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In this work, we address the formalisation of symmetric nets, a subclass of coloured Petri nets, refinement in COQ. We first provide a formalisation of the net models, and of their type refinement in COQ. Then the COQ proof assistant is used to prove the refinement correctness lemma. An example adapted from a protocol example illustrates our work.
Intermediate verification languages like Why3 and Boogie have made it much easier to build program verifiers, transforming the process into a logic compilation problem rather than a proof automation one. Why3 in particular implements a rich logic for program specification with polymorphism, algebraic data types, recursive functions and predicates, and inductive predicates; it translates this logic to over a dozen solvers and proof assistants. Accordingly, it serves as a backend for many tools, including Frama-C, EasyCrypt, and GNATProve for Ada SPARK. But how can we be sure that these tools are correct? The alternate foundational approach, taken by tools like VST and CakeML, provides strong guarantees by implementing the entire toolchain in a proof assistant, but these tools are harder to build and cannot directly take advantage of SMT solver automation. As a first step toward enabling automated tools with similar foundational guarantees, we give a formal semantics in Coq for the logic fragment of Why3. We show that our semantics are useful by giving a correct-by-construction natural deduction proof system for this logic, using this proof system to verify parts of Why3's standard library, and proving sound two of Why3's transformations used to convert terms and formulas into the simpler logics supported by the backend solvers.
Systems of the utmost consequence need a means to establish authenticity of software and data. Cryptosystems implement authentication, but can be vulnerable to cryptographic and implementation attacks. With the threat of quantum cryptographic attacks, “post-quantum” cryptosystems (PQCs) must be henceforth used in these systems. However, the new cryptography needs new ways to, rigorously and machine-checkably, prove systems free of vulnerabilities. We propose a retargetable capability to rapidly instantiate proven correct postquantum cryptosystems through novel proof-carrying synthesis and proof-automation technique, extending those proven successful on existing systems. This capability is crucial to meeting the cryptographic requirements for future high-consequence systems. Since specifications for high consequence cryptography are presently captured in a domain specific language known as Cryptol. While this can enable convenient fully automated reasoning about Cryptol specificaitons and implementations via the Software Analysis Workbench (SAW), Cryptol has expressivity gaps, so that cryptosystems with probabilistic programming features like Falcon cannot be fully expressed in the language. Moreover, SAW’s automation fails for programs and specificaitons with inductive and recursive structure, as in the Sphincs+ PQC. Finally, Cryptol and SAW together represent some 200,000 lines of unverified Haskell, so that the any guarantees about high consequence cryptography are presently contingent on a large, unverified, yet trusted computing base. The first step of the larger project of agile, assured crpytography is therefore to provide a formal, mechanized semantics for Cryptol, so that the specifications expressed by cryptographers in Cryptol can be reasoned about and compiled into performant implementations with a foundational, machine checkable certificate of correctness. This report describes our work on this first step, culminating in the design of a certified denotational interpreter, in Coq, for core Cryptol.
The need for a small step semantics and more generally for a thorough documentation and understanding of Coq's tacticals and PVS's strategies arise with their growing use and the progressive uncovering of their subtleties. The purpose of the following study is to provide a simple and clear formal framework to describe their detailed semantics, and highlight their differences and similarities.
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The Space Shuttle Redesigned Solid Rocket Motor (RSRM) Certification Program provides confidence that the RSRM and its components/subsystems meet or exceed Mission Oriented Requirements when manufactured per design requirements and specified/approved processes. Certification is based on documented results of tests, analyses, inspections, similarity, and demonstrations. Evidencing information is provided to certify that each RSRM component/subsystem satisfies design, mission related requirements and objectives.
We present VOQC, the first verified optimizer for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, a small quantum intermediate representation, which is deeply embedded in Coq. Optimizations and other transformations are expressed as Coq functions, which are proved correct with respect to a semantics of SQIR programs. SQIR programs denote complex-valued matrices, as is standard in quantum computation, but we treat matrices symbolically to reason about programs that use an arbitrary number of quantum bits. SQIR’s careful design and our provided automation make it possible to write and verify a broad range of optimizations in VOQC, including full-circuit transformations from cutting-edge optimizers.
We develop a formalization of floating-point numbers in PVS based on a well-known formalization in Coq. We first describe the definitions of all the needed notions, e.g., floating-point number, format, rounding modes, etc.; then, we present an application to polynomial evaluation for elementary function evaluation. The application already existed in Coq, but our formalization shows a clear improvement in the quality of the result due to the automation provided by PVS. We finally integrate our formalization into a PVS hardware-level formalization of the IEEE-854 standard previously developed at NASA.
