Verification of floating point programs

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

Emerging trends proceedings of the 17th International Conference on Theorem Proving in Higher Order Logics: TPHOLs 2004

technical reportThis volume constitutes the proceedings of the Emerging Trends track of the 17th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2004) held September 14-17, 2004 in Park City, Utah, USA. The TPHOLs conference covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification. There were 42 papers submitted to TPHOLs 2004 in the full research cate- gory, each of which was refereed by at least 3 reviewers selected by the program committee. Of these submissions, 21 were accepted for presentation at the con- ference and publication in volume 3223 of Springer?s Lecture Notes in Computer Science series. In keeping with longstanding tradition, TPHOLs 2004 also offered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief introductory talk and then discuss their work at a poster session. The work-in-progress papers are held in this volume, which is published as a 2004 technical report of the School of Computing at the University of Utah

Verification of floating point programs

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

Verified compilation and optimization of floating-point kernels

When verifying safety-critical code on the level of source code, we trust the compiler to produce machine code that preserves the behavior of the source code. Trusting a verified compiler is easy. A rigorous machine-checked proof shows that the compiler correctly translates source code into machine code. Modern verified compilers (e.g. CompCert and CakeML) have rich input languages, but only rudimentary support for floating-point arithmetic. In fact, state-of-the-art verified compilers only implement and verify an inflexible one-to-one translation from floating-point source code to machine code. This translation completely ignores that floating-point arithmetic is actually a discrete representation of the continuous real numbers. This thesis presents two extensions improving floating-point arithmetic in CakeML. First, the thesis demonstrates verified compilation of elementary functions to floating-point code in: Dandelion, an automatic verifier for polynomial approximations of elementary functions; and libmGen, a proof-producing compiler relating floating-point machine code to the implemented real-numbered elementary function. Second, the thesis demonstrates verified optimization of floating-point code in: Icing, a floating-point language extending standard floating-point arithmetic with optimizations similar to those used by unverified compilers, like GCC and LLVM; and RealCake, an extension of CakeML with Icing into the first fully verified optimizing compiler for floating-point arithmetic.Bei der Verifizierung von sicherheitsrelevantem Quellcode vertrauen wir dem Compiler, dass er Maschinencode ausgibt, der sich wie der Quellcode verhält. Man kann ohne weiteres einem verifizierten Compiler vertrauen. Ein rigoroser maschinen-ü}berprüfter Beweis zeigt, dass der Compiler Quellcode in korrekten Maschinencode übersetzt. Moderne verifizierte Compiler (z.B. CompCert und CakeML) haben komplizierte Eingabesprachen, aber unterstützen Gleitkommaarithmetik nur rudimentär. De facto implementieren und verifizieren hochmoderne verifizierte Compiler für Gleitkommaarithmetik nur eine starre eins-zu-eins Übersetzung von Quell- zu Maschinencode. Diese Übersetzung ignoriert vollständig, dass Gleitkommaarithmetik eigentlich eine diskrete Repräsentation der kontinuierlichen reellen Zahlen ist. Diese Dissertation präsentiert zwei Erweiterungen die Gleitkommaarithmetik in CakeML verbessern. Zuerst demonstriert die Dissertation verifizierte Übersetzung von elementaren Funktionen in Gleitkommacode mit: Dandelion, einem automatischen Verifizierer für Polynomapproximierungen von elementaren Funktionen; und libmGen, einen Beweis-erzeugenden Compiler der Gleitkommacode in Relation mit der implementierten elementaren Funktion setzt. Dann demonstriert die Dissertation verifizierte Optimierung von Gleitkommacode mit: Icing, einer Gleitkommasprache die Gleitkommaarithmetik mit Optimierungen erweitert die ähnlich zu denen in unverifizierten Compilern, wie GCC und LLVM, sind; und RealCake, eine Erweiterung von CakeML mit Icing als der erste vollverifizierte Compiler für Gleitkommaarithmetik

Design and Development of a Digital Radio Frequency Control System for Linear Accelerators

