DOCSLIB.ORG

Patrick Cousot

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Patrick Cousot Abstract Interpretation: From Theory to Tools Patrick Cousot cims.nyu.edu/~pcousot/ pc12ou)(sot@cims$*.nyu.edu ICSME 2014, Victoria, BC, Canada, 2014-10-02 1 © P. Cousot Bugs everywhere! Ariane 5.01 failure Patriot failure Mars orbiter loss Russian Proton-M/DM-03 rocket (overflow error) (float rounding error) (unit error) carrying 3 Glonass-M satellites (unknown programming error :) unsigned int payload = 18; /* Sequence number + random bytes */ unsigned int padding = 16; /* Use minimum padding */ /* Check if padding is too long, payload and padding * must not exceed 2^14 - 3 = 16381 bytes in total. */ OPENSSL_assert(payload + padding <= 16381); /* Create HeartBeat message, we just use a sequence number * as payload to distuingish different messages and add * some random stuff. * - Message Type, 1 byte * - Payload Length, 2 bytes (unsigned int) * - Payload, the sequence number (2 bytes uint) * - Payload, random bytes (16 bytes uint) * - Padding */ buf = OPENSSL_malloc(1 + 2 + payload + padding); p = buf; /* Message Type */ *p++ = TLS1_HB_REQUEST; /* Payload length (18 bytes here) */ s2n(payload, p); /* Sequence number */ s2n(s->tlsext_hb_seq, p); /* 16 random bytes */ RAND_pseudo_bytes(p, 16); p += 16; /* Random padding */ RAND_pseudo_bytes(p, padding); ret = dtls1_write_bytes(s, TLS1_RT_HEARTBEAT, buf, 3 + payload + padding); Heartbleed (buffer overrun) ICSME 2014, Victoria, BC, Canada, 2014-10-02 2 © P. Cousot Bugs everywhere! Ariane 5.01 failure Patriot failure Mars orbiter loss Russian Proton-M/DM-03 rocket (overflow error) (float rounding error) (unit error) carrying 3 Glonass-M satellites (unknown programming error :) unsigned int payload = 18; /* Sequence number + random bytes */ unsigned int padding = 16; /* Use minimum padding */ /* Check if padding is too long, payload and padding * must not exceed 2^14 - 3 = 16381 bytes in total. */ OPENSSL_assert(payload + padding <= 16381); /* Create HeartBeat message, we just use a sequence number * as payload to distuingish different messages and add * some random stuff. * - Message Type, 1 byte * - Payload Length, 2 bytes (unsigned int) * - Payload, the sequence number (2 bytes uint) * - Payload, random bytes (16 bytes uint) * - Padding */ buf = OPENSSL_malloc(1 + 2 + payload + padding); These are great proofs of the p = buf; /* Message Type */ *p++ = TLS1_HB_REQUEST; • /* Payload length (18 bytes here) */ s2n(payload, p); /* Sequence number */ s2n(s->tlsext_hb_seq, p); /* 16 random bytes */ RAND_pseudo_bytes(p, 16); presence of bugs! p += 16; /* Random padding */ RAND_pseudo_bytes(p, padding); ret = dtls1_write_bytes(s, TLS1_RT_HEARTBEAT, buf, 3 + payload + padding); Heartbleed (buffer overrun) ICSME 2014, Victoria, BC, Canada, 2014-10-02 3 © P. Cousot On the limits of bug finding • Giant software manufacturers can rely on gentle end- users to find myriads of bugs; • But what about: can passengers really help? • Is dynamic/static bug finding always enough? • Proving the absence of bugs is much better! ICSME 2014, Victoria, BC, Canada, 2014-10-02 4 © P. Cousot Formal Methods ICSME 2014, Victoria, BC, Canada, 2014-10-02 5 © P. Cousot Formal Methods • Mathematical and engineering principles applied to the specification, design, construction, verification, maintenance, and evolution of very high quality software • Strongly promoted by Harlan D. Mills since the 70’s e.g. • Harlan D. Mills: The New Math of Computer Programming. Commun. ACM 18(1): 43-48 (1975) • Harlan D. Mills: Software Development. IEEE Trans. Software Eng. 2(4): 265-273 (1976) • Harlan D. Mills: Function Semantics for Sequential Programs. IFIP Congress 1980: 241-250 • ... ICSME 2014, Victoria, BC, Canada, 2014-10-02 6 © P. Cousot Main formal methods for verification • Objective: prove automatically that a program does satisfy a specification given either explicitly or implicitly (e.g. absence of runtime errors) • Deductive methods: use a theorem prover/proof assistant to check a user-provided proof argument • Enumerative, symbolic, bounded, solver(e.g. Z3)- based, interpolation, statistical, etc model-checking: check the specification by enumerating finitely many possibilities • Abstract interpretation: use approximation ideas to consider infinitely many possiblilities ICSME 2014, Victoria, BC, Canada, 2014-10-02 7 © P. Cousot Fundamental limitations • By Gödel’s undecidability, no perfect solution is and will ever be possible: • Deductive methods: the burden is on the end-user and the proofs are exponential in the size of programs • Model-checking: severe unsolved scalability problem • Abstract interpretation: may produce false alarms (but no false negative) • Unsound methods (Coverity, Klocwork, Purify, etc): no correctness guarantee at all. ICSME 