Achieving high biochemical production in biotransformations of renewable resources requires using concentrated cultures that not only generate the product of interest but also produce abundant microbial cell waste. We explored the concept of gaining value from microbial cells by producing intracellular products in tandem with a desired extracellular product. Specifically, we engineered a strain ofNovosphingobium aromaticivorans to extracellularly produce 2-pyrone-4,6-dicarboxylic acid (PDC) from aromatic substrates and to intracellularly accumulate astaxanthin along with coenzyme Q 10 , all of which are products of industrial interest. Achieving the goal of concurrent production of intracellular and extracellular products required the creative application of bioreactor engineering principles. Although a continuously fed membrane bioreactor (MBR) maximized extracellular product biosynthesis, it had a negative effect on intracellular product accumulation. However, operating the MBR as a sequencing batch reactor (MBR-SBR) with a step-feed resulted in stable concurrent production of both extracellular and intracellular products. With aromatics extracted from poplar biomass, we achieved productivities of 1.14 g of PDC/L-h for the extracellular product and 0.04 mg of astaxanthin/L-h and 0.64 mg of CoQ 10 /L-h for intracellular products, respectively. Our findings demonstrate that the mode of operation of a bioreactor impacts the simultaneous production of intracellular and extracellular products byN. aromaticivorans.
The zinc (Zn) stable isotope system has emerged as a powerful tool for investigating natural and anthropogenic processes of interest to disciplines extending from the Earth and planetary sciences to biomedical research. In nature, Zn isotopes typically fractionate ( 66 Zn/ 64 Zn) within the range of –1 and +1 permil (‰), and however, analytical limitations restrict the application of the Zn isotope system. Specifically, there is a lack of well-characterised matrix-matched reference materials covering most Zn isotope applications that are essential for validating laboratory performance, particularly given the contamination prone nature of Zn. Furthermore, the increasing demand for analysis of size-limited materials and sample types displaying small, sub-permil level Zn isotope variations requires improvements in measurement procedures. To address these limitations, the δ 66 Zn values of two pure Zn solutions and eighteen reference materials including the previously uncharacterised RGM-2, BCR-279, DOLT-4, DOLT-5, NASS-7, SBC-1, SGR-1b, MESS-3 and HISS-1, and the understudied QLO-1, SDC-1, BCR-414, NASS-6 and COQ-1 materials are reported. Furthermore, a 70 Zn- 67 Zn double-spike design has been implemented that routinely achieves intermediate measurement precision better than ± 0.02‰. This represents at least a two-fold improvement when compared with other double-spike designs, providing a robust platform of δ 66 Zn values required for quality control procedures.
This Proceedings includes both a paper from the implementors of PVS providing guidance for PVS strategy writers and a tutorial on PVS strategy writing distilled from the experience of three PVS users who have written extensive sets of PVS user strategies. Following these are three full papers from the higher-order logic theorem proving community that discuss PVS strategies to enhance arithmetic and other interactive reasoning in PVS; implementing first-order tactics in higher-order provers; and a proposed technique for specifying small step semantics that can be used in multiple higher order logic theorem provers, with illustrations from both Coq and PVS. The Proceedings concludes with three position papers for a panel session that discuss three settings in which development of PVS strategies is worth while.
Topics covered include: Model Checking - My 27-Year Quest to Overcome the State Explosion Problem; Applying Formal Methods to NASA Projects: Transition from Research to Practice; TLA+: Whence, Wherefore, and Whither; Formal Methods Applications in Air Transportation; Theorem Proving in Intel Hardware Design; Building a Formal Model of a Human-Interactive System: Insights into the Integration of Formal Methods and Human Factors Engineering; Model Checking for Autonomic Systems Specified with ASSL; A Game-Theoretic Approach to Branching Time Abstract-Check-Refine Process; Software Model Checking Without Source Code; Generalized Abstract Symbolic Summaries; A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing; Component-Oriented Behavior Extraction for Autonomic System Design; Automated Verification of Design Patterns with LePUS3; A Module Language for Typing by Contracts; From Goal-Oriented Requirements to Event-B Specifications; Introduction of Virtualization Technology to Multi-Process Model Checking; Comparing Techniques for Certified Static Analysis; Towards a Framework for Generating Tests to Satisfy Complex Code Coverage in Java Pathfinder; jFuzz: A Concolic Whitebox Fuzzer for Java; Machine-Checkable Timed CSP; Stochastic Formal Correctness of Numerical Algorithms; Deductive Verification of Cryptographic Software; Coloured Petri Net Refinement Specification and Correctness Proof with Coq; Modeling Guidelines for Code Generation in the Railway Signaling Context; Tactical Synthesis Of Efficient Global Search Algorithms; Towards Co-Engineering Communicating Autonomous Cyber-Physical Systems; and Formal Methods for Automated Diagnosis of Autosub 6000.
