Related papers: The Tensor-Plus Calculus
In this paper we develop a symbolic algorithm to calculate multivariate power series expansions of univariate polynomials over general base rings. We use this to give a complete power series algorithm to calculate the dual intersection…
We give parallel algorithms for string diagrams represented as structured cospans of ACSets. Specifically, we give linear (sequential) and logarithmic (parallel) time algorithms for composition, tensor product, construction of diagrams from…
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
Milner's bigraphs are a general framework for reasoning about distributed and concurrent programming languages. Notably, it has been designed to encompass both the pi-calculus and the Ambient calculus. This paper is only concerned with…
We introduce the fermionic ZW calculus, a string-diagrammatic language for fermionic quantum computing (FQC). After defining a fermionic circuit model, we present the basic components of the calculus, together with their interpretation, and…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to intermediate variables (``states'') of dimension lower than the…
Let $P$ be a finitely generated commutative semiring. It was shown recently that if $P$ is a parasemifield (i.e. the multiplicative reduct of $P$ is a group) then $P$ cannot contain the positive rationals $\mathbb{Q}^+$ as its subsemiring.…
We develop a diagrammatic proof system for a fragment of structural semantics inspired by the Greimas semiotic square, using spider diagrams as the underlying formalism. The basic terms are represented as diagrammatic configurations, and…
The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. The titular category has nice formal properties: it is bicomplete and is a symmetric monoidal category, with…
Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
We introduce two families of diagrammatic monoidal supercategories. The first family, depending on an associative superalgebra, generalizes the oriented Brauer category. The second, depending on an involutive superalgebra, generalizes the…
We study categorical models for the unitless fragment of multiplicative linear logic. We find that the appropriate notion of model is a special kind of promonoidal category. Since the theory of promonoidal categories has not been developed…
Commutative languages with the semilinear property (SLIP) can be naturally recognized by real-time NLOG-SPACE multi-counter machines. We show that unions and concatenations of such languages can be similarly recognized, relying on -- and…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
The paper introduces mixed networks, a new framework for expressing and reasoning with probabilistic and deterministic information. The framework combines belief networks with constraint networks, defining the semantics and graphical…