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Articoli di riviste sul tema "Refinement and proof"

Autore: Grafiati

Pubblicato: 31 agosto 2024

Ultima modifica: 31 luglio 2025

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1

Schellhorn, Gerhard. "Verification of ASM Refinements Using Generalized Forward Simulation." JUCS - Journal of Universal Computer Science 7, no. (11) (2001): 952–79. https://doi.org/10.3217/jucs-007-11-0952.

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This paper describes a generic proof method for the correctness of refinements of Abstract State Machines based on commuting diagrams. The method generalizes forward simulations from the refinement of I/O automata by allowing arbitrary m:n diagrams, and by combining it with the refinement of data structures.

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2

Mulder, Ike, and Robbert Krebbers. "Proof Automation for Linearizability in Separation Logic." Proceedings of the ACM on Programming Languages 7, OOPSLA1 (2023): 462–91. http://dx.doi.org/10.1145/3586043.

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Recent advances in concurrent separation logic enabled the formal verification of increasingly sophisticated fine-grained ( i.e. , lock-free) concurrent programs. For such programs, the golden standard of correctness is linearizability , which expresses that concurrent executions always behave as some valid sequence of sequential executions. Compositional approaches to linearizability (such as contextual refinement and logical atomicity) make it possible to prove linearizability of whole programs or compound data structures ( e.g. , a ticket lock) using proofs of linearizability of their indiv

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3

Brucker, Achim, Frank Rittinger, and Burkhart Wolff. "HOL-Z 2.0: A Proof Environment for Z-Specifications." JUCS - Journal of Universal Computer Science 9, no. (2) (2003): 152–72. https://doi.org/10.3217/jucs-009-02-0152.

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We present a new proof environment for the specification language Z. The basis is a semantic representation of Z in a structure-preserving, shallow embedding in Isabelle/HOL. On top of the embedding, new proof support for the Z schema calculus and for proof structuring are developed. Thus, we integrate Z into a well-known and trusted theorem prover with advanced deduction technology such as higher-order rewriting, tableaux-based provers and arithmetic decision procedures. A further achievement of this work is the integration of our embedding into a new tool-chain providing a Z-oriented type ch

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4

Song, Youngju, and Dongjae Lee. "Refinement Composition Logic." Proceedings of the ACM on Programming Languages 8, ICFP (2024): 573–601. http://dx.doi.org/10.1145/3674645.

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One successful approach to verifying programs is refinement, where one establishes that the implementation (e.g., in C) behaves as specified in its mathematical specification. In this approach, the end result (a whole implementation refines a whole specification) is often established via composing multiple “small” refinements. In this paper, we focus on the task of composing refinements. Our key observation is a novel correspondence between the task of composing refinements and the task of proving entailments in modern separation logic. This correspondence is useful. First, it unlocks tools an

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5

Schellhorn, Gerhard, and Wolfgang Ahrendt. "Reasoning about Abstract State Machines: The WAM Case Study." JUCS - Journal of Universal Computer Science 3, no. (4) (1997): 377–413. https://doi.org/10.3217/jucs-003-04-0377.

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This paper describes the first half of the formal verification of a Prolog compiler with the KIV ("Karlsruhe Interactive Verifier") system. Our work is based on [BR95], where an operational Prolog semantics is defined using the formalism of Gurevich Abstract State Machines, and then refined in several steps to the Warren Abstract Machine (WAM). We define a general translation of sequential Abstract State Machines to Dynamic Logic, which formalizes correctness of such refinement steps as a deduction problem. A proof technique for verification is presented, which corresponds to the informal use

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6

Derrick, John, Simon Doherty, Brijesh Dongol, Gerhard Schellhorn, and Heike Wehrheim. "Verifying correctness of persistent concurrent data structures: a sound and complete method." Formal Aspects of Computing 33, no. 4-5 (2021): 547–73. http://dx.doi.org/10.1007/s00165-021-00541-8.

