Formal Specification and Verification


 Arline Willis
 2 years ago
 Views:
Transcription
1 Formal Specification and Verification Stefan Ratschan Katedra číslicového návrhu Fakulta informačních technologíı České vysoké učení technické v Praze Stefan Ratschan (FIT ČVUT) PIPSC / 19
2 History of System Design build try Stefan Ratschan (FIT ČVUT) PIPSC / 19
3 History of System Design build model test model Intel Pentium FDIV bug (1994) implement model Stefan Ratschan (FIT ČVUT) PIPSC / 19
4 History of System Design build model prove correctness implement model Stefan Ratschan (FIT ČVUT) PIPSC / 19
5 Example Modulo 8 counter: State: S. = B 3 v 0 = v 0 v 1 = v 0 v 1 v 2 = (v 0 v 1 ) v 2 Stefan Ratschan (FIT ČVUT) PIPSC / 19
6 Example: Digital Circuit Transition relation: T S S T ((v 0, v 1, v 2 ), (v 0, v 1, v 2 )). = ((v 0, v 1, v 2 ), (v 0, v 1, v 2)) (v 0 v 0) (v 1 v 0 v 1 ) (v 2 (v 0 v 1 ) v 2 ) Nondeterminism Stefan Ratschan (FIT ČVUT) PIPSC / 19
7 Formal Specification Transition System: Set of states S Set I S of initial states Transition relation R S S For example: S = B n, I, R given by formulas in propositional logic S is program state (program counter + ranges of variables) I, R given by computer program S = {1,..., n} R n, R given by clock checks and resets: timed systems/automata S = R n, I given by (in)equalities, R given by ordinary differential equations (models of physical systems) S = {1,..., n}, I, R given by (in)equalities, ordinary differential equations, and discrete rules: hybrid (dynamical) systems (models of embedded systems) Stefan Ratschan (FIT ČVUT) PIPSC / 19
8 Formal Specification How to specify whether a given system behaves correctly? First we have to specify properties of single states: state properties Example: error(s): state s is an error state zero(s): state s represents zero Now we can extend this to one behavior of system: A path in a transition system (S, I, R) is an infinite sequence of states s 0 s 1 s 2... s.t. s 0 I, for all i {0, 1,... }, (s i, s i+1 ) R. How to specify whether a given path shows correct/incorrect behavior? Stefan Ratschan (FIT ČVUT) PIPSC / 19
9 Properties on Paths π State property g holds on first element of path: π = g : g(π(0)) State property holds on next element of path: π = Xg : π 1 = g Train eventually reaches full speed π = Fg : there is k 0 s.t. π k = g (F: in the future ) Number of motor rotations always stays in safe area π = Gg : for all k 0, π k = g (G: globally ) The train eventually stops and until then the doors remain closed π = guh : there is i s.t. π i = h and for all j < i, π j = g (U: until ) As long as the plane does not reach full height the fasten seat belts sign is on π = grh : for all j 0, if for all i < j, not π i = g then π j = h (R: release ) Stefan Ratschan (FIT ČVUT) PIPSC / 19
10 Combining Operators If the elevator is called, it will eventually show up (g Fh). The train will never move with open doors G (g h) So: Boolean combinations (,, ). Combining temporal operators. For example: FGg: Eventually property g will hold forever. GFg: Always eventually g will hold. Result: Linear Temporal Logic (LTL) Syntax: every state property is an LTL formula If g and h are LTL formulas then also Xg, guh, grh, Fg, Gg, and guh, g, g h, g h, are LTL formulas. Stefan Ratschan (FIT ČVUT) PIPSC / 19
11 Semantics For a path π and LTL formulas g, h, π = g iff g is a state property and g(π(0)) π = Xg iff π 1 = g π = Fg iff there is k 0 s.t. π k = g π = Gg iff for all k 0, π k = g π = guh iff there is i s.t. π i = h and for all j < i, π j = g. π = grh iff for all j 0, if for all i < j, not π i = g then π j = h π = g iff not π = g π = g h iff π = g and π = h π = g h iff π = g or π = h Stefan Ratschan (FIT ČVUT) PIPSC / 19
12 Specification of System We already can specify correctness of one path. Correctness of system: = g iff for all paths π of, π = g Industrial Usage: PSL (property specification language) LTL + regular expressions Stefan Ratschan (FIT ČVUT) PIPSC / 19
13 Formal Verification Problem: Even finite transition systems may have paths of infinite length! Checking G ok: Check prefixes of paths of length 1, 2,... : bounded model checking BMC(n) In Boolean case, individual checks can be done efficiently by SAT (in practice, not in theory) Especially: Bugs can often be found fast Bounded model checking algorithms for other types of systems: Software: CBMC [Clarke et al., 2004] Hybrid Systems: isat [Fränzle and Herde, 2007, Fränzle et al., 2007]... Stefan Ratschan (FIT ČVUT) PIPSC / 19
