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David Walker

Publications and source records attributed to David Walker.

At least 19 recordsLinked to original sources
arXiv2026

Kleene Algebra with Transitive Commutativity Conditions

Kleene algebra (KA) provides a foundational algebraic framework for reasoning about program structure and control flow. To capture equivalences arising from reordering or independence of actions, Kozen [1996] purposed that KA can be extended with commutativity conditions, that is, equations of the form { ab = ba | (a,b) \in C }, where C is a binary relation on constant symbols. This paper studies the following question: for which relations C is the equational theory of KA+C decidable? Early related work [Bertoni et al. 1982; Ibarra 1978] showed that regular languages modulo commutativity conditions C are decidable if and only if C is transitive. For Kleene algebra KA and commutativity conditions C, however, the situation is substantially more difficult. Only very recently, Kuznetsov [2023] showed that the equational theory of Kleene algebra KA+C is undecidable under certain specific commutativity conditions, settling the first nontrivial cases more than 25 years after the corresponding problem for KA* +C was resolved by Kozen [1996]. Nevertheless, the decidability problem of KA+C remained open. In this work, we resolve this question completely by showing that the equational theory of KA+C is decidable if and only if C is transitive. Moreover, we strengthen the result in both directions. On the negative side, we show that when C is not transitive, the universality problem for KA+C is already undecidable. On the positive side, we show that for transitive C, the equational theories of KA* +C and KA+C coincide.

cs.PL↗
arXiv2026

Network Analysis with Parametric NetKAT

Network engineers often need to perform network diagnosis and inference tasks, which frequently require answers to enumeration questions such as "Which packets from the Internet arrive at host C?" or "Which single-link failures disconnect my network?" Parametric NetKAT is a new domain-specific language that combines elements of NetKAT, Relational NetKAT, and Weighted NetKAT into a single system and extends them with parameters, allowing users to pose such enumeration questions directly over network models. This paper presents the design and semantics of Parametric NetKAT and illustrates its utility through a series of examples. It shows how to compile Parametric NetKAT into NetKAT automata, develops new algorithms for efficiently collecting satisfying valuations, and proves the correctness of these procedures. Finally, it evaluates the performance of Parametric NetKAT on a collection of benchmarks drawn from industrial sources.

cs.PL↗
arXiv2026

CB-VER: A Stable Foundation for Modular Control Plane Verification

Network operators are often interested in verifying \emph{eventually-stable properties} of network control planes: properties of control plane states that hold eventually, and hold forever thereafter, provided the operating environment remains unchanged. Examples include eventually-stable reachability, access control, or path length properties. In this work, we introduce \textsc{CB-Ver}, a new framework for verifying such properties, based on the key idea of a \emph{converges-before graph} (CB-graph for short). When a user provides interfaces for each network component, \textsc{CB-Ver} checks the necessary component-by-component requirements in parallel using an SMT solver. In addition, the tool automatically synthesizes a CB-graph and checks whether it connects all nodes in a network -- if it does, the interfaces are valid and users can check whether additional eventually-stable properties are implied. Moreover, the CB-graph can then be used to determine fault tolerance properties of the network. We formalize our verification algorithm in the Lean theorem proving environment and prove its soundness. We evaluate the performance of \textsc{CB-Ver} on a range of benchmarks that demonstrate its ability to verify expressive properties in reasonable time. Finally, we demonstrate it is possible to automatically generate suitable interfaces by turning the problem around: Given a CB-graph, we use an off-the-shelf Constrained Horn Clause (CHC) solver to synthesize interfaces for every network component that together ensure the given correctness property.

cs.NI↗
arXiv2026

Dynamics, Complexity and Time Series Analysis

The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not essential and readers are only assumed to have familiarity with foundational undergraduate mathematics topics of calculus, linear algebra and rudimentary statistics. A variety of extended topics on recent publications and research activities in the field have been included in the last four chapters, which the interested reader may use as an introduction into further reading. A collection of exercises and questions both theoretical and computational are also included in this text.

math.DS↗
arXiv2024

Pseudosymmetry in Tetragonal Perovskite SrIrO$_3$ Synthesized under High Pressure

In this study, we report a tetragonal perovskite structure of SrIrO$_3$ (P4/mmm, a = 3.9362(9) \r{A}, c = 7.880(3) \r{A}) synthesized at 6 GPa and 1400 $\deg$C, employing the ambient pressure monoclinic SrIrO$_3$ with distorted 6H structure as a precursor. The crystal structure of tetragonal SrIrO3 was evaluated on the basis of single crystal and powder X-ray diffraction. A cubic indexing was observed attributed to overlooked superlattice reflections. Weak fractional peaks in the H and K dimensions suggest possible structure modulation by oxygen defects. Magnetization study reveals weak paramagnetic behavior down to 2 K, indicative of the interplay between spin-orbit coupling, electron correlations, and crystal electric field. Additionally, measurements of electrical resistivity display metallic behavior with an upturn at about 54 K, ascribed to weak electron localization and possible structural defects.