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AbstractNon-volatile memory (NVM), aka persistent memory, is a new memory paradigm that preserves its contents even after power loss. The expected ubiquity of NVM has stimulated interest in the design of persistent concurrent data structures, together with associated notions of correctness. In this paper, we present a formal proof technique for durable linearizability, which is a correctness criterion that extends linearizability to handle crashes and recovery in the context ofNVM.Our proofs are based on refinement of Input/Output automata (IOA) representations of concurrent data structures. T

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7

Bohrer, Brandon, and André Platzer. "Structured Proofs for Adversarial Cyber-Physical Systems." ACM Transactions on Embedded Computing Systems 20, no. 5s (2021): 1–26. http://dx.doi.org/10.1145/3477024.

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Many cyber-physical systems (CPS) are safety-critical, so it is important to formally verify them, e.g. in formal logics that show a model’s correctness specification always holds. Constructive Differential Game Logic ( CdGL ) is such a logic for (constructive) hybrid games, including hybrid systems. To overcome undecidability, the user first writes a proof, for which we present a proof-checking tool. We introduce Kaisar , the first language and tool for CdGL proofs, which until now could only be written by hand with a low-level proof calculus. Kaisar’s structured proofs simplify challenging C

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8

Mylonakis, Nikos. "Proof Assistance for Refinement in Type Theory." Electronic Notes in Theoretical Computer Science 37 (2000): 1–21. http://dx.doi.org/10.1016/s1571-0661(05)01134-5.

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9

Peng, Jie, Tangliu Wen, Yiguo Yang, and Guoming Huang. "An Event-B Approach to the Development of Fork/Join Parallel Programs." EAI Endorsed Transactions on AI and Robotics 1 (February 18, 2022): 1–6. http://dx.doi.org/10.4108/airo.v1i.16.

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Fork/Join is a simple but effective technique for exploiting the parallelism. When developing a parallel program using Fork/Join, one of the main things is how a large task is decomposed into subtasks whose results can be combined as a final result. In this paper we show how to develop Fork/Join parallel programs through refinement and decomposition. We take Fork/Join style task decomposition as a refinement which we call Fork/Join refinement. Proof obligations of refinement can ensure the correctness of decomposition. For practical application, we provide a refinement pattern for the Fork/Joi

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10

Farissi, Abdallah El. "Simple proof and refinement of Hermite-Hadamard inequality." Journal of Mathematical Inequalities, no. 3 (2010): 365–69. http://dx.doi.org/10.7153/jmi-04-33.

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11

Cansell, Dominique, Dominique Méry, and Cyril Proch. "System-on-chip design by proof-based refinement." International Journal on Software Tools for Technology Transfer 11, no. 3 (2009): 217–38. http://dx.doi.org/10.1007/s10009-009-0104-7.

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12

Gregersen, Simon Oddershede, Alejandro Aguirre, Philipp G. Haselwarter, Joseph Tassarotti, and Lars Birkedal. "Almost-Sure Termination by Guarded Refinement." Proceedings of the ACM on Programming Languages 8, ICFP (2024): 203–33. http://dx.doi.org/10.1145/3674632.

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Almost-sure termination is an important correctness property for probabilistic programs, and a number of program logics have been developed for establishing it. However, these logics have mostly been developed for first-order programs written in languages with specific syntactic patterns for looping. In this paper, we consider almost-sure termination for higher-order probabilistic programs with general references. This combination of features allows for recursion and looping to be encoded through a variety of patterns. Therefore, rather than developing proof rules for reasoning about particula

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13

Mimouni, Sanae, and Mohamed Bouhdadi. "A Mechanized Formal Refinement Proof of Modbus Communication Using Event-B Proof System." International Journal of Intelligent Engineering and Systems 11, no. 4 (2018): 97–106. http://dx.doi.org/10.22266/ijies2018.0831.10.