14 Full LTL? Unbounded Case? Full LTL [Biere et al., 2003] For every LTL formula φ, for all n, = φ implies BMC(φ, n) Opposite direction? Observation: = Gs iff BMC(Gs, S ) If system does not fulfill Gs then it has an error path of length at most S Theorem for all finite transition system, for all LTL formula φ there is a bound n s.t. for all n n, BMC(φ, n ) iff = φ But: bound may be huge! Stefan Ratschan (FIT ČVUT) PIPSC / 19
15 Unbounded Model Checking If we want to prove correctness over unbounded time, or we search for a bug that shows up after long time. Reach set computation: let R be the set of initial states add reachable state reachable from R until no more new reachable states If for all x R, ok(x), then = G ok. For full LTL (and other temporal logics), more complicated [Clarke et al., 1999]. Stefan Ratschan (FIT ČVUT) PIPSC / 19
16 Unbounded Model Checking for Specific System Types In Boolean case, sets can be represented by (reduced ordered) binary decision diagrams (BDD) BDDs provide a unique representation for Boolean formulas Hence can be used equivalence checking (i.e., specification is another circuit) Other systems: Software: Huge field of software model checking [Jhala and Majumdar, 2009] Timed automata: Uppaal (http://www.uppaal.org) Hybrid systems: HyTech [Henzinger et al., 1997] PHAver [Frehse, 2008] HSolver [Ratschan and She, 2007] Stefan Ratschan (FIT ČVUT) PIPSC / 19
17 Literature I Armin Biere, Alessandro Cimatti, Edmund M. Clarke, Ofer Strichman, and Yunshan Zhu. Bounded model checking. volume 58 of Advances in Computers, pages Elsevier, doi: DOI: /S (03) Edmund Clarke, Daniel Kroening, and Flavio Lerda. A tool for checking ANSIC programs. In Kurt Jensen and Andreas Podelski, editors, Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2004), volume 2988 of Lecture Notes in Computer Science, pages Springer, ISBN X. Edmund M. Clarke, Orna Grumberg, and Doron A. Peled. Model Checking. MIT Press, Stefan Ratschan (FIT ČVUT) PIPSC / 19
18 Literature II M. Fränzle, C. Herde, S. Ratschan, T. Schubert, and T. Teige. Efficient solving of large nonlinear arithmetic constraint systems with complex boolean structure. JSAT Journal on Satisfiability, Boolean Modeling and Computation, Special Issue on SAT/CP Integration, 1: , Martin Fränzle and Christian Herde. Hysat: An efficient proof engine for bounded model checking of hybrid systems. Formal Methods in System Design, 30(3): , Goran Frehse. Phaver: algorithmic verification of hybrid systems past hytech. International Journal on Software Tools for Technology Transfer (STTT), 10(3): , doi: /s x. Thomas A. Henzinger, PeiHsin Ho, and Howard WongToi. HYTECH: a model checker for hybrid systems. International Journal on Software Tools for Technology Transfer (STTT), 1: , Stefan Ratschan (FIT ČVUT) PIPSC / 19
19 Literature III Ranjit Jhala and Rupak Majumdar. Software model checking. ACM Comput. Surv., 41(4):1 54, ISSN doi: Stefan Ratschan and Zhikun She. Safety verification of hybrid systems by constraint propagation based abstraction refinement. ACM Transactions in Embedded Computing Systems, 6(1), Stefan Ratschan (FIT ČVUT) PIPSC / 19
Model Checking: An Introduction
Announcements Model Checking: An Introduction Meeting 2 Office hours M 1:30pm2:30pm W 5:30pm6:30pm (after class) and by appointment ECOT 621 Moodle problems? Fundamentals of Programming Languages CSCI
More informationFormal Verification and Lineartime Model Checking
Formal Verification and Lineartime Model Checking Paul Jackson University of Edinburgh Automated Reasoning 21st and 24th October 2013 Why Automated Reasoning? Intellectually stimulating and challenging
More informationBuilding SMTbased Software Model Checkers: an Experience Report
Building SMTbased Software Model Checkers: an Experience Report Alessandro Armando Artificial Intelligence Laboratory (AILab) Dipartimento di Informatica Sistemistica e Telematica (DIST) University of
More informationAlgorithmic Software Verification
Algorithmic Software Verification (LTL Model Checking) Azadeh Farzan What is Verification Anyway? Proving (in a formal way) that program satisfies a specification written in a logical language. Formal
More informationThe Course. http://www.cse.unsw.edu.au/~cs3153/
The Course http://www.cse.unsw.edu.au/~cs3153/ Lecturers Dr Peter Höfner NICTA L5 building Prof Rob van Glabbeek NICTA L5 building Dr Ralf Huuck NICTA ATP building 2 Plan/Schedule (1) Where and When Tuesday,
More informationT79.186 Reactive Systems: Introduction and Finite State Automata
T79.186 Reactive Systems: Introduction and Finite State Automata Timo Latvala 14.1.2004 Reactive Systems: Introduction and Finite State Automata 11 Reactive Systems Reactive systems are a class of software
More informationlogic language, static/dynamic models SAT solvers Verified Software Systems 1 How can we model check of a program or system?