2014, Victoria, BC, Canada, 2014-10-02 8 © P. Cousot The Evolution of Formal Methods ICSME 2014, Victoria, BC, Canada, 2014-10-02 9 © P. Cousot testing are returned to the development team for cor- A traditional project experiencing, say, five rection. If quality is not acceptable, the software is errors/KLOC in function testing may have encount- removed from testing and returned to the develop- ered 25 or more errors per KLOC when measured ment team for rework and reverification. from first execution in unit testing. Quality compar- The process of Cleanroom development and cer- isons between traditional and Cleanroom software tification is carried out incrementally. Integration is are meaningful when measured from first execution. continuous, and system functionality grows with the Experience has shown that there is a qualitative addition of successive increments. When the final difference in the complexity of errors found in increment is complete, the system is complete. Cleanroom and traditional code. Errors left behind Because at each stage the harmonious operation of by Cleanroom correctness verification, if any, tend to future increments at the next level of refinement is be simple mistakes easily found and fixed by statis- predefmed by increments already in execution, inter- tical testing, not decp design or interface errars. face and design errors are rare. Cleanroom errors are not only infrequent, but The Cleanroom process is being successfully usually simple as well. applied in IBM and other organizations. The tech- Highhghts of Cleanroom projects reported in nology requires some training and practice, but Table 1Change are described below:of Scale builds on existing skills and software engineering practices. It is readily applied to both new system• 1993: IBM Flight Control. A III-I60 helicopter avionics development and re-engineering and extension of component was developed on schedule in three existing systems. The IBM Cleanroom Software increments comprising 33 KLOC of JOVIAL [SI. Technology Center (CSTC) [4] provides technology A total of 79 corrections were required during statis- transfer support to Cleanroom teams through educa- tical certification for an error rate of 2.3 errors per tion and consultation. KLOC for verified software with no prior execution or debugging. Cleanroom quality results • 2013: Astrée IBM COBOL checks Structuring automatically Facility the (COBOL/SI;).absence of Table 1 summarizes quality results from anyCOBOL/SF, runtime IBM’serror firstin thecommercial control/command Cleanroom Cleanroom projects. Earlier results are reported in softwareproduct, was of developedthe A380 byand a A400Msix-person by team. abstract The [SI. The projects report a ”certification testing interpretationproduct automatically i.e. > 1000 transforms KLOC of unstructuredC failure rate;” for example, the rate for the IBM Flight COBOL programs into functionally equivalent struc- Control project was 2.3 errors per KLOC, andHarlan for D. Mills: Zerotured Defect Software: form Cleanroom for improved Engineering. Advances understandability in Computers 36: 1-41 (1993) and main- the IBM COBOL Structuring Facility project,Patrick 3.4 Cousot, Radhia Cousot, Jérôme Feret, Laurent Mauborgne, Antoine Miné, Xavier Rival: Why does Astrée scale up? Formal Methods in tenance.System Design 35 (3):It 229-264 makes (2009) use of proprietary graph-theoretic errors per KLOC. These numbers represent all algorithms, and exhibits a level of complexity on the errors found in all testing, measured from first-everICSME 2014, Victoria, BC, Canada,order 2014-10-02 of a COBOL compiler. 10 © P. Cousot execution through test completion. That is, the rates The current version of the 85 KLOC PL/I represent residual errors present in the software fol- product required 52 KLOC of new code and 179 lowing correctness verification by development corrections during statistical certification of five teams. increments, for a rate of 3.4 errors per KLOC [7]. The projects in Table 1 produced over a half a Several major components completed certification million lines of Cleanroom code with a range of 0 to with no errors found. In an early support program 5.1 errors per KLOC for an average of 3.3 errors per at a major aerospace corporation, six months of KLOC found in all testing, a remarkable quality intensive use resulted in no functional equivalence achievement indeed. errors ever found [SI. Productivity, including all Traditionally developed software does not specification, design, verification, certification, user undergo correctness verification. It goes from devel- publications, and management, averaged 740 LOC opment to unit testing and debugging, then more per person-month. Challenging schedules defined for debugging in function and system testing. At entry competitive reasons were all met.