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14

Mutluergil, Suha Orhun, and Serdar Tasiran. "A mechanized refinement proof of the Chase–Lev deque using a proof system." Computing 101, no. 1 (2018): 59–74. http://dx.doi.org/10.1007/s00607-018-0635-4.

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15

Buchsbaum, Christian, and Martin U. Schmidt. "Rietveld refinement of a wrong crystal structure." Acta Crystallographica Section B Structural Science 63, no. 6 (2007): 926–32. http://dx.doi.org/10.1107/s0108768107050823.

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Rietveld refinements are generally used to confirm crystal structures solved from powder diffraction data. If the Rietveld refinement converges with low R values and with a smooth difference curve, and the structure looks chemically sensible, the resulting structure is generally considered to be close to the correct crystal structure. Here we present a counter example: The Rietveld refinement of the X-ray powder pattern of γ-quinacridone with the crystal structure of β-quinacridone gives quite a smooth difference curve; the resulting crystal structure looks reasonable in terms of molecular con

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16

el Mimouni, Sanae, and Mohamed Bouhdadi. "Event Based Formalization of Communication Properties for an E-Commerce Protocol: An Event-B Approach." International Journal of Engineering Research in Africa 37 (August 2018): 78–90. http://dx.doi.org/10.4028/www.scientific.net/jera.37.78.

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The objective of this paper aims at modeling and analysis of communication properties of an E-commerce protocol with the Event-B language. NetBill protocol is developed for selling and buying of information and goods through the Internet. In this approach, we have used Event-B as proof-based development method which integrates proof techniques for writing specifications and building the model systematically using refinement, the key point is to start with a very abstract model of the system under development. Step by step details are added to this first model by building a series of more concr

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17

Luo, Zhaohui. "Program specification and data refinement in type theory." Mathematical Structures in Computer Science 3, no. 3 (1993): 333–63. http://dx.doi.org/10.1017/s0960129500000256.

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The study of type theory may offer a uniform language for modular programming, structured specification and logical reasoning. We develop an approach to program specification and data refinement in a type theory with a strong logical power and nice structural mechanisms to show that it provides an adequate formalism for modular development of programs and specifications. Specification of abstract data types is considered, and a notion of abstract implementation between specifications is defined in the type theory and studied as a basis for correct and modular development of programs by stepwis

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18

Méry, Dominique, and Neeraj Kumar Singh. "Formal Specification of Medical Systems by Proof-Based Refinement." ACM Transactions on Embedded Computing Systems 12, no. 1 (2013): 1–25. http://dx.doi.org/10.1145/2406336.2406351.

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19

Cimatti, Alessandro, and Stefano Tonetta. "Contracts-refinement proof system for component-based embedded systems." Science of Computer Programming 97 (January 2015): 333–48. http://dx.doi.org/10.1016/j.scico.2014.06.011.

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20

Dümbgen, Lutz. "A simple proof and refinement of Wielandt's eigenvalue inequality." Statistics & Probability Letters 25, no. 2 (1995): 113–15. http://dx.doi.org/10.1016/0167-7152(94)00212-q.

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21

BANACH, RICHARD, and CZESŁAW JESKE. "Retrenchment and refinement interworking: the tower theorems." Mathematical Structures in Computer Science 25, no. 1 (2014): 135–202. http://dx.doi.org/10.1017/s0960129514000061.

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Retrenchment is a flexible model evolution formalism that compensates for the limitations imposed by specific formulations of refinement. Its refinement-like proof obligations feature additional predicates for accommodating design data describing the model change. The best results are obtained when refinement and retrenchment cooperate, the paradigmatic scheme for this being the commuting square or tower, in which ‘horizontal retrenchment rungs’ commute with ‘vertical refinement columns’ to navigate through a much more extensive design space than permitted by refinement alone. In practice, the

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22

GORRIERI, ROBERTO, and UGO MONTANARI. "TOWARDS HIERARCHICAL DESCRIPTION OF SYSTEMS: A PROOF SYSTEM FOR STRONG PREFIXING." International Journal of Foundations of Computer Science 01, no. 03 (1990): 277–93. http://dx.doi.org/10.1142/s0129054190000205.

