Related papers: Meadow enriched ACP process algebras
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
Probability trees are one of the simplest models of causal generative processes. They possess clean semantics and -- unlike causal Bayesian networks -- they can represent context-specific causal dependencies, which are necessary for e.g.…
An equational axiomatisation of probability functions for one-dimensional event spaces in the language of signed meadows is expanded with conditional values. Conditional values constitute a so-called signed vector meadow. In the presence of…
We introduce an axiomatization for the notion of computation. Based on the idea of Brouwer choice sequences, we construct a model, denoted by $E$, which satisfies our axioms and $E \models \mathrm{ P \neq NP}$. In other words, regarding…
We provide an expository account of some of the Hopf algebras that can be defined using trees, labeled trees, ordered trees and heap ordered trees. We also describe some actions of these Hopf algebras on algebra of functions.
A quantum process encodes the causal structure that relates quantum operations performed in local laboratories. The process matrix formalism includes as special cases quantum mechanics on a fixed background space-time, but also allows for…
There exists a rich literature of rule formats guaranteeing different algebraic properties for formalisms with a Structural Operational Semantics. Moreover, there exist a few approaches for automatically deriving axiomatizations…
Generic open quantum dynamics can be described by two seemingly very distinct approaches: a top down approach by considering an (unknown) environment coupled to the system and affects the observed dynamics of the system; or a bottom up…
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…
For the past several decades, programmers have been modeling things in the world with trees using hierarchies of classes and object-oriented programming (OOP) languages. In this paper, we describe a novel approach to programming, called…
Machine learning models have been successfully used in many scientific and engineering fields. However, it remains difficult for a model to simultaneously utilize domain knowledge and experimental observation data. The application of…
We extend truly concurrent process algebra APTC with timing related properties. Just like ACP with timing, APTC with timing also has four parts: discrete relative timing, discrete absolute timing, continuous relative timing and continuous…
We present families of combinatorial classes described as trees with nodes that can carry one of two types of "flowers": integer partitions or integer compositions. Two parameters on the flowers of trees will be considered: the number of…
The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is not merely equivalent to NRQM…
We introduce Neural Conditional Probability (NCP), an operator-theoretic approach to learning conditional distributions with a focus on statistical inference tasks. NCP can be used to build conditional confidence regions and extract key…
The opaqueness of deep NLP models has motivated the development of methods for interpreting how deep models predict. Recently, work has introduced hierarchical attribution, which produces a hierarchical clustering of words, along with an…
For \math{p\ge 1}, we prove that every forest with \math{p} trees whose sizes are $a_1,..., a_p$ can be embedded in any graph containing at least $\sum_{i=1}^p (a_i + 1)$ vertices and having a minimum degree at least $\sum_{i=1}^p a_i$.
Traditional methods for the analysis of compositional data consider the log-ratios between all different pairs of variables with equal weight, typically in the form of aggregated contributions. This is not meaningful in contexts where it is…
We discuss the deal of imperfectness of atomic actions in reality with the background of process algebras. And we show the applications of the imperfect actions in verification of computational systems.