Load more

Recommended publications
  • Abstract Interpretation
    Colloquium d’informatique de l’UPMC Sorbonne Universités Abstract Interpretation 29 septembre 2016, 18:00, Amphi 15 4 Place Jussieu, 75005 Paris Patrick Cousot [email protected]@yu.e1du cs.nyu.edu/~pcousot Abstract interpretation, Colloquium d’informatique de l’UPMC Sorbonne Universités, 29 Septembre 2016 1 © P. Cousot This is an abstract interpretation Abstract interpretation, Colloquium d’informatique de l’UPMC Sorbonne Universités, 29 Septembre 2016 2 © P. Cousot Scientific research Abstract interpretation, Colloquium d’informatique de l’UPMC Sorbonne Universités, 29 Septembre 2016 3 © P. Cousot Scientific research • In Mathematics/Physics: trend towards unification and synthesis through universal principles • In Computer science: trend towards dispersion and parcellation through a ever-growing collection of local ad-hoc techniques for specific applications An exponential process, will stop! Abstract interpretation, Colloquium d’informatique de l’UPMC Sorbonne Universités, 29 Septembre 2016 4 © P. Cousot Example: reasoning on computational structures WCET Operational Security protocole Systems biology Axiomatic verification semantics semantics analysis Abstraction Dataflow Model Database refinement Confidentiality checking analysis analysis query Type Partial Obfuscation Dependence Program evaluation inference synthesis Denotational analysis Separation Effect logic Grammar systems semantics CEGAR analysis Theories Program Termination Statistical Trace combination transformation proof semantics model-checking Interpolants Abstract Shape Code analysis
    [Show full text]
  • Precise and Scalable Static Program Analysis of NASA Flight Software
    Precise and Scalable Static Program Analysis of NASA Flight Software G. Brat and A. Venet Kestrel Technology NASA Ames Research Center, MS 26912 Moffett Field, CA 94035-1000 650-604-1 105 650-604-0775 brat @email.arc.nasa.gov [email protected] Abstract-Recent NASA mission failures (e.g., Mars Polar Unfortunately, traditional verification methods (such as Lander and Mars Orbiter) illustrate the importance of having testing) cannot guarantee the absence of errors in software an efficient verification and validation process for such systems. Therefore, it is important to build verification tools systems. One software error, as simple as it may be, can that exhaustively check for as many classes of errors as cause the loss of an expensive mission, or lead to budget possible. Static program analysis is a verification technique overruns and crunched schedules. Unfortunately, traditional that identifies faults, or certifies the absence of faults, in verification methods cannot guarantee the absence of errors software without having to execute the program. Using the in software systems. Therefore, we have developed the CGS formal semantic of the programming language (C in our static program analysis tool, which can exhaustively analyze case), this technique analyses the source code of a program large C programs. CGS analyzes the source code and looking for faults of a certain type. We have developed a identifies statements in which arrays are accessed out Of static program analysis tool, called C Global Surveyor bounds, or, pointers are used outside the memory region (CGS), which can analyze large C programs for embedded they should address.