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The problem of relating system descriptions at different levels of abstraction is addressed in the context of process description languages. As a case study, we introduce two nondeterministic languages. The latter is a simple extension of the former and is obtained by adding to its signature an operator of strong prefixing for making atomic the execution of a sequence of actions. The two languages are intended to be a specification and an implementation language, respectively. To directly relate them, we introduce a mapping, called atomic action refinement, from actions of the former to atomic

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23

Méry, Dominique, and Stephan Merz. "Specification and Refinement of Access Control." JUCS - Journal of Universal Computer Science 13, no. (8) (2007): 1073–93. https://doi.org/10.3217/jucs-013-08-1073.

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We consider the extension of fair event system specifications by concepts of access control (prohibitions, user rights, and obligations). We give proof rules for verifying that an access control policy is correctly implemented in a system, and consider preservation of access control by refinement of event systems. Prohibitions and obligations are expressed as properties of traces and are preserved by standard refinement notions of event systems. Preservation of user rights is not guaranteed by construction; we propose to combine implementation-level user rights and obligations to implement hig

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24

Büchi, Martin, and Emil Sekerinski. "A Foundation for Refining Concurrent Objects." Fundamenta Informaticae 44, no. 1-2 (2000): 25–61. https://doi.org/10.3233/fun-2000-441-202.

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We study the notion of class refinement in a concurrent object-oriented setting. Our model is based on a combination of action systems and classes. An action system describes the behavior of a concurrent, distributed, or interactive system in terms of the atomic actions that can take place during the execution of the system. Classes serve as templates for creating objects. To express concurrency with objects, we add actions to classes. We define class refinement based on trace refinement of action systems. Additionally, we give a simulation-based proof rule. We show that the easier to apply si

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25

Qiu, Longfei, Yoonseung Kim, Ji-Yong Shin, Jieung Kim, Wolf Honoré, and Zhong Shao. "LiDO: Linearizable Byzantine Distributed Objects with Refinement-Based Liveness Proofs." Proceedings of the ACM on Programming Languages 8, PLDI (2024): 1140–64. http://dx.doi.org/10.1145/3656423.

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Byzantine fault-tolerant state machine replication (SMR) protocols, such as PBFT, HotStuff, and Jolteon, are essential for modern blockchain technologies. However, they are challenging to implement correctly because they have to deal with any unexpected message from byzantine peers and ensure safety and liveness at all times. Many formal frameworks have been developed to verify the safety of SMR implementations, but there is still a gap in the verification of their liveness. Existing liveness proofs are either limited to the network level or do not cover popular partially synchronous protocols

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26

Lai, Tri. "Proof of a refinement of Blum’s conjecture on hexagonal dungeons." Discrete Mathematics 340, no. 7 (2017): 1617–32. http://dx.doi.org/10.1016/j.disc.2017.03.003.

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27

Bejenaru, Ioan. "The multilinear restriction estimate: a short proof and a refinement." Mathematical Research Letters 24, no. 6 (2017): 1585–603. http://dx.doi.org/10.4310/mrl.2017.v24.n6.a1.

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28

Choppy, Christine, Micaela Mayero, and Laure Petrucci. "Coloured Petri net refinement specification and correctness proof with Coq." Innovations in Systems and Software Engineering 6, no. 3 (2010): 195–202. http://dx.doi.org/10.1007/s11334-010-0131-2.

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29

Atiya, D., S. King, and J. C. P. Woodcock. "Simpler Reasoning About System Properties: a Proof-by-Refinement Technique." Electronic Notes in Theoretical Computer Science 137, no. 2 (2005): 5–22. http://dx.doi.org/10.1016/j.entcs.2005.04.022.

