Related papers: The Name-Passing Calculus
Nominal sets provide a foundation for reasoning about names. They are used primarily in syntax with binders, but also, e.g., to model automata over infinite alphabets. In this paper, nominal sets are related to nominal renaming sets, which…
The cost of deriving actionable knowledge from large datasets has been decreasing thanks to a convergence of positive factors: low cost data generation, inexpensively scalable storage and processing infrastructure (cloud), software…
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…
This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
Narrowing is a well-known technique that adds to term rewriting mechanisms the required power to search for solutions to equational problems. Rewriting and narrowing are well-studied in first-order term languages, but several problems…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
In this paper we propose a calculus for expressing algorithms for programming languages transformations. We present the type system and operational semantics of the calculus, and we prove that it is type sound. We have implemented our…
A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…