The new control system for Radio Frequency (RF) structures at Legnaro National Laboratories (LNL) is presented in this document. LNL is one of the four national laboratories of the National Institute for Nucler Physics (INFN) and it is devoted to basic research in nuclear physics and nuclear-astrophysics, together with applications of nuclear technologies. The subject of this Ph.D. thesis is indeed the development of a fully digital RF feedback system, focusing on the validation of the RF controller, its programming and its integration in the particle accelerator control system. The RF controller interacts directly with the cavities and it works in a real-time closed loop. It is a set of analog and digital electronics which provides phase, amplitude and frequency corrections to stabilize the RF field in presence of disturbances and vibrations due to other subsystems of the accelerator. The control algorithm is implemented via a programmable device as an FPGA. This increases dramatically the flexibility and the programmability of the controller. The digital board of the RF controller can work in a wide range of the RF spectrum. It is a versatile tool, easy to adapt to 40/80/160/352 MHz resonators, thus spanning all types of cavities of the final SPES configuration. At LNL, it may be used to control RF cavities like bunchers to pulse the beam, superconducting cavities to accelerate the beam and RF quadrupoles (RFQ) to both accelerate and focus the beam. Most of them work in superconducting condition, while the other ones in normal condition. The controlling and the monitoring of the RF controller is done by the particle accelerator control system based on EPICS (Experimental Physics and Industrial Control System). It is a widely adopted software framework for control systems. EPICS is a set of tools, libraries and applications developed collaboratively and used worldwide to create distributed soft real-time control systems for scientific instruments such as particle accelerators. Beam transport was carried out with the 8 cavities working in superconducting mode with the new instruments. The controller kept locked the cavities for few days. In this time the controller has proven to be more stable and reliable than the precedent system. The first chapter of the document introduces the SPES and ALPI facility and the RF subsystem to a certain level of details: RF acceleration concepts and Low Level RF (LLRF) control for an optimum energy gain of the particle beam. In order to better understand the issues faced during the design of the control system it is useful to derive mathematical models of the RF cavities. This is the subject of the second chapter. In the third chapter the disturbance sources of the accelerating field are listed, besides clarifying the stability requirements, the frequency tuning of the cavities and their driving modes. Furthermore, the choice of the frequency sampling is outlined. The fourth chapter introduces the controller in detail. The boards functionalities are highlighted, the fundamental elements of the boards are described as well as the communication between components and boards. The fifth, sixth and seventh chapters describe the main contribution of this Ph.D. thesis. The firmware development for the Field Programmable Field Array, that is the heart of the RF controller, is covered in chapter five, emphasizing the module for the communication with the accelerator control system and the module that implements the control algorithms. The sixth chapter gives an overview of the EPICS framework, focusing on the driver support, the integration of the RF controller with the EPICS based control system is further expanded while in the last section the RF cavity tuning is explained. The seventh chapter is split in two sections. The first section lists the tests performed in order to qualify the boards of the RF controller. The second section analyzes some key parameters acquired during a successful beam test in real working conditions, where the performance of the new controller has been evaluated. Finally, a concluding chapter summarizes the results obtained so far and outlines improvements and future upgrades that can implement new functionalities in the Radio Frequency control system

