Finite difference methods fengshui: alignment through a mathematics of arrays

Numerous scientific-computational domains make use of array data. The core computing of the numerical methods and the algorithms involved is related to multi-dimensional array manipulation. Memory layout and the access patterns of that data are crucial to the optimal performance of the array-based computations. As we move towards exascale computing, writing portable code for efficient data parallel computations is increasingly requiring an abstract productive working environment. To that end, we present the design of a framework for optimizing scientific array-based computations, building a case study for a Partial Differential Equations solver. By embedding the Mathematics of Arrays formalism in the Magnolia programming language, we assemble a software stack capable of abstracting the continuous high-level application layer from the discrete formulation of the collective array-based numerical methods and algorithms and the final detailed low-level code. The case study lays the groundwork for achieving optimized memory layout and efficient computations while preserving a stable abstraction layer independent of underlying algorithms and changes in the architecture.Peer ReviewedPostprint (author's final draft

Extending the Nested Parallel Model to the Nested Dataflow Model with Provably Efficient Schedulers

The nested parallel (a.k.a. fork-join) model is widely used for writing parallel programs. However, the two composition constructs, i.e. "$\parallel$" (parallel) and "$;$" (serial), are insufficient in expressing "partial dependencies" or "partial parallelism" in a program. We propose a new dataflow composition construct "$\leadsto$" to express partial dependencies in algorithms in a processor- and cache-oblivious way, thus extending the Nested Parallel (NP) model to the \emph{Nested Dataflow} (ND) model. We redesign several divide-and-conquer algorithms ranging from dense linear algebra to dynamic-programming in the ND model and prove that they all have optimal span while retaining optimal cache complexity. We propose the design of runtime schedulers that map ND programs to multicore processors with multiple levels of possibly shared caches (i.e, Parallel Memory Hierarchies) and provide theoretical guarantees on their ability to preserve locality and load balance. For this, we adapt space-bounded (SB) schedulers for the ND model. We show that our algorithms have increased "parallelizability" in the ND model, and that SB schedulers can use the extra parallelizability to achieve asymptotically optimal bounds on cache misses and running time on a greater number of processors than in the NP model. The running time for the algorithms in this paper is $O\left(\frac{\sum_{i=0}^{h-1} Q^{*}({\mathsf t};\sigma\cdot M_i)\cdot C_i}{p}\right)$, where $Q^{*}$ is the cache complexity of task ${\mathsf t}$, $C_i$ is the cost of cache miss at level-$i$ cache which is of size $M_i$, $\sigma\in(0,1)$ is a constant, and $p$ is the number of processors in an $h$-level cache hierarchy

Transforming ASN.1 Specifications into CafeOBJ to assist with Property Checking

The adoption of algebraic specification/formal method techniques by the networks' research community is happening slowly but steadily. We work towards a software environment that can translate a protocol's specification, from Abstract Syntax Notation One (ASN.1 - a very popular specification language with many applications), into the powerful algebraic specification language CafeOBJ. The resulting code can be used to check, validate and falsify critical properties of systems, at the pre-coding stage of development. In this paper, we introduce some key elements of ASN.1 and CafeOBJ and sketch some first steps towards the implementation of such a tool including a case study.Comment: 8 pages, 12 figure

COST Action IC 1402 ArVI: Runtime Verification Beyond Monitoring -- Activity Report of Working Group 1

This report presents the activities of the first working group of the COST Action ArVI, Runtime Verification beyond Monitoring. The report aims to provide an overview of some of the major core aspects involved in Runtime Verification. Runtime Verification is the field of research dedicated to the analysis of system executions. It is often seen as a discipline that studies how a system run satisfies or violates correctness properties. The report exposes a taxonomy of Runtime Verification (RV) presenting the terminology involved with the main concepts of the field. The report also develops the concept of instrumentation, the various ways to instrument systems, and the fundamental role of instrumentation in designing an RV framework. We also discuss how RV interplays with other verification techniques such as model-checking, deductive verification, model learning, testing, and runtime assertion checking. Finally, we propose challenges in monitoring quantitative and statistical data beyond detecting property violation

Prototyping Formal System Models with Active Objects

We propose active object languages as a development tool for formal system models of distributed systems. Additionally to a formalization based on a term rewriting system, we use established Software Engineering concepts, including software product lines and object orientation that come with extensive tool support. We illustrate our modeling approach by prototyping a weak memory model. The resulting executable model is modular and has clear interfaces between communicating participants through object-oriented modeling. Relaxations of the basic memory model are expressed as self-contained variants of a software product line. As a modeling language we use the formal active object language ABS which comes with an extensive tool set. This permits rapid formalization of core ideas, early validity checks in terms of formal invariant proofs, and debugging support by executing test runs. Hence, our approach supports the prototyping of formal system models with early feedback.Comment: In Proceedings ICE 2018, arXiv:1810.0205

Towards Practical Graph-Based Verification for an Object-Oriented Concurrency Model

To harness the power of multi-core and distributed platforms, and to make the development of concurrent software more accessible to software engineers, different object-oriented concurrency models such as SCOOP have been proposed. Despite the practical importance of analysing SCOOP programs, there are currently no general verification approaches that operate directly on program code without additional annotations. One reason for this is the multitude of partially conflicting semantic formalisations for SCOOP (either in theory or by-implementation). Here, we propose a simple graph transformation system (GTS) based run-time semantics for SCOOP that grasps the most common features of all known semantics of the language. This run-time model is implemented in the state-of-the-art GTS tool GROOVE, which allows us to simulate, analyse, and verify a subset of SCOOP programs with respect to deadlocks and other behavioural properties. Besides proposing the first approach to verify SCOOP programs by automatic translation to GTS, we also highlight our experiences of applying GTS (and especially GROOVE) for specifying semantics in the form of a run-time model, which should be transferable to GTS models for other concurrent languages and libraries.Comment: In Proceedings GaM 2015, arXiv:1504.0244

Towards composition of verified hardware devices

Computers are being used where no affordable level of testing is adequate. Safety and life critical systems must find a replacement for exhaustive testing to guarantee their correctness. Through a mathematical proof, hardware verification research has focused on device verification and has largely ignored system composition verification. To address these deficiencies, we examine how the current hardware verification methodology can be extended to verify complete systems