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30

Simić, Danijela. "Using Small -Step Refinement for Algorithm Verification in Computer Science Education." International Journal for Technology in Mathematics Education 22, no. 4 (2015): 155–62. http://dx.doi.org/10.1564/tme_v22.4.03.

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Stepwise program refinement techniques can be used to simplify program verification. Programs are better understood since their main properties are clearly stated, and verification of rather complex algorithms is reduced to proving simple statements connecting successive program specifications. Additionally, it is easy to analyse similar algorithms and to compare their properties within a single formalization. Usually, formal analysis is not done in the educational setting due to complexity of verification and a lack of tools and procedures to make comparison easy. Verification of an algorithm

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31

Sándor, József. "On certain inequalities for the prime counting function." Notes on Number Theory and Discrete Mathematics 27, no. 4 (2021): 149–53. http://dx.doi.org/10.7546/nntdm.2021.27.4.149-153.

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32

Cohen, Stephen D., and A. M. W. Glass. "Composites of translations and odd rational powers act freely." Bulletin of the Australian Mathematical Society 51, no. 1 (1995): 73–81. http://dx.doi.org/10.1017/s0004972700013903.

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It is shown that no non-trivial composition of translations x ↦ x + a and odd rational powers x ↦p/q, where p,q are odd co-prime integers, positive or negative with p/q≠±, acts like the identity on a field of characteristic zero. This extends a theorem of Adeleke, Glass, and Morley in which only odd positive rational powers were considered. Moreover, the nature of the proof itself (by field theory) is a simplification and natural refinement of previous proofs. It has applications in other settings.

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33

Horváth, László. "Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications." Mathematics 13, no. 10 (2025): 1563. https://doi.org/10.3390/math13101563.

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In this paper, starting from abstract versions of a result of Bennett given by Niculescu, we derive new majorization-type integral inequalities for convex functions using finite signed measures. The proof of the main result is based on a generalization of a recently discovered majorization-type integral inequality. As applications of the results, we give simple proofs of the integral Jensen and Lah–Ribarič inequalities for finite signed measures, generalize and extend known results, and obtain an interesting new refinement of the Hermite–Hadamard–Fejér inequality.

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34

Farzan, Azadeh, Dominik Klumpp, and Andreas Podelski. "Stratified Commutativity in Verification Algorithms for Concurrent Programs." Proceedings of the ACM on Programming Languages 7, POPL (2023): 1426–53. http://dx.doi.org/10.1145/3571242.

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The importance of exploiting commutativity relations in verification algorithms for concurrent programs is well-known. They can help simplify the proof and improve the time and space efficiency. This paper studies commutativity relations as a first-class object in the setting of verification algorithms for concurrent programs. A first contribution is a general framework for abstract commutativity relations . We introduce a general soundness condition for commutativity relations, and present a method to automatically derive sound abstract commutativity relations from a given proof. The method c

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35

Komlós, János, and Endre Szemerédi. "Topological cliques in graphs II." Combinatorics, Probability and Computing 5, no. 1 (1996): 79–90. http://dx.doi.org/10.1017/s096354830000184x.

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Sándor, József. "On an Arithmetic Inequality." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 1 (2014): 257–61. http://dx.doi.org/10.2478/auom-2014-0021.

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37

Li, Jie, Kai Hu, Jian Zhu, Jean-Paul Bodeveix, and Yafei Ye. "Formal Modelling of PBFT Consensus Algorithm in Event-B." Wireless Communications and Mobile Computing 2022 (October 14, 2022): 1–17. http://dx.doi.org/10.1155/2022/4467917.

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The practical Byzantine Fault Tolerance (PBFT) is a classical consensus algorithm that has been widely applied in an alliance blockchain system to make all nodes agree to certain transactions under the assumption that the proportion of Byzantine nodes is no more than 1/3. It is prevalent due to its performance, simplicity, and claimed correctness. However, any vulnerability of the consensus algorithm can lead to a significant loss in finance because no one can change the transaction results after execution. This paper proposes a formal development method of the PBFT algorithm by horizontal ref

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38

Bobkov, Sergey G., Gennadiy P. Chistyakov, and Friedrich Götze. "Richter’s local limit theorem, its refinement, and related results*." Lithuanian Mathematical Journal 63, no. 2 (2023): 138–60. http://dx.doi.org/10.1007/s10986-023-09598-9.

