Laboratory for Advanced Software Engineering Research UMASS Lori A. Clarke University of Massachusetts Finite State Verification: An Emerging Technology for Validating Software Systems

Laboratory for Advanced Software Engineering Research UMASS Outline of Presentation Lay of the Land: –Testing, Theorem-proving based verification, Finite state verification(FSV) Overview of FSV Look at 3 Different Approaches to FSV –Model Checking –Flow Equations –Data Flow Analysis Major Challenges to be Addressed

Laboratory for Advanced Software Engineering Research UMASS Sorry State of Affairs Testing consumes about half the cost of s/w development Maintenance consumes about 80% of the full life cycle costs--much of that devoted to testing Most companies use ad hoc QA practices Unhappy with the results; Unhappy with the cost –Failed projects –Delayed product releases

Laboratory for Advanced Software Engineering Research UMASS Testing can: –Uncover failures –Show specifications are (not) met for specific test cases –Be an indication of overall reliability cannot: –Prove that a program will/will not behave in a particular way

Laboratory for Advanced Software Engineering Research UMASS Must do better! Increasing number of high assurance applications –Medical applications –Flight control software –Electronic commerce Increasing number of complex systems –Systems of systems –Distributed systems

Laboratory for Advanced Software Engineering Research UMASS Distributed Systems Better performance, better flexibility, but there is a cost distributed systems are more difficult to test than sequential systems –number of execution paths can grow exponentially with the number of processes –Testing can not even demonstrate that a system works on the selected/executed test data

Laboratory for Advanced Software Engineering Research UMASS T1T ,6 2,6 5,9 3,6 4 1,7 2,71,8 3,72,8 3,8 7 Complexity of Distributed Systems

Laboratory for Advanced Software Engineering Research UMASS T1T ,6 2,6 5,9 3,6 4 1,7 2,71,8 3,72,8 3,8 7 Uncertainty of Testing X:=1 X: =2 X==?

Laboratory for Advanced Software Engineering Research UMASS Formal Verification: An Alternative to Testing Theorem Proving Based Verification –Use mathematical reasoning –Prove properties about all possible executions –Difficult and error prone Finite State Verification –Reason about a finite model of the system –Prove properties about all possible executions, but not as powerful as theorem proving –Almost a totally automated process

Laboratory for Advanced Software Engineering Research UMASS Spectrum of Difficulty Ad-hoc Testing Systematic Testing Theorem Proving Finite State Verification Arbitrary testcases Reqts based test planning Requirements captured as properties Properties guaranteed on all possible executions

Laboratory for Advanced Software Engineering Research UMASS Finite State Verification (FSV) Holds the promise of providing a cost effective way of verifying important properties about a system –Not all faults are created equal –Invest effort into most important properties Several promising prototypes –Reachability Based SPIN or Symbolic Model Checking (SMV) –Flow Equations Integer Necessary Conditions (INCA) –Data Flow Analysis FLAVERS

Laboratory for Advanced Software Engineering Research UMASS Property System Property Translator System Translator Reasoning Engine System Model Property Verified Property Representation High-Level Architecture of FSV Systems Counter Examples for Model

Laboratory for Advanced Software Engineering Research UMASS Conservative Analysis If property verified, property holds for all possible executions of the system If property not verified: –An error OR –A spurious result System model abstracts information to be tractable Conservative abstractions over-approximate behavior If inconsistency relies upon over-approximations, then a spurious result –e.g. counter example corresponds to an infeasible path

Laboratory for Advanced Software Engineering Research UMASS System Model Depends on property being verified Eliminate information that does not impact the proof Abstraction techniques allows “states” in the model to be reduced/collapsed

Laboratory for Advanced Software Engineering Research UMASS Some Properties of Properties State-based versus event-based Once temperature is greater than 100 degrees, lock is true Elevator door closes before elevator moves Single locations versus (sub)paths –Deadlock or race conditions –Sequences of states or events Safety versus Liveness

Laboratory for Advanced Software Engineering Research UMASS A quick look at three approaches to FSV Model Checking Flow Equations Data Flow Analysis Big Disclaimer!