5. LTL, CTL Last part: Alloy logic language, static/dynamic models SAT solvers Today: Temporal Logic (LTL, CTL) Verified Software Systems 1 Overview How can we model check of a program or system? Modeling
More informationAutomatabased Verification  I
CS3172: Advanced Algorithms Automatabased Verification  I Howard Barringer Room KB2.20: email: howard.barringer@manchester.ac.uk March 2006 Supporting and Background Material Copies of key slides (already
More informationhttp://aejm.ca Journal of Mathematics http://rema.ca Volume 1, Number 1, Summer 2006 pp. 69 86
Atlantic Electronic http://aejm.ca Journal of Mathematics http://rema.ca Volume 1, Number 1, Summer 2006 pp. 69 86 AUTOMATED RECOGNITION OF STUTTER INVARIANCE OF LTL FORMULAS Jeffrey Dallien 1 and Wendy
More informationVerification of multiagent systems via ordered binary decision diagrams: an algorithm and its implementation
Verification of multiagent systems via ordered binary decision diagrams: an algorithm and its implementation Franco Raimondi Alessio Lomuscio Department of Computer Science King s College London London
More informationOn the Modeling and Verification of SecurityAware and ProcessAware Information Systems
On the Modeling and Verification of SecurityAware and ProcessAware Information Systems 29 August 2011 What are workflows to us? Plans or schedules that map users or resources to tasks Such mappings may
More informationFormal Verification Coverage: Computing the Coverage Gap between Temporal Specifications
Formal Verification Coverage: Computing the Coverage Gap between Temporal Specifications Sayantan Das Prasenjit Basu Ansuman Banerjee Pallab Dasgupta P.P. Chakrabarti Department of Computer Science & Engineering
More informationA Logic Approach for LTL System Modification
A Logic Approach for LTL System Modification Yulin Ding and Yan Zhang School of Computing & Information Technology University of Western Sydney Kingswood, N.S.W. 1797, Australia email: {yding,yan}@cit.uws.edu.au
More informationIntroduction to Software Verification
Introduction to Software Verification Orna Grumberg Lectures Material winter 201314 Lecture 4 5.11.13 Model Checking Automated formal verification: A different approach to formal verification Model Checking
More informationFormal Verification by Model Checking
Formal Verification by Model Checking Natasha Sharygina Carnegie Mellon University Guest Lectures at the Analysis of Software Artifacts Class, Spring 2005 1 Outline Lecture 1: Overview of Model Checking
More informationIntroduction to Formal Methods. Các Phương Pháp Hình Thức Cho Phát Triển Phần Mềm
Introduction to Formal Methods Các Phương Pháp Hình Thức Cho Phát Triển Phần Mềm Outline Introduction Formal Specification Formal Verification Model Checking Theorem Proving Introduction Good papers to
More informationSoftware Modeling and Verification
Software Modeling and Verification Alessandro Aldini DiSBeF  Sezione STI University of Urbino Carlo Bo Italy 34 February 2015 Algorithmic verification Correctness problem Is the software/hardware system
More informationVerification of hybrid dynamical systems
Verification of hybrid dynamical systems Jüri Vain Tallinn Technical University/Institute of Cybernetics vain@ioc.ee Outline What are Hybrid Systems? Hybrid automata Verification of hybrid systems Verification
More informationAutomatic Conversion Software for the Safety Verification of Goalbased Control Programs
Automatic Conversion Software for the Safety Verification of Goalbased Control Programs Julia M. B. Braman and Richard M. Murray Abstract Fault tolerance and safety verification of control systems are
More informationTablebased Software Designs: Bounded Model Checking and Counterexample Tracking
Tablebased Software Designs: Bounded Model Checking and Counterexample Tracking Noriyuki Katahira 1, Weiqiang Kong 1, Wanpeng Qian 1, Masahiko Watanabe 2, Tetsuro Katayama 3, Akira Fukuda 4 1 Fukuoka
More informationThe Model Checker SPIN
The Model Checker SPIN Author: Gerard J. Holzmann Presented By: Maulik Patel Outline Introduction Structure Foundation Algorithms Memory management Example/Demo SPINIntroduction Introduction SPIN (Simple(
More informationModel Checking II Temporal Logic Model Checking
1/32 Model Checking II Temporal Logic Model Checking Edmund M Clarke, Jr School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 2/32 Temporal Logic Model Checking Specification Language:
