Related papers: Effective Operations of Type 2 in Pcas
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
We study two different ways to enhance PAFAS, a process algebra for modelling asynchronous timed concurrent systems, with non-blocking reading actions. We first add reading in the form of a read-action prefix operator. This operator is very…
Exterior power operations on the higher $K$-groups of a quasi-compact scheme have recently been constructed by Taelman and the authors by purely algebraic means. In this paper, we prove two formulae that help to compute these operations.…
We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the…
We discuss a new concept of definitizability of a normal operator on Krein spaces. For this new concept we develop a functional calculus $\phi \mapsto \phi(N)$ which is the proper analogue of $\phi \mapsto \int \phi \, dE$ in the Hilbert…
We generalize the construction of multitildes in the aim to provide multitilde operators for regular languages. We show that the underliying algebraic structure involves the action of some operads. An operad is an algebraic structure that…
Tensor operations are surging as the computational building blocks for a variety of scientific simulations and the development of high-performance kernels for such operations is known to be a challenging task. While for operations on one-…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
Probabilistic programs with dynamic computation graphs can define measures over sample spaces with unbounded dimensionality, which constitute programmatic analogues to Bayesian nonparametrics. Owing to the generality of this model class,…
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…
The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…
The Functional Machine Calculus (FMC) was recently introduced as a generalization of the lambda-calculus to include higher-order global state, probabilistic and non-deterministic choice, and input and output, while retaining confluence. The…
We study how to infer new choices from prior choices using the framework of choice functions, a unifying mathematical framework for decision-making based on sets of preference orders. In particular, we define the natural (most conservative)…
It is well known that strict $\omega$-categories, strict $\omega$-functors, strict natural $\omega$-transformations, and so on, form a strict $\omega$-category. A similar property for weak $\omega$-categories is one of the main hypotheses…
Constraint automata (CA) constitute a coordination model based on finite automata on infinite words. Originally introduced for modeling of coordinators, an interesting new application of CAs is implementing coordinators (i.e., compiling CAs…
We establish a canonical normal form for the iterates of a curved differential in curved differential algebras (CDA). This operator calculus clarifies the underlying algebraic structure of CDAs and bypasses the need for complex…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
In this paper, we present a novel approach to decompose a given piecewise affine (PWA) function into two convex PWA functions. Convex decompositions are useful to speed up or distribute evaluations of PWA functions. Different approaches to…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…