45 research outputs found

    Programming with Numerical Uncertainties

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    Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. In many domains, roundoff errors are not the only source of inaccuracy and measurement as well as truncation errors further increase the uncertainty of the computed results. Adequate tools are needed to help users select suitable approximations (data types and algorithms) which satisfy their accuracy requirements, especially for safety- critical applications. Determining that a computation produces accurate results is challenging. Roundoff errors and error propagation depend on the ranges of variables in complex and non-obvious ways; even determining these ranges accurately for nonlinear programs poses a significant challenge. In numerical loops, roundoff errors grow, in general, unboundedly. Finally, due to numerical errors, the control flow in the finite-precision implementation may diverge from the ideal real-valued one by taking a different branch and produce a result that is far-off of the expected one. In this thesis, we present techniques and tools for automated and sound analysis, verification and synthesis of numerical programs. We focus on numerical errors due to roundoff from floating-point and fixed-point arithmetic, external input uncertainties or truncation errors. Our work uses interval or affine arithmetic together with Satisfiability Modulo Theories (SMT) technology as well as analytical properties of the underlying mathematical problems. This combination of techniques enables us to compute sound and yet accurate error bounds for nonlinear computations, determine closed-form symbolic invariants for unbounded loops and quantify the effects of discontinuities on numerical errors. We can furthermore certify the results of self-correcting iterative algorithms. Accuracy usually comes at the expense of resource efficiency: more precise data types need more time, space and energy. We propose a programming model where the scientist writes his or her numerical program in a real-valued specification language with explicit error annotations. It is then the task of our verifying compiler to select a suitable floating-point or fixed-point data type which guarantees the needed accuracy. Sometimes accuracy can be gained by simply re-arranging the non-associative finite-precision computation. We present a scalable technique that searches for a more optimal evaluation order and show that the gains can be substantial. We have implemented all our techniques and evaluated them on a number of benchmarks from scientific computing and embedded systems, with promising results

    Verification of floating point programs

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    In this thesis we present an approach to automated verification of floating point programs. Existing techniques for automated generation of correctness theorems are extended to produce proof obligations for accuracy guarantees and absence of floating point exceptions. A prototype automated real number theorem prover is presented, demonstrating a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The prototype is tested on correctness theorems for two simple yet nontrivial programs, proving exception freedom and tight accuracy guarantees automatically. The prover demonstrates a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The experiments show how function intervals can be used to combat the information loss problems that limit the applicability of traditional interval arithmetic in the context of hard real number theorem proving

    Verification of floating point programs

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    In this thesis we present an approach to automated verification of floating point programs. Existing techniques for automated generation of correctness theorems are extended to produce proof obligations for accuracy guarantees and absence of floating point exceptions. A prototype automated real number theorem prover is presented, demonstrating a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The prototype is tested on correctness theorems for two simple yet nontrivial programs, proving exception freedom and tight accuracy guarantees automatically. The prover demonstrates a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The experiments show how function intervals can be used to combat the information loss problems that limit the applicability of traditional interval arithmetic in the context of hard real number theorem proving.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

    Automatic Numerical Solving for Auto-active Verification of Floating-Point Programs

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    We present a new process for the verification of numerical programs with tight functional specifications that feature exact arithmetic including selected transcendental functions. The process, which simplifies, derives bounds, and safely eliminates floating-point operations from Verification Conditions (VCs) produced by Why3, is capable of automatically verifying such specifications and is implemented in our new open source tool named PropaFP. We evaluate PropaFP alongside the state-of-the-art in formal verification of floating-point programs where we find that the process is able to verify specifications that current tools are unable to verify. We also present novel branch-and-prune contractions based on linearisations of conjunctions that consist of nonlinear real inequalities with differentiable expressions. These linearisations and contractions are implemented in our new open source numerical prover named LPPaver. The contractions we have discovered are used to significantly improve the ‘pruning’ step of our branch-and-prune algorithm. We evaluate LPPaver alongside state-of-the-art automated solvers for problems involving nonlinear real arithmetic. LPPaver performs comparably and, in some cases, better than these solvers. Together, PropaFP and LPPaver yield the first fully automatically verified implementations of the sine and square root functions with tight functional specifications

    Computer Aided Verification

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    The open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency

    Security and Privacy for the Modern World

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    The world is organized around technology that does not respect its users. As a precondition of participation in digital life, users cede control of their data to third-parties with murky motivations, and cannot ensure this control is not mishandled or abused. In this work, we create secure, privacy-respecting computing for the average user by giving them the tools to guarantee their data is shielded from prying eyes. We first uncover the side channels present when outsourcing scientific computation to the cloud, and address them by building a data-oblivious virtual environment capable of efficiently handling these workloads. Then, we explore stronger privacy protections for interpersonal communication through practical steganography, using it to hide sensitive messages in realistic cover distributions like English text. Finally, we discuss at-home cryptography, and leverage it to bind a user’s access to their online services and important files to a secure location, such as their smart home. This line of research represents a new model of digital life, one that is both full-featured and protected against the security and privacy threats of the modern world

    Tools and Algorithms for the Construction and Analysis of Systems

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    This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers

    Computer Aided Verification

    Get PDF
    The open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency
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