Proceedings of the Second NASA Formal Methods Symposium

This publication contains the proceedings of the Second NASA Formal Methods Symposium sponsored by the National Aeronautics and Space Administration and held in Washington D.C. April 13-15, 2010. Topics covered include: Decision Engines for Software Analysis using Satisfiability Modulo Theories Solvers; Verification and Validation of Flight-Critical Systems; Formal Methods at Intel -- An Overview; Automatic Review of Abstract State Machines by Meta Property Verification; Hardware-independent Proofs of Numerical Programs; Slice-based Formal Specification Measures -- Mapping Coupling and Cohesion Measures to Formal Z; How Formal Methods Impels Discovery: A Short History of an Air Traffic Management Project; A Machine-Checked Proof of A State-Space Construction Algorithm; Automated Assume-Guarantee Reasoning for Omega-Regular Systems and Specifications; Modeling Regular Replacement for String Constraint Solving; Using Integer Clocks to Verify the Timing-Sync Sensor Network Protocol; Can Regulatory Bodies Expect Efficient Help from Formal Methods?; Synthesis of Greedy Algorithms Using Dominance Relations; A New Method for Incremental Testing of Finite State Machines; Verification of Faulty Message Passing Systems with Continuous State Space in PVS; Phase Two Feasibility Study for Software Safety Requirements Analysis Using Model Checking; A Prototype Embedding of Bluespec System Verilog in the PVS Theorem Prover; SimCheck: An Expressive Type System for Simulink; Coverage Metrics for Requirements-Based Testing: Evaluation of Effectiveness; Software Model Checking of ARINC-653 Flight Code with MCP; Evaluation of a Guideline by Formal Modelling of Cruise Control System in Event-B; Formal Verification of Large Software Systems; Symbolic Computation of Strongly Connected Components Using Saturation; Towards the Formal Verification of a Distributed Real-Time Automotive System; Slicing AADL Specifications for Model Checking; Model Checking with Edge-valued Decision Diagrams; and Data-flow based Model Analysis

Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport

A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications.Väitöstutkimuksen tuloksena on kehitetty uusi tietokoneohjelma varauksettomien ja varauksellisten hiukkasten kuten neutronien, fotonien ja elektronien etenemisen mallinnukseen. MultiTrans-ohjelma mahdollistaa säteilyn etenemisen mallinnuksen mielivaltaisessa 3D-geometriassa. Laskentageometria generoidaan suoraan CAD-mallista, jolloin voidaan käyttää moderneja suunnittelutyökaluja. Laskentaverkko on puumaisesti itsetarkentuva materiaalien rajapinnoilla, joissa hila muodostuu automaattisesti hienojakoisimmaksi. Näin monimutkainenkin geometria voidaan kuvata yksityiskohtaisesti merkittävästi pienemmällä hilapisteiden määrällä verrattuna tasajakoiseen hilaan. Laskentaverkon puumaisuudesta seuraa että ongelmalle löytyy aina myös karkeammat hilaesitykset. Tällöin kuljetusyhtälön iteratiivisessa ratkaisussa voidaan käyttää ns. moniverkkotekniikkaa jossa ongelma ratkaistaan ensin hyvin karkeassa esityksessä ja tätä ratkaisua käytetään alkuarvauksena yhä hienojakoisemmissa hiloissa. Näin nopeutetaan iteratiivisen ratkaisun löytymistä huomattavasti. Myös laskentaverkon puumaisuus ja sen myötä hilapisteiden vähäisempi määrä nopeuttaa iteratiivista ratkaisua. Kyseessä on tiettävästä ensimmäinen puumoniverkkotekniikan sovellutus säteilyn etenemisen mallinnukseen. MultiTransia on testattu erilaisten sädehoitojen (esimerkiksi VTT:n Otaniemen ydintutkimusreaktorilla annettavan boorineutronikaappaushoidon) sekä reaktorifysiikan laskentaongelmiin. Ongelmaksi on jossain määrin osoittautunut säteilyn kulkeutumisyhtälölle käytetty yksinkertaistettu palloharmoninen kehitelmä, jonka tarkkuus ei kaikissa tapauksissa vastaa asetettuja vaatimuksia

Tools and Algorithms for the Construction and Analysis of Systems

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

Real-Time Selective Harmonic Minimization for Multilevel Inverters Using Genetic Algorithm and Artificial Neural Network Angle Generation

This work approximates the selective harmonic elimination problem using Artificial Neural Networks (ANN) to generate the switching angles in an 11-level full bridge cascade inverter powered by five varying DC input sources. Each of the five full bridges of the cascade inverter was connected to a separate 195W solar panel. The angles were chosen such that the fundamental was kept constant and the low order harmonics were minimized or eliminated. A non-deterministic method is used to solve the system for the angles and to obtain the data set for the ANN training. The method also provides a set of acceptable solutions in the space where solutions do not exist by analytical methods. The trained ANN is a suitable tool that brings a small generalization effect on the angles\u27 precision and is able to perform in real time (50/60Hz time window)