41 research outputs found
Foliations for solving equations in groups: free, virtually free, and hyperbolic groups
We give an algorithm for solving equations and inequations with rational
constraints in virtually free groups. Our algorithm is based on Rips
classification of measured band complexes. Using canonical representatives, we
deduce an algorithm for solving equations and inequations in hyperbolic groups
(maybe with torsion). Additionnally, we can deal with quasi-isometrically
embeddable rational constraints.Comment: 70 pages, 7 figures, revised version. To appear in Journal of
Topolog
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science
Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)
The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..
The Algebra of Open and Interconnected Systems
Herein we develop category-theoretic tools for understanding network-style
diagrammatic languages. The archetypal network-style diagrammatic language is
that of electric circuits; other examples include signal flow graphs, Markov
processes, automata, Petri nets, chemical reaction networks, and so on. The key
feature is that the language is comprised of a number of components with
multiple (input/output) terminals, each possibly labelled with some type, that
may then be connected together along these terminals to form a larger network.
The components form hyperedges between labelled vertices, and so a diagram in
this language forms a hypergraph. We formalise the compositional structure by
introducing the notion of a hypergraph category. Network-style diagrammatic
languages and their semantics thus form hypergraph categories, and semantic
interpretation gives a hypergraph functor.
The first part of this thesis develops the theory of hypergraph categories.
In particular, we introduce the tools of decorated cospans and corelations.
Decorated cospans allow straightforward construction of hypergraph categories
from diagrammatic languages: the inputs, outputs, and their composition are
modelled by the cospans, while the 'decorations' specify the components
themselves. Not all hypergraph categories can be constructed, however, through
decorated cospans. Decorated corelations are a more powerful version that
permits construction of all hypergraph categories and hypergraph functors.
These are often useful for constructing the semantic categories of diagrammatic
languages and functors from diagrams to the semantics. To illustrate these
principles, the second part of this thesis details applications to linear
time-invariant dynamical systems and passive linear networks.Comment: 230 pages. University of Oxford DPhil Thesi