    [Show full text]
  • Lecture Notes in Computer Science 1145 Edited by G
    Lecture Notes in Computer Science 1145 Edited by G. Goos, J. Hartmanis and J. van Leeuwen Advisory Board: W. Brauer D. Gries J. Stoer Radhia Cousot David A. Schmidt (Eds.) Static Analysis Third International Symposium, SAS '96 Aachen, Germany, September 24-26, 1996 Proceedings ~ Springer Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editors Radhia Cousot l~cole Polytechnique, Laboratoire d'Inforrnatique F-91128 Palaiseau Cedex, France E-mail: radhia.cousot @lix.polytechnique.fr David A. Schmidt Kansas State University, Department of Computing and Information Sciences Manhattan, KS 66506, USA E-maih [email protected] Cataloging-in-Publication data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Static analysis : third international symposium ; proceedings / SAS '96, Aachen, Germany, September 24 - 26, 1996. Radhia Cousot ; David A. Schmidt (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo : Springer, 1996 (Lecture notes in computer science ; Vol. 1145) ISBN 3-540-61739-6 NE: Cousot, Radhia [Hrsg.]; SAS <3, 1996, Aachen>; GT CR Subject Classification (1991): D.1, D.2.8, D.3.2-3,F.3.1-2, F.4.2 ISSN 0302-9743 ISBN 3-540-61739-6 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer -Verlag.
    [Show full text]
  • On Abstraction in Software Verification ‹
    On Abstraction in Software Verification ‹ Patrick Cousot1 and Radhia Cousot2 1 École normale supérieure, Département d'informatique, 45 rue d'Ulm, 75230 Paris cedex 05, France [email protected] www.di.ens.fr/~cousot/ 2 CNRS & École polytechnique, Laboratoire d'informatique, 91128 Palaiseau cedex, France [email protected] lix.polytechnique.fr/~rcousot Abstract. We show that the precision of static abstract software check- ing algorithms can be enhanced by taking explicitly into account the ab- stractions that are involved in the design of the program model/abstract semantics. This is illustrated on reachability analysis and abstract test- ing. 1 Introduction Most formal methods for reasoning about programs (such as deductive meth- ods, software model checking, dataflow analysis) do not reason directly on the trace-based operational program semantics but on an approximate model of this semantics. The abstraction involved in building the model of the program seman- tics is usually left implicit and not discussed. The importance of this abstraction appears when it is made explicit for example in order to discuss the soundness and (in)completeness of temporal-logic based verification methods [1, 2]. The purpose of this paper is to discuss the practical importance of this ab- straction when designing static software checking algorithms. This is illustrated on reachability analysis and abstract testing. 2 Transition Systems We follow [3, 4] in formalizing a hardware or software computer system by a transition system xS; t; I; F; Ey with set of states S, transition relation t Ď pS ˆ Sq, initial states I Ď S, erroneous states E Ď S, and final states F Ď S.
    [Show full text]
  • Caterina Urban
    CATERINA URBAN DATE AND PLACE OF BIRTH March 9th, 1987, Udine, Italy NATIONALITY Italian ADDRESS École Normale Supérieure, 45 rue d’Ulm, 75005 Paris, France EMAIL [email protected] WEBPAGE https://caterinaurban.github.io DBLP http://dblp.org/pers/hd/u/Urban:Caterina GOOGLE SCHOLAR http://scholar.google.it/citations?user=4-u1_HIAAAAJ CURRENT POSITION • INRIA, Paris, France — Research Scientist (Chargé de Recherche), Feb 2019 - Now EDUCATION • École Normale Supérieure, Paris, France — Ph.D. in Computer Science, Dec 2011 - July 2015 Subject: Static Analysis by Abstract Interpretation of Functional Temporal Properties of Programs Advisors: Radhia Cousot (Emeritus Research Director, CNRS, Paris, France) and Antoine Miné (Research Scientist, CRNS, Paris, France) Final mark: summa cum laude • Menlo College, Atherton, USA — Fifth Summer School on Formal Techniques, May 2015 • Università degli Studi di Udine, Italy — Master’s degree in Computer Science, Fall 2009 - Fall 2011 Final mark: summa cum laude • Università degli Studi di Udine, Italy — Bachelor’s degree in Computer Science, Fall 2006 - Fall 2009 Final mark: summa cum laude GRANTS • Industrial Grant, Fujitsu: “Formal Verification Techniques for Machine Learning Systems”, Oct 2021 - Sep 2022 • Industrial Grant, Airbus: “State of the Art in Formal Methods for Artificial Intelligence”, 2020 • Principal Investigator, ETH Career Seed Grant, ETH Zurich: “Static Analysis for Data Science Applications”, 30kCHF, Jan 2017 - Dec 2017 AWARDS AND HONORS • Invited Paper at IJCAI 2016 - Sister Conference
