semiring and generalize sparse and dense tensor algebra, relational algebra, and graph…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
The FAIR Principles aim to make data and knowledge Findable, Accessible, Interoperable, and Reusable, yet current digital infrastructures often lack a unifying semantic framework that bridges human cognition and machine-actionability. In…
This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave)…