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We give a detailed exposition of the proof of Richter’s local limit theorem in a refined form and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing).We also discuss related quantitative bounds for characteristic functions and Laplace transforms.

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Grimmett, Geoffrey R., Tobias J. Osborne, and Petra F. Scudo. "Bounded Entanglement Entropy in the Quantum Ising Model." Journal of Statistical Physics 178, no. 1 (2019): 281–96. http://dx.doi.org/10.1007/s10955-019-02432-y.

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AbstractA rigorous proof is presented of the boundedness of the entanglement entropy of a block of spins for the ground state of the one-dimensional quantum Ising model with sufficiently strong transverse field. This is proved by a refinement of the stochastic geometric arguments in the earlier work by Grimmett et al. (J Stat Phys 131:305–339, 2008). The proof utilises a transformation to a model of classical probability called the continuum random-cluster model. Our method of proof is fairly robust, and applies also to certain disordered systems.

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Sumners, Rob. "Proof Reduction of Fair Stuttering Refinement of Asynchronous Systems and Applications." Electronic Proceedings in Theoretical Computer Science 249 (May 2, 2017): 78–94. http://dx.doi.org/10.4204/eptcs.249.6.

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Dousse, Jehanne. "A combinatorial proof and refinement of a partition identity of Siladić." European Journal of Combinatorics 39 (July 2014): 223–32. http://dx.doi.org/10.1016/j.ejc.2014.01.008.

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42

Kawamata, Fuga, Hiroshi Unno, Taro Sekiyama, and Tachio Terauchi. "Answer Refinement Modification: Refinement Type System for Algebraic Effects and Handlers." Proceedings of the ACM on Programming Languages 8, POPL (2024): 115–47. http://dx.doi.org/10.1145/3633280.

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Algebraic effects and handlers are a mechanism to structure programs with computational effects in a modular way. They are recently gaining popularity and being adopted in practical languages, such as OCaml. Meanwhile, there has been substantial progress in program verification via refinement type systems . While a variety of refinement type systems have been proposed, thus far there has not been a satisfactory refinement type system for algebraic effects and handlers. In this paper, we fill the void by proposing a novel refinement type system for languages with algebraic effects and handlers.

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Andriamiarina, Bruno, Dominique Méry, and Kumar Singh. "Revisiting snapshot algorithms by refinement-based techniques." Computer Science and Information Systems 11, no. 1 (2014): 251–70. http://dx.doi.org/10.2298/csis130122007a.

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The snapshot problem addresses a collection of important algorithmic issues related to distributed computations, which are used for debugging or recovering distributed programs. Among existing solutions, Chandy and Lamport have proposed a simple distributed algorithm. In this paper, we explore the correct-byconstruction process to formalize the snapshot algorithms in distributed system. The formalization process is based on a modeling language Event B, which supports a refinement-based incremental development using RODIN platform. These refinement-based techniques help to derive correct distri

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Pulte, Christopher, Dhruv C. Makwana, Thomas Sewell, Kayvan Memarian, Peter Sewell, and Neel Krishnaswami. "CN: Verifying Systems C Code with Separation-Logic Refinement Types." Proceedings of the ACM on Programming Languages 7, POPL (2023): 1–32. http://dx.doi.org/10.1145/3571194.

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Despite significant progress in the verification of hypervisors, operating systems, and compilers, and in verification tooling, there exists a wide gap between the approaches used in verification projects and conventional development of systems software. We see two main challenges in bringing these closer together: verification handling the complexity of code and semantics of conventional systems software, and verification usability. We describe an experiment in verification tool design aimed at addressing some aspects of both: we design and implement CN, a separation-logic refinement type sys

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Kashio, Tomokazu. "Fermat curves and a refinement of the reciprocity law on cyclotomic units." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 741 (2018): 255–73. http://dx.doi.org/10.1515/crelle-2015-0081.

