相关论文: On execution spaces of PV-programs

Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure…

We present a sheaf-theoretic construction of shape space -- the space of all shapes. We do this by describing a homotopy sheaf on the poset category of constructible sets, where each set is mapped to its Persistent Homology Transform (PHT).…

A semi-projective representation is a homomorphism of a finite group into the group of semi-projective transformations of a finite dimensional vector space over a field. Schur's concept of a representation group for projective…

Asynchronous programming is a ubiquitous systems programming idiom to manage concurrent interactions with the environment. In this style, instead of waiting for time-consuming operations to complete, the programmer makes a non-blocking call…

The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…

Topologists are sometimes interested in space-valued diagrams over a given index category, but it is tricky to say what such a diagram even is if we look for a notion that is stable under equivalence. The same happens in (homotopy) type…

Many security and software testing applications require checking whether certain properties of a program hold for any possible usage scenario. For instance, a tool for identifying software vulnerabilities may need to rule out the existence…

Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational…

We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…

We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is…

This article reviews recent progress in the development of the computing framework vector symbolic architectures (VSA) (also known as hyperdimensional computing). This framework is well suited for implementation in stochastic, emerging…

For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces…

Complex Systems were identified and studied in different fields, such as physics, biology, and economics. These systems exhibit exciting properties such as self-organization, robust order, and emergence. In recent years, software systems…

We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines $\Gamma$-spaces and framed…

We explore recursive programming with extensible data types. Row types make the structure of data types first class, and can express a variety of type system features including record subtyping and combination of case branches. Our goal is…

Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…

We present symQV, a symbolic execution framework for writing and verifying quantum computations in the quantum circuit model. symQV can automatically verify that a quantum program complies with a first-order specification. We formally…

This paper proposes new semantics for nondeterministic program execution, replacing the standard relational semantics for propositional dynamic logic (PDL). Under these new semantics, program execution is represented as fundamentally…

Operational semantics has established itself as a flexible but rigorous means to describe the meaning of programming languages. Oftentimes, it is felt necessary to keep a semantics small, for example to facilitate its use for model checking…

We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked examples.