    [Show full text]
  • Abstract Interpretation and Application to Logic Programs ∗
    Abstract Interpretation and Application to Logic Programs ∗ Patrick Cousot Radhia Cousot LIENS, École Normale Supérieure LIX, École Polytechnique 45, rue d’Ulm 91128 Palaiseau cedex (France) 75230 Paris cedex 05 (France) [email protected] [email protected] Abstract. Abstract interpretation is a theory of semantics approximation which is usedfor the con­ struction of semantics-basedprogram analysis algorithms (sometimes called“data flow analysis”), the comparison of formal semantics (e.g., construction of a denotational semantics from an operational one), the design of proof methods, etc. Automatic program analysers are used for determining statically conservative approximations of dy­ namic properties of programs. Such properties of the run-time behavior of programs are useful for debug­ ging (e.g., type inference), code optimization (e.g., compile-time garbage collection, useless occur-check elimination), program transformation (e.g., partial evaluation, parallelization), andeven program cor­ rectness proofs (e.g., termination proof). After a few simple introductory examples, we recall the classical framework for abstract interpretation of programs. Starting from a standardoperational semantics formalizedas a transition system, classes of program properties are first encapsulatedin collecting semantics expressedas fixpoints on partial orders representing concrete program properties. We consider invariance properties characterizing the descendant states of the initial states (corresponding to top/down or forward analyses), the ascendant states of the final states (corresponding to bottom/up or backward analyses) as well as a combination of the two. Then we choose specific approximate abstract properties to be gatheredabout program behaviors andexpress them as elements of a poset of abstract properties. The correspondencebetween concrete andabstract properties is establishedby a concretization andabstraction function that is a Galois connection formalizing the loss of information.
    [Show full text]
  • 1 Employment 2 Education 3 Grants
    STEPHEN F. SIEGEL Curriculum Vitæ Department of Computer and Information Sciences email: [email protected] 101 Smith Hall web: http://vsl.cis.udel.edu/siegel.html University of Delaware tel: (302) 831{0083, fax: (302) 831{8458 Newark, DE 19716 citizenship: U.S.A. 1 Employment Associate Professor, Department of Computer and Information Sciences and Department of Math- ematical Sciences, University of Delaware, September 2012 to present Assistant Professor, Department of Computer and Information Sciences and Department of Math- ematical Sciences, University of Delaware, September 2006 to August 2012 Senior Research Scientist, Laboratory for Advanced Software Engineering Research, Department of Computer Science, University of Massachusetts Amherst, August 2001 to August 2006 Senior Software Engineer, Laboratory for Advanced Software Engineering Research, Department of Computer Science, University of Massachusetts Amherst, August 1998 to July 2001 Visiting Assistant Professor, Department of Mathematics, University of Massachusetts Amherst, September 1996 to August 1998 Visiting Assistant Professor, Department of Mathematics, Northwestern University, September 1993 to June 1996 2 Education Ph.D., Mathematics, University of Chicago, August 1993 (Advisor: Prof. Jonathan L. Alperin) M.Sc., Mathematics, Oxford University, June 1989 B.A., Mathematics, University of Chicago, June 1988 3 Grants • Principal Investigator, National Science Foundation Award CCF-0953210 Supplement 001, Extension of TASS to Chapel, June 1, 2011 { May 31, 2012. Award amount: $99,333. • Principal Investigator, National Science Foundation Award CNS-0958512, Computing Research Infras- tructure program, II-New: System Acquisition for the Development of Scalable Parallel Algorithms for Scientific Computing, May 1, 2010 { April 30, 2013. Co-PIs: Peter B. Monk, Douglas M. Swany, and Krzysztof Szalewicz.