Laboratory for Advanced Software Engineering Research UMASS Model Checking: some history Originally proposed for hardware Early 80’s: E. Clarke and Emerson; Quielle and Sifakis Late 80’s: Improved algorithms and property notations (E. Clarke, Emerson, Sistla) 90’s: Symbolic Model Checking (SMV) and other optimizations (Burch, E. Clarke, Dill, Long, and McMillan) Current: Hybrid approaches

Laboratory for Advanced Software Engineering Research UMASS Model Checking Properties usually expressed in a temporal logic System represented as a (possibly “abstracted”) reachability graph –State based Reasoning engine propagates valid subformulas through the graph

Laboratory for Advanced Software Engineering Research UMASS Temporal Logic Property System Property Translator System Translator Subformula propagation State-based Reachability Graph Property Verified Property Representation High-Level Architecture of Model Checking Counter Examples for Model

Laboratory for Advanced Software Engineering Research UMASS Representing Properties CTL operators –G - globally –F - future –X- next –U - until At a state in the model: –AG p means that for all paths from this state, p is true and will remain true –EF p means that for some path from this state, p will eventually be true

Laboratory for Advanced Software Engineering Research UMASS Propagating Propositions p AF p

Laboratory for Advanced Software Engineering Research UMASS Example: mutual exclusion protocol * reachability graph n1,n2, turn=0 t1,n2, turn=1 c1,n2, turn=1 t1,t2, turn=1 c1,t2, turn=1 n1,t2, turn=2 n1,c2, turn=2 t1,t2, turn=2 t1,c2, turn=2 * McMillan

Laboratory for Advanced Software Engineering Research UMASS Example Property AG(t1=>AF c1) If process1 tries (t1) to get the lock then eventually it gets into its critical region (c1) Note, would like to prove this for all processes but FSV approaches usually must instantiate property (and system)

Laboratory for Advanced Software Engineering Research UMASS Example: propagation n1,n2, turn=0 t1,n2, turn=1 c1,n2, turn=1 t1,t2, turn=1 c1,t2, turn=1 n1,t2, turn=2 n1,c2, turn=2 t1,t2, turn=2 t1,c2, turn=2 AF c1 AG(t1=>AF c1) AF c1 t1=> AF c1

Laboratory for Advanced Software Engineering Research UMASS Formula Propagation Propagate until no change –propagate from smaller to larger subformulas –“smart” algorithm: linear in the size of model and size of the formula Many optimization techniques –Symbolic model checking –Use efficient algorithms that propagate subformula for sets of values

Laboratory for Advanced Software Engineering Research UMASS Symbolic Model Checking With abstraction, nodes may represent sets of values –BDD –Worst case bound exponential in size of the model –For some examples, able to deal with states a b b c ab+c 01 a b c c c c

Laboratory for Advanced Software Engineering Research UMASS Some observations: Model Checking Worst case bound linear in size of the model –Model exponential Experimentally often very effective Not clear if model checking or symbolic model checking is superior –Depends on the problem

Laboratory for Advanced Software Engineering Research UMASS Flow Equations: some history Originally proposed for designs Early 80’s: Initial development (Avrunin, Dillon, and Wileden) 90’s: Optimized and extended to real-time (Avrunin, Buy, Corbett, Dillon, and Wileden) Current: INCA prototype (Avrunin, Corbett, and Siegel)

Laboratory for Advanced Software Engineering Research UMASS Flow Equations Model system as finite state automata Use extended network flow inequalities to capture legal flow through a concurrent system Represent negation of the property as a set of inequalities

Laboratory for Advanced Software Engineering Research UMASS Solving the Set of Inequalities Determine if combined system of inequalities is consistent –Use integer linear programming If consistent, there is a set of flows through automata that violate the property Provides guidance for trace through the model (but may not be executable)

Laboratory for Advanced Software Engineering Research UMASS PropertySystem Property Translator FSA Translator Integer Linear Programming System Set of Inequalities Property Verified (no solution) Set of Inequalities High-Level Architecture of INCA Counter Examples for Model (solution) System Translator FSA’s

Laboratory for Advanced Software Engineering Research UMASS Example: Process Flow Equations x1 = x0 + x2 x1 = x2 + x3 x0 = 1; x3 = 1 x9 = x8 + x10 x9 = x10 + x11 x8 = 1; x11 = 1 x5 + x7 = x4 + x6 x5 = x6 x4 = 1; x7 = 1 x1 x2 x4 x5 x6 x9 x10x0x8 x3 x7 x11 a a’ b’ b