More informationDevelopment of dynamically evolving and selfadaptive software. 1. Background
Development of dynamically evolving and selfadaptive software 1. Background LASER 2013 Isola d Elba, September 2013 Carlo Ghezzi Politecnico di Milano DeepSE Group @ DEIB 1 Requirements Functional requirements
More informationModel Checking based Software Verification
Model Checking based Software Verification 18.52006 Keijo Heljanko Keijo.Heljanko@tkk.fi Department of Computer Science and Engineering Helsinki University of Technology http://www.tcs.tkk.fi/~kepa/ 1/24
More informationA Classification of Model Checkingbased Verification Approaches for Software Models
A Classification of Model Checkingbased Verification Approaches for Software Models Petra Brosch, Sebastian Gabmeyer, Martina Seidl Sebastian Gabmeyer Business Informatics Group Institute of Software
More informationOptimizationbased Trajectory Generation with Linear Temporal Logic Specifications
Optimizationbased Trajectory Generation with Linear Temporal Logic Specifications Eric M. Wolff, Ufuk Topcu, and Richard M. Murray Abstract We present a mathematical programmingbased method for optimal
More informationScheduling Home Health Care with Separating Benders Cuts in Decision Diagrams
Scheduling Home Health Care with Separating Benders Cuts in Decision Diagrams André Ciré University of Toronto John Hooker Carnegie Mellon University INFORMS 2014 Home Health Care Home health care delivery
More informationInvGen: An Efficient Invariant Generator
InvGen: An Efficient Invariant Generator Ashutosh Gupta and Andrey Rybalchenko Max Planck Institute for Software Systems (MPISWS) Abstract. In this paper we present InvGen, an automatic linear arithmetic
More informationSoftware Verification and Testing. Lecture Notes: Temporal Logics
Software Verification and Testing Lecture Notes: Temporal Logics Motivation traditional programs (whether terminating or nonterminating) can be modelled as relations are analysed wrt their input/output
More informationAnalysis of Boolean Programs
Analysis of Boolean Programs Patrice Godefroid 1 Mihalis Yannakakis 2 1 Microsoft Research, pg@microsoft.com 2 Columbia University, mihalis@cs.columbia.edu Abstract. Boolean programs are a popular abstract
More informationChecking MTL Properties of Discrete Timed Automata via Bounded Model Checking
Checing MTL Properties of Discrete Timed Automata via Bounded Model Checing Extended Abstract Bożena WoźnaSzcześnia and Andrzej Zbrzezny IMCS, Jan D lugosz University. Al. Armii Krajowej 13/15, 42200
More informationModel Checking of Software
Model Checking of Software Patrice Godefroid Bell Laboratories, Lucent Technologies SpecNCheck Page 1 August 2001 A Brief History of Model Checking Prehistory: transformational programs and theorem proving
More informationStatic Program Transformations for Efficient Software Model Checking
Static Program Transformations for Efficient Software Model Checking Shobha Vasudevan Jacob Abraham The University of Texas at Austin Dependable Systems Large and complex systems Software faults are major
More informationFormal Verification of Software
Formal Verification of Software Sabine Broda Department of Computer Science/FCUP 12 de Novembro de 2014 Sabine Broda (DCCFCUP) Formal Verification of Software 12 de Novembro de 2014 1 / 26 Formal Verification
More informationImage Computation and Predicate Refinement for RTL Verilog using Word Level Proofs
Image Computation and Predicate Refinement for RTL Verilog using Word Level Proofs Daniel Kroening ETH Zurich Natasha Sharygina University of Lugano Abstract Automated abstraction is the enabling technique
More informationSoftware Model Checking: Theory and Practice
Software Model Checking: Theory and Practice Lecture: Secification Checking  Temoral Logic Coyright 2004, Matt Dwyer, John Hatcliff, and Robby. The syllabus and all lectures for this course are coyrighted
More informationBounded LTL Model Checking with Stable Models
Under consideration for publication in Theory and Practice of Logic Programming 1 Bounded LTL Model Checking with Stable Models KEIJO HELJANKO and ILKKA NIEMELÄ Helsinki University of Technology Department
More informationnpsolver A SAT Based Solver for Optimization Problems
npsolver A SAT Based Solver for Optimization Problems Norbert Manthey and Peter Steinke Knowledge Representation and Reasoning Group Technische Universität Dresden, 01062 Dresden, Germany peter@janeway.inf.tudresden.de