cond-mat.mtrl-sci↗
arXiv2024

Evolutionary Computation and Explainable AI: A Roadmap to Understandable Intelligent Systems

Artificial intelligence methods are being increasingly applied across various domains, but their often opaque nature has raised concerns about accountability and trust. In response, the field of explainable AI (XAI) has emerged to address the need for human-understandable AI systems. Evolutionary computation (EC), a family of powerful optimization and learning algorithms, offers significant potential to contribute to XAI, and vice versa. This paper provides an introduction to XAI and reviews current techniques for explaining machine learning models. We then explore how EC can be leveraged in XAI and examine existing XAI approaches that incorporate EC techniques. Furthermore, we discuss the application of XAI principles within EC itself, investigating how these principles can illuminate the behavior and outcomes of EC algorithms, their (automatic) configuration, and the underlying problem landscapes they optimize. Finally, we discuss open challenges in XAI and highlight opportunities for future research at the intersection of XAI and EC. Our goal is to demonstrate EC's suitability for addressing current explainability challenges and to encourage further exploration of these methods, ultimately contributing to the development of more understandable and trustworthy ML models and EC algorithms.

cs.NE↗
arXiv2024

Relational Network Verification

Relational network verification is a new approach to validating network changes. In contrast to traditional network verification, which analyzes specifications for a single network snapshot, relational network verification analyzes specifications concerning two network snapshots (e.g., pre- and post-change snapshots) and captures their similarities and differences. Relational change specifications are compact and precise because they specify the flows or paths that change between snapshots and then simply mandate that other behaviors of the network "stay the same", without enumerating them. To achieve similar guarantees, single-snapshot specifications need to enumerate all flow and path behaviors that are not expected to change, so we can check that nothing has accidentally changed. Thus, precise single-snapshot specifications are proportional to network size, which makes them impractical to generate for many real-world networks. To demonstrate the value of relational reasoning, we develop a high-level relational specification language and a tool called Rela to validate network changes. Rela first compiles input specifications and network snapshot representations to finite state transducers. It then checks compliance using decision procedures for automaton equivalence. Our experiments using data on complex changes to a global backbone (with over 10^3 routers) find that Rela specifications need fewer than 10 terms for 93% of them and it validates 80% of them within 20 minutes.

cs.NI↗
arXiv2024

Automated Optimization of Parameterized Data-Plane Programs with Parasol

Programmable data planes allow for sophisticated applications that give operators the power to customize the functionality of their networks. Deploying these applications, however, often requires tedious and burdensome optimization of their layout and design, in which programmers must manually write, compile, and test an implementation, adjust the design, and repeat. In this paper we present Parasol, a framework that allows programmers to define general, parameterized network algorithms and automatically optimize their various parameters. The parameters of a Parasol program can represent a wide variety of implementation decisions, and may be optimized for arbitrary, high-level objectives defined by the programmer. Furthermore, optimization may be tailored to particular environments by providing a representative sample of traffic. We show how we implement the Parasol framework, which consists of a sketching language for writing parameterized programs, and a simulation-based optimizer for testing different parameter settings. We evaluate Parasol by implementing a suite of ten data-plane applications, and find that Parasol produces a solution with comparable performance to hand-optimized P4 code within a two-hour time budget.

cs.NI↗
arXiv2023

Impersonating a Superconductor: High-Pressure BaCoO$_3$, an Insulating Ferromagnet

We report the high-pressure synthesis (6 GPa, 1200 $^{\circ}$C) and ambient pressure characterization of hexagonal HP-BaCoO$_3$. The material (with the 2H crystal structure) has a short intrachain Co-Co distance of about 2.07 $\text{\r{A}}$. Our magnetization investigation revealed robust diamagnetic behavior below approximately 130 K when exposed to weak applied magnetic fields (10 Oe) and a distinct half-levitation phenomenon below that temperature, such as is often observed for superconductors. Its field-dependent magnetization profile, however, unveils the characteristics of ferromagnetism, marked by a substantial magnetic retentivity of 0.22(1) ${\mu}_B$/Co at a temperature of 2 K. Electrical resistivity measurements indicate that HP-BaCoO$_3$ is a ferromagnetic insulator, not a superconductor.