    [Show full text]
  • Reliability and Safety of Critical Device Software Systems Neeraj Kumar Singh
    Reliability and Safety of Critical Device Software Systems Neeraj Kumar Singh To cite this version: Neeraj Kumar Singh. Reliability and Safety of Critical Device Software Systems. Other [cs.OH]. Université Henri Poincaré - Nancy 1, 2011. English. NNT : 2011NAN10129. tel-01746287 HAL Id: tel-01746287 https://hal.univ-lorraine.fr/tel-01746287 Submitted on 29 Mar 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. AVERTISSEMENT Ce document est le fruit d'un long travail approuvé par le jury de soutenance et mis à disposition de l'ensemble de la communauté universitaire élargie. Il est soumis à la propriété intellectuelle de l'auteur. Ceci implique une obligation de citation et de référencement lors de l’utilisation de ce document. D’autre part, toute contrefaçon, plagiat, reproduction illicite encourt une poursuite pénale. ➢ Contact SCD Nancy 1 : [email protected] LIENS Code de la Propriété Intellectuelle. articles L 122. 4 Code de la Propriété Intellectuelle. articles L 335.2- L 335.10 http://www.cfcopies.com/V2/leg/leg_droi.php http://www.culture.gouv.fr/culture/infos-pratiques/droits/protection.htm UFR STMIA École Doctorale IAEM Lorraine Fiabilité et Sûreté des Systèmes Informatiques Critiques Thèse présentée et soutenue publiquement le 15 novembre 2011 pour l’obtention du Doctorat de l’Université Henri Poincaré - Nancy 1 (Mention : informatique) par Neeraj Kumar SINGH Composition du jury : Rapporteurs : Prof.
    [Show full text]
  • Project-Team Abstraction Abstract Interpretation
    INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE Project-Team Abstraction Abstract Interpretation Paris - Rocquencourt Theme : Programs, Verification and Proofs c t i v it y ep o r t 2009 Table of contents 1. Team .................................................................................... 1 2. Overall Objectives ........................................................................ 1 2.1. Overall Objectives 1 2.2. Highlights of the Year 2 3. Scientific Foundations .....................................................................2 3.1. Abstract Interpretation Theory 2 3.2. Formal Verification by Abstract Interpretation 2 3.3. Advanced Introductions to Abstract Interpretation 3 4. Application Domains ......................................................................3 4.1. Certification of Safety Critical Software 3 4.2. Security Protocols 4 4.3. Abstraction of Biological Cell Signaling Networks 4 5. Software ................................................................................. 5 5.1. The Astrée Static Analyzer 5 5.2. The Apron Numerical Abstract Domain Library 5 5.3. Translation Validation 6 5.4. ProVerif 6 5.5. CryptoVerif 7 6. New Results .............................................................................. 8 6.1. Space Software Validation using Abstract Interpretation 8 6.2. Why does Astrée scale up? 8 6.3. Design of the Apron Library 8 6.4. Hierarchy of Semantics by Abstract Interpretation and Formal Proofs 9 6.5. Semantics Design by Abstract Interpretation 9 6.5.1. Bi-inductive Definitions and Bifinitary Semantics of the Eager Lambda-Calculus 9 6.5.2. Abstract Semantics of Resolution-Based Logic Languages 9 6.6. Verification of Security Protocols in the Formal Model 10 6.6.1. Book Chapter on Using Horn Clauses for the Verification of Security Protocols 10 6.6.2. Extensions of ProVerif 10 6.7. Verification of Security Protocols in the Computational Model 11 6.7.1.
    [Show full text]
  • Introduction to Abstract Interpretation
    Introduction to Abstract Interpretation Bruno Blanchet D´epartement d'Informatique Ecole´ Normale Sup´erieure, Paris and Max-Planck-Institut fur¨ Informatik [email protected] November 29, 2002 Abstract We present the basic theory of abstract interpretation, and its application to static program analysis. The goal is not to give an exhaustive view of abstract interpretation, but to give enough background to make papers on abstract interpretation more under- standable. Notations: λx.M denotes the function that maps x to M. f[x 7! M] denotes the function f extended so that x is mapped to M. If f was already defined at x, the new binding replaces the old one. 1 Introduction The goal of static analysis is to determine runtime properties of programs without executing them. (Scheme of an analyzer: Program ! Analyzer ! Properties.) Here are some examples of properties can be proved by static analysis: • For optimization: { Dead code elimination { Constant propagation { Live variables { Stack allocation (more complex) • For verification: { Absence of runtime errors: division by zero, square root of negative numbers, overflows, array index out of bounds, pointer dereference outside objects, . { Worst-case execution time (see Wilhelm's work with his team and AbsInt) { Security properties (secrecy, authenticity of protocols, . ) 1 However, most interesting program properties are undecidable. The basic result to show undecidability is the undecidability of the halting problem. Proof By contradiction. Assume that there exists Halt(P,E) returning Yes when P termi- nates on entry E, No otherwise. Consider P'(P) = if Halt(P,P) then loop else stop. • If P'(P') loops, Halt(P',P') = true, so P'(P') stops: contradiction.