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Abstract We define a “period-ring-valued beta function” and give a reciprocity law on its special values. The proof is based on some results of Rohrlich and Coleman concerning Fermat curves. We also have the following application. Stark’s conjecture implies that the exponentials of the derivatives at s=0 of partial zeta functions are algebraic numbers which satisfy a reciprocity law under certain conditions. It follows from Euler’s formulas and properties of cyclotomic units when the base field is the rational number field. In this paper, we provide an alternative proof of a weaker result by u

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Gäher, Lennard, Michael Sammler, Ralf Jung, Robbert Krebbers, and Derek Dreyer. "RefinedRust: A Type System for High-Assurance Verification of Rust Programs." Proceedings of the ACM on Programming Languages 8, PLDI (2024): 1115–39. http://dx.doi.org/10.1145/3656422.

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Abstract (sommario):

Rust is a modern systems programming language whose ownership-based type system statically guarantees memory safety, making it particularly well-suited to the domain of safety-critical systems. In recent years, a wellspring of automated deductive verification tools have emerged for establishing functional correctness of Rust code. However, none of the previous tools produce foundational proofs (machine-checkable in a general-purpose proof assistant), and all of them are restricted to the safe fragment of Rust. This is a problem because the vast majority of Rust programs make use of unsafe code

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Abrial, Jean-Raymond, and Dominique Cansell. "Formal Construction of a Non-blocking Concurrent Queue Algorithm." JUCS - Journal of Universal Computer Science 11, no. (5) (2005): 744–70. https://doi.org/10.3217/jucs-011-05-0744.

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This paper contains a completely formal (and mechanically proved) development of some algorithms dealing with a linked list supposed to be shared by various processes. These algorithms are executed in a highly concurrent fashion by an unknown number of such independent processes. These algorithms have been first presented in [MS96] by M.M. Michael and M.L. Scott. Two other developments of the same algorithms have been proposed recently in [YS03] (using the 3VMC Model Checker developed by E. Yahav) and in [DGLM04] (using I/O Automata and PVS).

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Jacobs, Philipp, Andreas Houben, Werner Schweika, Andrei L. Tchougréeff, and Richard Dronskowski. "A Rietveld refinement method for angular- and wavelength-dispersive neutron time-of-flight powder diffraction data." Journal of Applied Crystallography 48, no. 6 (2015): 1627–36. http://dx.doi.org/10.1107/s1600576715016520.

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This paper introduces a two-dimensional extension of the well established Rietveld refinement method for modeling neutron time-of-flight powder diffraction data. The novel approach takes into account the variation of two parameters, diffraction angle 2θ and wavelength λ, to optimally adapt to the varying resolution function in diffraction experiments. By doing so, the refinement against angular- and wavelength-dispersive data gets rid of common data-reduction steps and also avoids the loss of high-resolution information typically introduced by integration. In a case study using a numerically s

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Nguyen, Linh Anh. "Negative Ordered Hyper-Resolution as a Proof Procedure for Disjunctive Logic Programming." Fundamenta Informaticae 70, no. 4 (2006): 351–66. https://doi.org/10.3233/fun-2006-70404.

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Abstract (sommario):

We prove that negative hyper-resolution using any liftable and well-founded ordering refinement is a sound and complete procedure for answering queries in disjunctive logic programs. In our formulation, answers of queries are defined using disjunctive substitutions, which are more flexible than answer literals used in theorem proving systems.

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50

Bessenrodt, Christine. "A Combinatorial Proof of a Refinement of the Andrews—Olsson Partition Identity." European Journal of Combinatorics 12, no. 4 (1991): 271–76. http://dx.doi.org/10.1016/s0195-6698(13)80109-6.

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