Dynamic array bound checks are crucial elements for the security of a Java Virtual Machines. These dynamic checks are however expensive and several static analysis techniques have been proposed to eliminate explicit bounds checks. Such analyses require advanced numerical and symbolic manipulations that 1) penalize bytecode loading or dynamic compilation, 2) complexify the trusted computing base. Following the Foundational Proof Carrying Code methodology, our goal is to provide a lightweight bytecode verifier for eliminating array bound checks that is both efficient and trustable. In this work, we define a generic relational program analysis for an imperative, stackoriented byte code language with procedures, arrays and global variables and instantiate it with a relational abstract domain as polyhedra. The analysis has automatic inference of loop invariants and method pre-/post-conditions, and efficient checking of analysis results by a simple checker. Invariants, which can be large, can be specialized for proving a safety policy using an automatic pruning technique which reduces their size. The result of the analysis can be checked efficiently by annotating the program with parts of the invariant together with certificates of polyhedral inclusions. The resulting checker is sufficiently simple to be entirely certified within the Coq proof assistant for a simple fragment of the Java bytecode language. During the talk, we will also report on our ongoing effort to scale this approach for the full sequential JVM.
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Fabrication of nuclear reactor components using additive manufacturing (AM) methods is now a practical option since the AM technologies have advanced to allow for building of complex parts with high quality materials. To assess the mechanical performance of printed components in reactor-relevant conditions and to build a property database for the AM 316L stainless steel (SS), mechanical testing and characterization were performed before and after neutron irradiation. In this work, miniature tensile specimens were irradiated at the High Flux Isotope Reactor (HFIR) to 0.2 and 2 displacements per atom (dpa) at 300 and 600°C. The AM 316L SS was tested in the as-built, stress-relieved, and solution-annealed conditions, and the wrought (WT) 316L SS in solution-annealed condition as a reference alloy. The baseline test result showed that the AM 316L SS, regardless of the post-build heat treatment, had higher strength than the WT 316L SS, but similar ductility. Post-irradiation tensile testing was conducted at RT, 300°C, and 500°C for selected irradiation conditions. Neutron irradiation induced significant changes in the mechanical behavior of the AM stainless steels, including both hardening and softening. Although the as-built 316L steel after 300°C irradiation showed necking just after yielding, the overall property changes of the as-printed alloy became less significant after 600°C irradiation. Irradiation-induced ductilization was also observed after the higher temperature irradiation. In general, the strength change was smaller in the relatively stronger as-built and stress-relieved AM SSs than in the solution-annealed AM and WT SSs. These relatively lower strength 316L SSs overall retained higher ductility in the irradiation conditions tested, but the stronger 316L SSs demonstrated a similar level of ductility after the higher temperature (600°C) irradiation. It is a positive assessment for the AM 316L materials that no embrittlement was observed within the test and irradiation conditions of the experiment.
Neutron irradiation tests were carried out on 3D-printed SiC derived from binderjet additive manufacturing and chemical vapor infiltration. Irradiation was carried to 2.3 dpa over a temperature range of 400–850 °C. Anisotropy that had been observed in the thermal conductivity of 3D-printed SiC prior to irradiation vanished after irradiation as the irradiation defect thermal resistivity accumulated in the material. No degradation in strength was observed in the material before or after irradiation, at various temperatures, or in different orientations. Electron microscopy of the microstructure after neutron irradiation showed distinct defect morphologies in the heterogenous material, but no evidence for irradiation-induced cracking or degradation in the microstructure was observed.
The SiC fuel matrix for advanced gas-cooled high temperature reactors as part of the Transformational Challenge Reactor program serves as the fuel particle container structure, a barrier to fission gas release, and a heat transfer medium. Its performance is particularly important because the fuel matrix must demonstrate good structural stability and thermal behaviors. An additive manufacturing methodology combining a binder jet 3D printing process with chemical vapor infiltration (CVI) for the production of SiC was recently developed. In this study, post irradiation examination by transmission electron microscopy shows that defect accumulation within the printed particles is very similar to other forms of high-purity SiC. However, damage accumulation was not directly observed in the CVI matrix because black spot damage and dislocation loops are difficult to image within the nanoscale highly faulted CVI matrix and because interstitial defects may rapidly annihilate at the stacking faults. Therefore, electron energy loss spectroscopy (EELS) analysis was used to analyze defect swelling in both the printed particles and the CVI matrix. The EELS analysis helped reveal that the radiation-induced swelling in the CVI matrix is similar to that of the printed SiC particles. This work shows that 3D printed SiC has behavior that is comparable to SiC processed by other means and that 3D printing could serve as a suitable processing technique for high-purity SiC for nuclear applications.
The present work offers and evaluates a correlation-based approach to determine the tensile properties of nuclear fuel cladding tubes. A set of model materials with known properties (i.e., austenitic and ferritic steels, fcc- and hcp-alloys) were tested to build a correlation between conventional tensile tests and ring (hoop) and tube (axial) tests. It was shown that close-to-linear relationships exist for the basic mechanical properties (i.e., yield and ultimate stress, uniform and total elongation) between the uniaxial tensile test data and the ring and tube test data. Using the ring and tube specimen geometries, the feasibility of the approach was demonstrated via manufacturing and testing specimens from irradiated Zr and FeCrAl nuclear fuel cladding tubes. Limitations caused by specific deformation mechanisms (e.g., high ductility of 304L steel) were discussed in detail. The approach can be extended to other tubular products with different geometry and dimensions.