Related papers: Weak morphisms of higher dimensional automata
In order to achieve competitive performance, abstract machines for Prolog and related languages end up being large and intricate, and incorporate sophisticated optimizations, both at the design and at the implementation levels. At the same…
We explore the combinatorial properties of the branching areas of execution paths in higher dimensional automata. Mathematically, this means that we investigate the combinatorics of the negative corner (or branching) homology of a globular…
This is a motivating tutorial introduction to a semantic analysis of programming languages using a graphical language as the representation of terms, and graph rewriting as a representation of reduction rules. We show how the graphical…
Hyperdimensional computing (HDC), also known as vector symbolic architectures (VSA), is a computing framework used within artificial intelligence and cognitive computing that operates with distributed vector representations of large fixed…
Writing parallel codes is difficult and exhibits a fundamental trade-off between abstraction and performance. The high level language abstractions designed to simplify the complexities of parallelism make certain assumptions that impacts…
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at chain complexes level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes…
Two new classes of finite automata, called General hexagonal Boustrophedon finite automata and General hexagonal returning finite automata operating on hexagonal grids, are introduced and analyzed. The work establishes the theoretical…
We show how the basic Combinatory Homomorphic Automatic Differentiation (CHAD) algorithm can be optimised, using well-known methods, to yield a simple, composable, and generally applicable reverse-mode automatic differentiation (AD)…
A three-way (resp., two-way) two-dimensional automaton has a read-only input head that moves in three (resp., two) directions on a finite array of cells labelled by symbols of the input alphabet. Restricting the input head movement of a…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines. To demonstrate the technique and support our claim, we transform…
We investigate if an existing notion of weak sequential convergence in a Hadamard space can be induced by a topology. We provide an answer on what we call weakly proper Hadamard spaces. A notion of dual space is proposed and it is shown…
Mazurkiewicz traces describe concurrent behaviors of distributed systems. Trace-closed word languages, which are "linearizations" of trace languages, constitute a weaker notion of concurrency but still give us tools to investigate the…
The purpose of this paper is to provide a construction to model shared-variable systems using higher-dimensional automata which is compositional in the sense that the parallel composition of completely independent systems is modeled by the…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic…
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…
We introduce trace definability, a weak notion of interpretability, and trace equivalence, a weak notion of equivalence for first order structures and theories. In particular we get an interesting weak equivalence notion for $\mathrm{NIP}$…
Higher-dimensional automata (HDAs) are models of non-interleaving concurrency for analyzing concurrent systems. There is a rich literature that deals with bisimulations for concurrent systems, and some of them have been extended to HDAs.…
After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator $A$ or, for short, a \emph{weak lower $A$-semi-frame} and we study its properties. In…