Related papers: A System of Dependent Types, with an Implementatio…
From autonomous vacuum cleaners to self-driving cars, intelligent mechanical systems are becoming an intrinsic part of our daily lives. In this work, a framework for the development of intelligent mechanical systems is presented.Considering…
Armstrong's axioms of functional dependency form a well-known logical system that captures properties of functional dependencies between sets of database attributes. This article assumes that there are costs associated with attributes and…
We give an overview of some developments in dependence and independence logic. This is a tiny selection, intended for a newcomer, from a rapidly growing literature on the topic. Furthermore, we discuss conditional independence atoms and we…
This article is concerned with automated complexity analysis of term rewrite systems. Since these systems underlie much of declarative programming, time complexity of functions defined by rewrite systems is of particular interest. Among…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…
We study the properties, in particular termination, of dependent types systems for lambda calculus and rewriting.
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
This is a draft of a chapter on mathematical logic and foundations for an upcoming handbook of computational proof assistants.
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
State machine formalisms equipped with hierarchy and parallelism allow to compactly model complex system behaviours. Such models can then be transformed into executable code or inputs for model-based testing and verification techniques.…
Type-level programming is an increasingly popular way to obtain additional type safety. Unfortunately, it remains a second-class citizen in the majority of industrially-used programming languages. We propose a new dependently-typed system…
This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…
There is an ongoing debate in computer science how algorithms should best be studied. Some scholars have argued that experimental evaluations should be conducted, others emphasize the benefits of formal analysis. We believe that this debate…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
A complex pervasive system is typically composed of many cooperating \emph{nodes}, running on machines with different capabilities, and pervasively distributed across the environment. These systems pose several new challenges such as the…
Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyze this combination of dynamics, ranging from mathematical descriptions,…
This write-up is the suggested lecture notes for a second level course on advanced topics in database systems for master's students of Computer Science with a theoretical focus. A prerequisite in algorithms and an exposure to database…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
In this article, we present a semantics-level adaption of the Optional Stopping Theorem, sketch an expected-cost analysis as its application, and survey different variants of the Optional Stopping Theorem that have been used in static…
I analyse differences in style between traditional prose mathematics writing and computer-formalised mathematics writing, presenting five case studies. I note two aspects where good style seems to differ between the two: in their…