Related papers: Bistable Biorders: A Sequential Domain Theory

We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…

Some techniques for the use of bitwise operations are described in the article. As an example, an open problem of isomorphism-free generations of combinatorial objects is discussed. An equivalence relation on the set of square binary…

We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respect to sublevel persistence modules. This relation is…

Nondeterminism introduced by race conditions and message reorderings makes parallel and distributed programming hard. Nevertheless, promising approaches such as LVars and CRDTs address this problem by introducing a partial order structure…

This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The clustering algorithm extracts the splitting information either from trajectories, first or second derivatives. Initial partition is based on gap…

This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…

A topological space is called Loeb if the collection of all its non-empty closed sets has a choice function. In this article, in the absence of the axiom of choice, connections between Loeb and sequential spaces are investigated. Among…

We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…

A partitioned process theory, as defined by Coecke, Fritz, and Spekkens, is a symmetric monoidal category together with an all-object-including symmetric monoidal subcategory. We think of the morphisms of this category as processes, and the…

Termination property of functions is an important issue in computability theory. In this paper, we show that repeated iterations of a function can induce an order amongst the elements of its domain set. Hasse diagram of the poset, thus…

Computational models typically assume that operations are applied in a fixed sequential order. In recent years several works have looked at relaxing this assumption, considering computations without any fixed causal structure and showing…

It is consistent that there is a partial order (P,<) of size aleph_1 such that every monotone (unary) function from P to P is first order definable in (P,<). The partial order is constructed in an extension obtained by finite support…

Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…

We study bisimulation and context equivalence in a probabilistic $\lambda$-calculus. The contributions of this paper are threefold. Firstly we show a technique for proving congruence of probabilistic applicative bisimilarity. While the…

We investigate partial functions and computability theory from within a constructive, univalent type theory. The focus is on placing computability into a larger mathematical context, rather than on a complete development of computability…

Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are used to represent ordered relations between entities in the domains. Examples are task…

We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution…

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization…

Recently, there has been growing interest in bicategorical models of programming languages, which are "proof-relevant" in the sense that they keep distinct account of execution traces leading to the same observable outcomes, while assigning…

In Chapter 3 of his Notes on constructive mathematics, Martin-L{\"o}f describes recursively constructed ordinals. He gives a constructively acceptable version of Kleene's computable ordinals. In fact, the Turing definition of computable…