More informationTemporal Logics. Computation Tree Logic
Temporal Logics CTL: definition, relationship between operators, adequate sets, specifying properties, safety/liveness/fairness Modeling: sequential, concurrent systems; maximum parallelism/interleaving
More informationToward ModelBased Verification of Adaptive Allocation Managers
Toward ModelBased Verification of Adaptive Allocation Managers William Leal, Frank Drews, Chang Liu, Lonnie Welch Ohio University { leal@cs.ohiou.edu, drews@ohiou.edu, changliu@cs.ohiou.edu, welch@ohio.edu
More informationSoftware Engineering using Formal Methods
Software Engineering using Formal Methods Model Checking with Temporal Logic Wolfgang Ahrendt 24th September 2013 SEFM: Model Checking with Temporal Logic /GU 130924 1 / 33 Model Checking with Spin model
More informationProgram Synthesis is a Game
Program Synthesis is a Game Barbara Jobstmann CNRS/Verimag, Grenoble, France Outline Synthesis using automata based game theory. MoBvaBon, comparison with MC and LTL. Basics Terminology Reachability/Safety
More informationToday s Agenda. Automata and Logic. Quiz 4 Temporal Logic. Introduction Buchi Automata Linear Time Logic Summary
Today s Agenda Quiz 4 Temporal Logic Formal Methods in Software Engineering 1 Automata and Logic Introduction Buchi Automata Linear Time Logic Summary Formal Methods in Software Engineering 2 1 Buchi Automata
More informationModeling and Verification of SampledData Hybrid Systems
Modeling and Verification of SampledData Hybrid Systems Abstract B. Izaias Silva and Bruce H. Krogh Dept. of Electrical and Computer Engineering, Carnegie Mellon University (Izaias /krogh)@cmu.edu We
More informationAutomated Route Planning for MilkRun Transport Logistics with the NuSMV Model Checker
IEICE TRANS. INF. & SYST., VOL.E96 D, NO.12 DECEMBER 2013 2555 PAPER Special Section on Parallel and Distributed Computing and Networking Automated Route Planning for MilkRun Transport Logistics with
More informationLTL Model Checking with Logic Based Petri Nets
LTL Model Checking with Logic Based Petri Nets Tristan M. Behrens and Jürgen Dix IfI Technical Report Series IfI0704 Impressum Publisher: Institut für Informatik, Technische Universität Clausthal JuliusAlbert
More informationSpecification and Analysis of Contracts Lecture 1 Introduction
Specification and Analysis of Contracts Lecture 1 Introduction Gerardo Schneider gerardo@ifi.uio.no http://folk.uio.no/gerardo/ Department of Informatics, University of Oslo SEFM School, Oct. 27  Nov.
More informationModel Checking of Global Power Management Strategies in Software with Temporal Logic Properties
Model Checking of Global Power Management Strategies in Software with Temporal Logic Properties Rajdeep Mukherjee Indian Institute of Technology Kharagpur rajdeep.mukherjee@cse.iitkgp.ernet.in Subhankar
More informationContextBounded Model Checking of LTL Properties for ANSIC Software. Jeremy Morse, Lucas Cordeiro, Bernd Fischer, Denis Nicole
ContextBounded Model Checking of LTL Properties for ANSIC Software Jeremy Morse, Lucas Cordeiro, Bernd Fischer, Denis Nicole Model Checking C Model checking: normally applied to formal state transition
More informationTeaching Software Model Checking
FORMED 2008 Teaching Software Model Checking Cyrille Artho 1 Research Center for Information Security (RCIS) National Institute of Advanced Industrial Science and Technology (AIST) Tokyo, Japan Kenji Taguchi
More informationA computational model for MapReduce job flow
A computational model for MapReduce job flow Tommaso Di Noia, Marina Mongiello, Eugenio Di Sciascio Dipartimento di Ingegneria Elettrica e Dell informazione Politecnico di Bari Via E. Orabona, 4 70125
More informationFundamentals of Software Engineering
Fundamentals of Software Engineering Model Checking with Temporal Logic Ina Schaefer Institute for Software Systems Engineering TU Braunschweig, Germany Slides by Wolfgang Ahrendt, Richard Bubel, Reiner
More informationSome facts about polynomials modulo m (Full proof of the Fingerprinting Theorem)
Some facts about polynomials modulo m (Full proof of the Fingerprinting Theorem) In order to understand the details of the Fingerprinting Theorem on fingerprints of different texts from Chapter 19 of the
More informationContextBounded Model Checking of LTL Properties for ANSIC Software