cond-mat.mtrl-sci↗
arXiv2023

Saggitarius: A DSL for Specifying Grammatical Domains

Common data types like dates, addresses, phone numbers and tables can have multiple textual representations, and many heavily-used languages, such as SQL, come in several dialects. These variations can cause data to be misinterpreted, leading to silent data corruption, failure of data processing systems, or even security vulnerabilities. Saggitarius is a new language and system designed to help programmers reason about the format of data, by describing grammatical domains -- that is, sets of context-free grammars that describe the many possible representations of a datatype. We describe the design of Saggitarius via example and provide a relational semantics. We show how Saggitarius may be used to analyze a data set: given example data, it uses an algorithm based on semi-ring parsing and MaxSAT to infer which grammar in a given domain best matches that data. We evaluate the effectiveness of the algorithm on a benchmark suite of 110 example problems, and we demonstrate that our system typically returns a satisfying grammar within a few seconds with only a small number of examples. We also delve deeper into a more extensive case study on using Saggitarius for CSV dialect detection. Despite being general-purpose, we find that Saggitarius offers comparable results to hand-tuned, specialized tools; in the case of CSV, it infers grammars for 84% of benchmarks within 60 seconds, and has comparable accuracy to custom-built dialect detection tools.

cs.PL↗
arXiv2023

Massively parallel quantum chemistry: PFAS on over 1 million cloud vCPUs

Accurate solutions to the electronic Schr\"odinger equation can provide valuable insight for electron interactions within molecular systems, accelerating the molecular design and discovery processes in many different applications. However, the availability of such accurate solutions are limited to small molecular systems due to both the extremely high computational complexity and the challenge of operating and executing these workloads on high-performance compute clusters. This work presents a massively scalable cloud-based quantum chemistry platform by implementing a highly parallelizable quantum chemistry method that provides a polynomial-scaling approximation to full configuration interaction (FCI). Our platform orchestrates more than one million virtual CPUs on the cloud to analyze the bond-breaking behaviour of carbon-fluoride bonds of per- and polyfluoroalkyl substances (PFAS) with near-exact accuracy within the chosen basis set. This is the first quantum chemistry calculation utilizing more than one million virtual CPUs on the cloud and is the most accurate electronic structure computation of PFAS bond breaking to date.

physics.chem-ph↗
arXiv2023

The Impact of Space-Filling Curves on Data Movement in Parallel Systems

Modern computer systems are characterized by deep memory hierarchies, composed of main memory, multiple layers of cache, and other specialized types of memory. In parallel and distributed systems, additional memory layers are added to this hierarchy. Achieving good performance for computational science applications, in terms of execution time, depends on the efficient use of this diverse and hierarchical memory. This paper revisits the use of space-filling curves to specify the ordering in memory of data structures used in representative scientific applications executing on parallel machines containing clusters of multicore CPUs with attached GPUs. This work examines the hypothesis that space-filling curves, such as Hilbert and Morton ordering, can improve data locality and hence result in more efficient data movement than row or column-based orderings. First, performance results are presented that show for what application parameterizations and machine characteristics this is the case, and are interpreted in terms of how an application interacts with the computer hardware and low-level software. This research particularly focuses on the use of stencil-based applications that form the basis of many scientific computations. Second, how space-filling curves impact data sharing in nearest-neighbour and stencil-based codes is considered.

cs.DC↗
arXiv2023

Experimental Investigation of Condensation Predictions for Dust-Enriched Systems

Condensation models describe the equilibrium distribution of elements between coexisting mineral solid solutions, silicate liquid, and vapor in a closed chemical system, vapor phase always present, using equations of state of the phases involved at a fixed total P (< 1 bar) and temperature T. The VAPORS code uses a CaO-MgO-Al$_2$O$_3$-SiO$_2$ liquid model at T above the stability field of olivine and the MELTS algorithm at lower T. Quenched high-T crystal + liquid assemblages are preserved in meteorites as Type B Ca-, Al-rich inclusions (CAIs) and olivine-rich ferromagnesian chondrules. Experimental tests of compositional regions may clarify the nature of the phases present, the phase boundaries, and the partition of trace elements among these phases. Twenty-three Pt-loop equilibrium experiments in seven phase fields on twelve bulk compositions at specific T and dust enrichment factors tested the predicted stability fields of forsteritic olivine (Mg$_2$SiO$_4$), enstatite (MgSiO$_3$), Cr-bearing spinel (MgAl$_2$O$_4$), perovskite (CaTiO$_3$), melilite (Ca$_2$Al$_2$SiO$_7$ - Ca$_2$Mg$_2$Si$_2$O$_7$) and/or grossite (CaAl4O7) crystallizing from liquid. Experimental results for forsterite, enstatite, and grossite are in very good agreement with predictions, both in chemistry and phase abundances. On the other hand, the stability of spinel with olivine, and stability of perovskite and gehlenite are quite different from predictions. Perovskite is absent in all experiments. Even at low oxygen fugacity (IW-3.4), the most TiO$_2$-rich experiments do not crystallize Al-, Ti-bearing calcic pyroxene. The stability of spinel and olivine together is limited to a smaller phase field than is predicted. The melilite stability field is much larger than predicted, indicating a deficiency of current liquid or melilite activity models. In that respect, these experiments contribute to improving the data for calibrating thermodynamic models including MELTS.