    [Show full text]
  • A Casual Introduction to Abstract Interpretation Examples of Abstractions
    CMACS Workshop on Systems Biology and Formals Methods (SBFM'12) Abstractions of Dora Maar by Picasso A casual introduction to Abstract Interpretation NYU, 29–30 March 2012 Patrick Cousot cs.nyu.edu/~pcousot di.ens.fr/~cousot CMACS Workshop on Systems Biology and Formals Methods (SBFM'12), NYU, 29–30 March 2012 1 © P. Cousot CMACS Workshop on Systems Biology and Formals Methods (SBFM'12), NYU, 29–30 March 2012 3 © P. Cousot Pixelation of a photo by Jay Maisel Examples of Abstractions www.petapixel.com/2011/06/23/how-much-pixelation-is-needed-before-a-photo-becomes-transformed/ P. Cousot & R. Cousot. A gentle introduction to formal verification of computer systems by abstract interpretation. In Logics and Languages for Reliability and Security, J. Esparza, O. Grumberg, & Image credit: Photograph by Jay Maisel M. Broy (Eds), NATO Science Series III: Computer and Systems Sciences, © IOS Press, 2010, Pages 1—29. CMACS Workshop on Systems Biology and Formals Methods (SBFM'12), NYU, 29–30 March 2012 2 © P. Cousot CMACS Workshop on Systems Biology and Formals Methods (SBFM'12), NYU, 29–30 March 2012 4 © P. Cousot II.P. Combination of abstract domains Abstract interpretation-based tools usually use several different abstract domains, since the design of a complex one is best decomposed into a combination of simpler abstract domains. Here are a few abstract 2 An old idea... domain examples used inNumerical the Astree´ static abstractions analyzer: in Astrée y y y 20 000 years old picture in a spanish cave: x x x Collecting semantics:1, 5 Intervals:20 Simple congruences:24 partial traces x [a, b] x a[b] ⌃ ⌅ y y y t x x The concrete is not always well-known! Octagons:25 Ellipses:26 Exponentials:27 x y a x2 + by2 axy d abt y(t) abt ± ± ⇥ − ⇥ − ⇥ ⇥ CMACS Workshop on Systems Biology and Formals Methods (SBFM'12), NYU, 29–30 March 2012 5 © P.
    [Show full text]
  • On Various Abstract Understandings of Abstract Interpretation
    1 On Various Abstract Understandings of Abstract Interpretation Patrick COUSOT Courant Institute of Mathematical Sciences New York University cp ousot@ ci ms. n u.ey ud , cimn.s u . e dy/u ˜ o spcu ot Abstract—We discuss several possible understandings and is correct/sound for all programs of a programming language, misunderstandings of Abstract Interpretation theory and practice it is necessary to compare the results of the static analysis at various levels of abstraction. with a formal definition of the program semantics (sometimes Keywords-Abstract Interpretation, Abstraction, Completeness, called a model) [7]. Formal methods, Semantics, Semantics, Soundness, Static anal- Abstract Interpretation goes much further by showing how ysis, Verification. to formally construct the static analyzer from the definition of program properties as specified by the semantics [8]. ABSTRACT INTERPRETATION FOR STATIC ANALYSIS These ideas lead to mechanically checked static analyzers Abstract Interpretation (see [10], [11] for gentle introduc- [19], and hopefully in the future, to mechanically constructed tions) can be, and is often, understood in a very narrow sense: static analyzers (as has been done by hand, e.g. in [3] for type an algorithm for static analysis of sequential programs with systems). widening and narrowing, even maybe restricted to interval analysis only. HIERARCHIES OF ABSTRACTIONS This was indeed the origin of the concept [6] and the very first fully automatic infinitary static analysis, rapidly followed A more profound understanding of Abstract Interpretation by more expressive and costly relational analyzes [15]. leads to a much broader scope of application. To cope with For programming languages, i.e. infinitely many pro- complex problems, e.g.
    [Show full text]