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  1. We present IronSync, an automated verification framework for concurrent code with shared memory. IronSync scales to complex systems by splitting system-wide proofs into isolated concerns such that each can be substantially automated. As a starting point, IronSync’s ownership type system allows a developer to straightforwardly prove both data safety and the logical correctness of thread-local operations. IronSync then introduces the concept of a Localized Transition System, which connects the correctness of local actions to the correctness of the entire system. We demonstrate IronSync by verifying two state-of-the-art concurrent systems comprising thousands of lines: a library for black-box replication on NUMA architectures, and a highly concurrent page cache.
    Free, publicly-accessible full text available July 10, 2024
  2. Abstract Background

    Studying the co-occurrence network structure of microbial samples is one of the critical approaches to understanding the perplexing and delicate relationship between the microbe, host, and diseases. It is also critical to develop a tool for investigating co-occurrence networks and differential abundance analyses to reveal the disease-related taxa–taxa relationship. In addition, it is also necessary to tighten the co-occurrence network into smaller modules to increase the ability for functional annotation and interpretability of  these taxa-taxa relationships.  Also, it is critical to retain the phylogenetic relationship among the taxa to identify differential abundance patterns, which can be used to resolve contradicting functions reported by different studies.

    Results

    In this article, we present Correlation and Consensus-based Cross-taxonomy Network Analysis (C3NA), a user-friendly R package for investigating compositional microbial sequencing data to identify and compare co-occurrence patterns across different taxonomic levels. C3NA contains two interactive graphic user interfaces (Shiny applications), one of them dedicated to the comparison between two diagnoses, e.g., disease versus control. We used C3NA to analyze two well-studied diseases, colorectal cancer, and Crohn’s disease. We discovered clusters of study and disease-dependent taxa that overlap with known functional taxa studied by other discovery studies and differential abundance analyses.

    Conclusion

    C3NA offers amore »new microbial data analyses pipeline for refined and enriched taxa–taxa co-occurrence network analyses, and the usability was further expanded via the built-in Shiny applications for interactive investigation.

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  3. Linear recurrence operators in characteristic p are classified by their p-curvature. For a recurrence operator L, denote by χ(L) the characteristic polynomial of its p-curvature. We can obtain information about the factorization of L by factoring χ(L). The main theorem of this paper gives an unexpected relation between χ(L) and the true singularities of L. An application is to speed up a fast algorithm for computing χ(L) by desingularizing L first. Another contribution of this paper is faster desingularization.
    Free, publicly-accessible full text available July 4, 2023
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  8. Free, publicly-accessible full text available July 14, 2023
  9. Reasoning about memory aliasing and mutation in software verification is a hard problem. This is especially true for systems using SMT-based automated theorem provers. Memory reasoning in SMT verification typically requires a nontrivial amount of manual effort to specify heap invariants, as well as extensive alias reasoning from the SMT solver. In this paper, we present a hybrid approach that combines linear types with SMT-based verification for memory reasoning. We integrate linear types into Dafny, a verification language with an SMT backend, and show that the two approaches complement each other. By separating memory reasoning from verification conditions, linear types reduce the SMT solving time. At the same time, the expressiveness of SMT queries extends the flexibility of the linear type system. In particular, it allows our linear type system to easily and correctly mix linear and nonlinear data in novel ways, encapsulating linear data inside nonlinear data and vice-versa. We formalize the core of our extensions, prove soundness, and provide algorithms for linear type checking. We evaluate our approach by converting the implementation of a verified storage system (about 24K lines of code and proof) written in Dafny, to use our extended Dafny. The resulting system uses linear typesmore »for 91% of the code and SMT-based heap reasoning for the remaining 9%. We show that the converted system has 28% fewer lines of proofs and 30% shorter verification time overall. We discuss the development overhead in the original system due to SMT-based heap reasoning and highlight the improved developer experience when using linear types.« less
    Free, publicly-accessible full text available April 29, 2023
  10. Free, publicly-accessible full text available February 22, 2023