ContextBounded Model Checking of LTL Properties for ANSIC Software Jeremy Morse 1, Lucas Cordeiro 2, Denis Nicole 1, Bernd Fischer 1 1 Electronics and Computer Science, University of Southampton, UK
More informationasked the Software Engineering Institute Publishes Software Technology Review A Cliffs Notes Approach for PEOs, PMs, IPTs, and Support Staff
ACQUISITION REFERENCE SOURCE Software Engineering Institute Publishes Software Technology Review A Cliffs Notes Approach for PEOs, PMs, IPTs, and Support Staff ROBERT ROSENSTEIN KIMBERLY BRUNE JOHN FOREMAN
More informationAn Approach to Model Checking Ada Programs
An Approach to Model Checking Ada Programs José Miguel Faria 1,2, João Martins 1, and Jorge Sousa Pinto 1 1 Departamento de Informática / CCTC, Universidade do Minho, Braga, Portugal 2 Critical Software,
More informationMonitoring Metric Firstorder Temporal Properties
Monitoring Metric Firstorder Temporal Properties DAVID BASIN, FELIX KLAEDTKE, SAMUEL MÜLLER, and EUGEN ZĂLINESCU, ETH Zurich Runtime monitoring is a general approach to verifying system properties at
More informationUsing Patterns and Composite Propositions to Automate the Generation of Complex LTL
University of Texas at El Paso DigitalCommons@UTEP Departmental Technical Reports (CS) Department of Computer Science 812007 Using Patterns and Composite Propositions to Automate the Generation of Complex
More informationA Static Analyzer for Large SafetyCritical Software. Considered Programs and Semantics. Automatic Program Verification by Abstract Interpretation
PLDI 03 A Static Analyzer for Large SafetyCritical Software B. Blanchet, P. Cousot, R. Cousot, J. Feret L. Mauborgne, A. Miné, D. Monniaux,. Rival CNRS École normale supérieure École polytechnique Paris
More informationFormal verification of contracts for synchronous software components using NuSMV
Formal verification of contracts for synchronous software components using NuSMV Tobias Polzer Lehrstuhl für Informatik 8 Bachelorarbeit 13.05.2014 1 / 19 Problem description and goals Problem description
More informationHOMEWORK 5 SOLUTIONS. n!f n (1) lim. ln x n! + xn x. 1 = G n 1 (x). (2) k + 1 n. (n 1)!
Math 7 Fall 205 HOMEWORK 5 SOLUTIONS Problem. 2008 B2 Let F 0 x = ln x. For n 0 and x > 0, let F n+ x = 0 F ntdt. Evaluate n!f n lim n ln n. By directly computing F n x for small n s, we obtain the following
More informationModeling, Verification and Testing using Timed and Hybrid. Automata. Stavros Tripakis and Thao Dang
Modeling, Verification and Testing using Timed and Hybrid Automata Stavros Tripakis and Thao Dang September 12, 2008 ii Contents 1 Modeling, Verification and Testing using Timed and Hybrid Automata 1 1.1
More informationSlides based in part on previous lectures by Mahesh Vishwanathan, and by Gul Agha January 21, 2014 1
Contact Information CS477 Formal Software Development Methods Elsa L Gunter 2112 SC, UIUC egunter@illinois.edu http://courses.engr.illinois.edu/cs477 Office: 2112 SC Office Hours: Wednesdays 11:00am 
More informationAutomatic Verification by Abstract Interpretation
Automatic Verification by Abstract Interpretation (Invited tutorial) Patrick Cousot École normale supérieure, Département d informatique, 45 rue d Ulm, 75230 Paris cedex 05, France Patrick.Cousot@ens.fr
More informationInformation Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay
Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture  17 ShannonFanoElias Coding and Introduction to Arithmetic Coding
More informationUsing Hybrid Automata to Express Realtime Properties in VSEII
From: FLAIRS01 Proceedings. Copyright 2001, AAAI (www.aaai.org). All rights reserved. Using Hybrid Automata to Express Realtime Properties in VSEII Andreas Nonnengart Georg Rock Werner Stephan* Deutsches
More informationFrom Hybrid DataFlow Languages to Hybrid Automata: A Complete Translation
From Hybrid DataFlow Languages to Hybrid Automata: A Complete Translation Peter Schrammel peter.schrammel@inria.fr (joint work with Bertrand Jeannet) INRIA Grenoble RhôneAlpes INRIA largescale initiative
More informationCombining Software and Hardware Verification Techniques
Formal Methods in System Design, 21, 251 280, 2002 c 2002 Kluwer Academic Publishers. Manufactured in The Netherlands. Combining Software and Hardware Verification Techniques ROBERT P. KURSHAN VLADIMIR
More informationTEACHING MODEL CHECKING TO UNDERGRADUATES
STUDIA UNIV. BABEŞ BOLYAI, INFORMATICA, Volume LV, Number 3, 2010 TEACHING MODEL CHECKING TO UNDERGRADUATES A.VESCAN AND M. FRENŢIU Abstract. The way program verification is taught in our faculty is firstly