astro-ph.EP↗
arXiv2023

Trace Element Partitioning between CAI-Type Melts and Grossite, Melilite, Hibonite, and Olivine

We determined the mineral-melt partition coefficients (Di's) and the compositional and/or temperature dependency between grossite, melilite, hibonite, olivine and Ca-, Al-inclusion (CAI)-type liquids for a number of light (LE), high field strength (HFSE), large ion lithophile (LILE), and rare earth (REE) elements including Li, Be, B, Sr, Zr, Nb, Ba, La, Ce, Eu, Dy, Ho, Yb, Hf, Ta, Th. A series of isothermal crystallization experiments was conducted at 5 kbar pressure and IW+1 in graphite capsules. The starting compositions were selected based on the calculated and experimentally confirmed phase relations during condensation in CI dust-enriched systems (Ebel and Grossman, 2000; Ebel, 2006; Ustunisik et al., 2014). Partition coefficients between melt and gehlenite, hibonite, and grossite show that the trace element budget of igneous CAIs is controlled by these three major Al-bearing phases in addition to pyroxene. In general, LE, LILE, REE, and HFSE partition coefficients (by mass) decrease in the order of Di(Gehlenite-Melt) > Di(Hibonite-Melt) > Di(Grossite-Melt). Results suggest that Di(Gehlenite-Melt) vary by a factor of 2-3 in different melt compositions at the same T (~1500 C). Increased melt Al and Ca, relative to earlier work, increases the compatibility of Di(Gehlenite-Melt), and also the compatibility of Di(Hibonite-Melt), especially for La and Ce. Olivine partitioning experiments confirm that olivine contribution to the trace element budget of CAIs is small due to the low Di(Olivine-Melt) at a range of temperatures while D-Eu, Yb(Olivine-Melt) are sensitive to changes in T and oxygen fugacity. The development of a predictive model for partitioning in CAI-type systems would require more experimental data and the use of analytical instruments capable of obtaining single phase analyses for crystals < 5 micron.

astro-ph.EP↗
arXiv2023

Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology

Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimise the selection of parameters such as embedding lag. This paper aims to provide a comprehensive overview of the fundamentals of embedding theory for readers who are new to the subject. We outline a collection of existing methods for selecting embedding lag in both uniform and non-uniform delay embedding cases. Highlighting the poor dynamical explainability of existing methods of selecting non-uniform lags, we provide an alternative method of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, {\em Significant Times on Persistent Strands} (SToPS), uses persistent homology to construct a characteristic time spectrum that quantifies the relative dynamical significance of each time lag. We test our method on periodic, chaotic and fast-slow time series and find that our method performs similar to existing automated non-uniform embedding methods. Additionally, $n$-step predictors trained on embeddings constructed with SToPS was found to outperform other embedding methods when predicting fast-slow time series.

math.DS↗
arXiv2023

Non-centrosymmetric Sr$_{2}$IrO$_{4}$ obtained under High Pressure

Sr$_{2}$IrO$_{4}$ with strong spin-orbit coupling (SOC) and Hubbard repulsion (U) hosts Mott insulating states. The similar crystal structure, magnetic and electronic properties, particularly the $d$-wave gap observed in Sr$_{2}$IrO$_{4}$ enhanced the analogies to cuprate high-$T_{c}$ superconductor, La$_{2}$CuO$_{4}$. The incomplete analogy was due to the lack of broken inversion symmetry phases observed in Sr$_{2}$IrO$_{4}$. Here, under high pressure and high temperature conditions, we report a non-centrosymmetric Sr$_{2}$IrO$_{4}$. The crystal structure and its noncentrosymmetric character were determined by single crystal X-ray diffraction and high-resolution scanning transmission electron microscopy (HR-STEM). The magnetic characterization confirms the Ir$^{4+}$ with $S$ = 1/2 at low temperature in Sr$_{2}$IrO$_{4}$ with magnetic ordering occurred at around 86 K, where a larger moment is observed than the ambient pressure Sr$_{2}$IrO$_{4}$. Moreover, the resistivity measurement shows three-dimensional Mott variable-range hopping existed in the system. This non-centrosymmetric Sr$_{2}$IrO$_{4}$ phase appears to be a unique material to offer further understanding of high-$T_{c}$ superconductivity.

cond-mat.str-el↗