Related papers: Homotopy Bisimilarity for Higher-Dimensional Autom…

It has been proved by Bergh and Thaule that the higher mapping cone axiom is equivalent to the higher octahedral axiom for n-angulated categories. In this note, we use homotopy cartesian diagrams to give several new equivalent statements of…

Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can…

This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…

In this paper we present a unifying approach for deciding various bisimulations, simulation equivalences and preorders between two timed automata states. We propose a zone based method for deciding these relations in which we eliminate an…

In this paper, we address the construction of homotopy bicategories of $(\infty,2)$-categories, which we take as being modeled by 2-fold Segal spaces. Our main result is the concrete construction of a functor $h_2$ from the category of…

We give a specific cylinder functor for semifree dg categories. This allows us to construct a homotopy colimit functor explicitly. These two functors are "computable", specifically, the constructed cylinder functor sends a dg category of…

We investigate a canonical way of defining bisimilarity of systems when their semantics is given by a coreflection, typically in a category of transition systems. We use the fact, from Joyal et al., that coreflections preserve open…

In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…

There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…

We define a notion of normal form bisimilarity for the untyped call-by-value lambda calculus extended with the delimited-control operators shift and reset. Normal form bisimilarities are simple, easy-to-use behavioral equivalences which…

Closed (and simply-connected) manifolds whose dimensions are greater than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed…

We present a new approach to simple homotopy theory of polyhedra using finite topological spaces. We define the concept of collapse of a finite space and prove that this new notion corresponds exactly to the concept of a simplicial…

We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…

There has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems, but the comparison at this level is too coarse. Recently, a finer behavioral measure, bisimulation, has been introduced to fuzzy…

We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…

We introduce a deep multitask architecture to integrate multityped representations of multimodal objects. This multitype exposition is less abstract than the multimodal characterization, but more machine-friendly, and thus is more precise…

A local po-space is a gluing of topological spaces which are equipped with a closed partial ordering representing the time flow. They are used as a formalization of higher dimensional automata which model concurrent systems in computer…

Automata play important roles in wide area of computing and the growth of multicores calls for their efficient parallel implementation. Though it is known in theory that we can perform the computation of a finite automaton in parallel by…

Homotopy limits and colimits are homotopical replacements for the usual limits and colimits of category theory, which can be approached either using classical explicit constructions or the modern abstract machinery of derived functors. Our…

This note extends Quillen's Theorem A to a large class of categories internal to topological spaces. This allows us to show that under a mild condition a fully faithful and essentially surjective functor between such topological categories…