More informationA Classification of Model CheckingBased Verification Approaches for Software Models
Volt Second Workshop on Verification Of Model Transformations, 2013, A Classification of Model CheckingBased Verification Approaches for Software Models Sebastian Gabmeyer a Petra Brosch a Martina Seidl
More informationThe ProB Animator and Model Checker for B
The ProB Animator and Model Checker for B A Tool Description Michael Leuschel and Michael Butler Department of Electronics and Computer Science University of Southampton Highfield, Southampton, SO17 1BJ,
More informationCoverability for Parallel Programs
2015 http://excel.fit.vutbr.cz Coverability for Parallel Programs Lenka Turoňová* Abstract We improve existing method for the automatic verification of systems with parallel running processes. The technique
More informationAutomated ModelBased Testing of Embedded RealTime Systems
Automated ModelBased Testing of Embedded RealTime Systems Jan Peleska jp@tzi.de University of Bremen Bieleschweig Workshop 7 20060505 Outline TechnologieZentrum Informatik Objectives Basic concepts
More informationAutomataBased Verification of Temporal Properties on Running Programs Dimitra Giannakopoulou Klaus Havelund
AutomataBased Verification of Temporal Properties on Running Programs Dimitra Giannakopoulou Klaus Havelund RIACS Technical Report 01.21 August 2001 Presented at the 16 th IEEE International Conference
More informationINF5140: Specification and Verification of Parallel Systems
Motivation INF5140: Specification and Verification of Parallel Systems Lecture 1 Introduction: Formal Methods Gerardo Schneider Department of Informatics University of Oslo INF5140, Spring 2009 Outline
More informationONLINE EXERCISE SYSTEM A WebBased Tool for Administration and Automatic Correction of Exercises
ONLINE EXERCISE SYSTEM A WebBased Tool for Administration and Automatic Correction of Exercises Daniel Baudisch, Manuel Gesell and Klaus Schneider Embedded Systems Group, University of Kaiserslautern,
More informationVerification of Temporal Properties in Automotive Embedded Software
Verification of Temporal Properties in Automotive Embedded Software Djones Lettnin, Pradeep K. Nalla,Jürgen Ruf, Thomas Kropf and Wolfgang Rosenstiel University of Tübingen Department of Computer Engineering
More informationA Formal Approach for Safe Controllers Analysis
A Formal Approach for Safe Controllers Analysis Paulo Borges Mechanical Engineering Department, CT2M / University of Minho Campus of Azurém, 4800058 Guimarães, Portugal pborges@gmail.com José Machado
More informationWord Level Predicate Abstraction and Refinement for Verifying RTL Verilog
Word Level Predicate Abstraction and Refinement for Verifying RTL Verilog Himanshu Jain CMU SCS, Pittsburgh, PA 15213 Natasha Sharygina CMU SEI, Pittsburgh, PA 15213 Daniel Kroening ETH Zürich, Switzerland
More informationConstructing Automata from Temporal Logic Formulas : A Tutorial
Constructing Automata from Temporal Logic Formulas : A Tutorial Pierre Wolper Université de Liège, Institut Montefiore, B28, 4000 Liège, Belgium pw@montefiore.ulg.ac.be, http://www.montefiore.ulg.ac.be/~pw/
More informationRigorous Software Development CSCIGA 3033009
Rigorous Software Development CSCIGA 3033009 Instructor: Thomas Wies Spring 2013 Lecture 11 Semantics of Programming Languages Denotational Semantics Meaning of a program is defined as the mathematical
More informationModelChecking Verification for Reliable Web Service
ModelChecking Verification for Reliable Web Service Shin NAKAJIMA Hosei University and PRESTO, JST nkjm@i.hosei.ac.jp Abstract Modelchecking is a promising technique for the verification and validation
More informationRuntime Verification  Monitororiented Programming  Monitorbased Runtime Reflection
Runtime Verification  Monitororiented Programming  Monitorbased Runtime Reflection Martin Leucker Technische Universität München (joint work with Andreas Bauer, Christian Schallhart et. al) FLACOS
More information2 Temporal Logic Model Checking
Bounded Model Checking Using Satisfiability Solving Edmund Clarke 1, Armin Biere 2, Richard Raimi 3, and Yunshan Zhu 4 1 Computer Science Department, CMU, 5000 Forbes Avenue Pittsburgh, PA 15213, USA,
More informationVerification of Supervisory Control Software Using State Proximity and Merging
