Related papers: Restructuring a concurrent refinement algebra
Implementing a concurrent data structure typically begins with defining its sequential specification. However, when used \emph{as is}, a nontrivial sequential data structure, such as a linked list, a search tree, or a hash table, may expose…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Nested parallelism exists in scientific codes that are searching multi-dimensional spaces. However, implementations of nested parallelism often have overhead and load balance issues. The Orbital Analysis code we present exhibits a sparse…
The majority of modern systems exhibit sophisticated concurrent behaviour, where several system components modify and observe the system state with fine-grained atomicity. Many systems (e.g., multi-core processors, real-time controllers)…
Dense linear algebra kernels are critical for wireless applications, and the oncoming proliferation of 5G only amplifies their importance. Many such matrix algorithms are inductive, and exhibit ample amounts of fine-grain ordered…
We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
The method of refined algebraic quantization of constrained systems which is based on modification of the inner product of the theory rather than on imposing constraints on the physical states is generalized to the case of constrained…
Sequential computation is well understood but does not scale well with current technology. Within the next decade, systems will contain large numbers of processors with potentially thousands of processors per chip. Despite this, many…
Following our previous work, we suggest here a large class of algebras of scalars in which simultaneous and correlated computations can be performed owing to the existence of surjective algebra homomorphisms. This may replace the currently…
We propose a sparse interpolation construction and a practical coarsening algorithm for the algebraic multigrid (AMG) method, tailored towards H(curl). Building on the generalized AMG framework, we introduce an interior/exterior splitting…
Reduction operations are extensively employed in many computational problems. A reduction consists of, given a finite set of numeric elements, combining into a single value all elements in that set, using for this a combiner function. A…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
Concurrent data structures serve as fundamental building blocks for concurrent computing. Many concurrent counterparts have been designed for basic sequential mechanisms; however, one notable omission is a concurrent tree that supports…
This note makes an observation that significantly simplifies a number of previous parallel, two-way merge algorithms based on binary search and sequential merge in parallel. First, it is shown that the additional merge step of distinguished…
This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. On the semantic side, we show that the immediate consequence operator of a program…
Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal…
It is well known that we can use structural proof theory to refine, or generalize, existing paradigmatic computational primitives, or to discover new ones. Under such a point of view we keep developing a programme whose goal is establishing…
Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference…
This article explores an operational model for transition amplitudes between measurements proposed by Goyal et al. within the quantum reconstruction program. To classify suitable amplitude algebras, we distinguish mathematical axioms,…