Verification of Supervisory Control Software Using State Proximity and Merging Flavio Lerda 1, James Kapinski 2, Edmund M. Clarke 1, and Bruce H. Krogh 2 1 School of Computer Science flerda@cs.cmu.edu,
More informationTesting LTL Formula Translation into Büchi Automata
Testing LTL Formula Translation into Büchi Automata Heikki Tauriainen and Keijo Heljanko Helsinki University of Technology, Laboratory for Theoretical Computer Science, P. O. Box 5400, FIN02015 HUT, Finland
More informationWord Level Predicate Abstraction and Refinement for Verifying RTL Verilog
Word Level Predicate Abstraction and Refinement for Verifying RTL Verilog 28.1 Himanshu Jain CMU SCS, Pittsburgh, PA 15213 Natasha Sharygina CMU SCS and SEI, Pittsburgh, PA 15213 Daniel Kroening ETH Zürich,
More informationA Framework for the Semantics of Behavioral Contracts
A Framework for the Semantics of Behavioral Contracts Ashley McNeile Metamaxim Ltd, 48 Brunswick Gardens, London W8 4AN, UK ashley.mcneile@metamaxim.com Abstract. Contracts have proved a powerful concept
More informationFairness Modulo Theory: A New Approach to LTL Software Model Checking
Fairness Modulo Theory: A New Approach to LTL Software Model Checking Daniel Dietsch, Matthias Heizmann, Vincent Langenfeld, and Andreas Podelski University of Freiburg, Germany Artifact * AEC * CAV *
More informationMODEL CHECKING CONCURRENT AND REALTIME SYSTEMS: THE PAT APPROACH. LIU YANG (B.Sc. (Hons.), NUS)
MODEL CHECKING CONCURRENT AND REALTIME SYSTEMS: THE PAT APPROACH LIU YANG (B.Sc. (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF COMPUTER SCIENCE NATIONAL UNIVERSITY
More informationBusiness Process Verification: The Application of Model Checking and Timed Automata
Business Process Verification: The Application of Model Checking and Timed Automata Luis E. Mendoza Morales Processes and Systems Department, Simón Bolívar University, P.O. box 89000, Baruta, Venezuela,
More informationDevelopment of global specification for dynamically adaptive software
Development of global specification for dynamically adaptive software Yongwang Zhao School of Computer Science & Engineering Beihang University zhaoyw@act.buaa.edu.cn 22/02/2013 1 2 About me Assistant
More informationtutorial: hardware and software model checking
tutorial: hardware and software model checking gerard holzmann and anuj puri { gerard anuj } @research.belllabs.com Bell Labs, USA outline introduction (15 mins) theory and algorithms system modeling
More informationLaurea Specialistica in Ingegneria dell'automazione
Laurea Specialistica in Ingegneria dell'automazione Sistemi in Tempo Reale Luigi Palopoli email: palopoli@sssup.it Tel. 050 883444 Introduzione Lecture Introduction Outline Generalities The development
More informationModel Checking Distributed Software
Model Checking Distributed Software Sagar Chaki September 19, 2014 Software Engineering Institute Carnegie Mellon University Pittsburgh, PA 15213 Model Checking and Me 1997 : Ed visits IIT Kharagpur Just
More informationSECTION 102 Mathematical Induction
73 0 Sequences and Series 6. Approximate e 0. using the first five terms of the series. Compare this approximation with your calculator evaluation of e 0.. 6. Approximate e 0.5 using the first five terms
More informationFormal Verification Toolkit for Requirements and Early Design Stages
Formal Verification Toolkit for Requirements and Early Design Stages Julia M. Badger 1 and Sheena Judson Miller 2 1 NASA Johnson Space Center, Houston, TX 77058, USA 2 Barrios Technology, Houston, TX 77058,
More informationµz An Efficient Engine for Fixed points with Constraints
µz An Efficient Engine for Fixed points with Constraints Kryštof Hoder, Nikolaj Bjørner, and Leonardo de Moura Manchester University and Microsoft Research Abstract. The µz tool is a scalable, efficient
More informationEastern Washington University Department of Computer Science. Questionnaire for Prospective Masters in Computer Science Students
Eastern Washington University Department of Computer Science Questionnaire for Prospective Masters in Computer Science Students I. Personal Information Name: Last First M.I. Mailing Address: Permanent
More informationBrno University of Technology. PhD. Thesis. Symbolic Data Structures for Parametric Verification
Brno University of Technology Faculty of Information Technology PhD. Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Symbolic Data Structures for Parametric
More information