Laboratory for Advanced Software Engineering Research UMASS Example: Inter-process Flow Equations x1 x2 x4 x5 x6 x9 x10x0x8 x3 x7 x11 a a’ b’ b x1 = x5 x9 = x6

Laboratory for Advanced Software Engineering Research UMASS Solving for a property Property: For all paths, event a occurs more than event b represent complement ¬(x1 > x9) = = (x1 ≤ x9) x1 = x0 + x2 x1 = x2 + x3 x0 = 1; x3 = 1 x5 + x7 = x4 + x6 x5 = x6 x4 = 1; x7 = 1 x9 = x8 + x10 x9 = x10 + x11 x8 = 1; x11=1 x1 = x5 x9 =x6  j: 0 ≤ xj Solution exists e.g., x2, x10 = 0, all other xi = 1 => property does not hold

Laboratory for Advanced Software Engineering Research UMASS Seeing the counter example Property: For all paths, event a occurs more than event b x1 x2 x4 x5 x6 x9 x10 x0x8 x3 x7 x11 a a’ b’ b x2, x10 = 0, all other xi = 1

Laboratory for Advanced Software Engineering Research UMASS Some Limitations Integer Linear Programming has an exponential worst case bound Inter-process order information is not preserved –only checks whether event counts are consistent –Like most static techniques, may produce spurious results

Laboratory for Advanced Software Engineering Research UMASS Some Benefits Does not enumerate the state space! Integer linear Programming is often very efficient –Empirical evidence: linear inequality systems usually grow linearly and take sub-exponential times to solve In practice, INCA is usually an effective technique

Laboratory for Advanced Software Engineering Research UMASS Data Flow Based Verification: some history Mid-70’s: Originally proposed for def-ref anomalies in FORTRAN (Osterweil and Fosdick) Early 80’s: Extended to general properties (Olender and Osterweil) & concurrency (Taylor and Osterweil) 90’s: Deadlock detection (Masticola and Ryder); Efficient representation of concurrency & incremental precision improvement (Dwyer and L. Clarke) Recent: Optimizations, Java (Avrunin, L. Clarke, Cobleigh, Naumovich, and Osterweil)

Laboratory for Advanced Software Engineering Research UMASS Data Flow Analysis: FLAVERS Represents property as a finite state automaton System model is collection of annotated control flow graphs –Inter-process communication and interleavings are represented with additional edges –does not enumerate all reachable states –over-approximates relevant executable behaviors Reasoning engine based on data flow analysis

Laboratory for Advanced Software Engineering Research UMASS Property System Property Translator System Translator State Propagation Collection of annotated CFG’s Property Verified FSA High-Level Architecture of FSV Systems Counter Examples from Model

Laboratory for Advanced Software Engineering Research UMASS Modeling the System T1T ,6 2,6 5,9 3, , ,71,8 3,72,8 3,8 State explosion

Laboratory for Advanced Software Engineering Research UMASS Modeling the System T1T Automatically creates the program model from source code Instead of the state space, explicitly represents interleaved execution via edges Smaller model Loss of precision

Laboratory for Advanced Software Engineering Research UMASS Representing Properties Example: close, open,move 0 1 open close 2 move close move open

Laboratory for Advanced Software Engineering Research UMASS State Propagation States of the property are propagated through the model The property is proved if only accepting (non-accepting) states are contained in the final node of the model

Laboratory for Advanced Software Engineering Research UMASS Example public static void main (String [] args) { … if (elevatorStopped) {... openDoors(); } recordState(); if (elevatorStopped) {... closeDoors(); } moveToNextFloor(); } if open close if move

Laboratory for Advanced Software Engineering Research UMASS Example if open close if move close, open,move 0 1 open close 2 move close move open {0} {1} {0,1} {0} {0,2}

Laboratory for Advanced Software Engineering Research UMASS Property System Property Translator System Translator State Propagation System model Property Verified... Constraints FSA Incrementally Improving Precision Counter Examples for Model

Laboratory for Advanced Software Engineering Research UMASS Example with Constraints if open close if move S==trueS==false S==true 0 21 viol S==true S==false S==true S==false S==true Constraint close, open,move 0 1 open close 2 move close move open Property (0,0) (0,1) (1,1) (1,viol)

Laboratory for Advanced Software Engineering Research UMASS Example with Constraints if open close if move S==trueS==false S==true 0 21 viol S==true S==false S==true S==false S==true Constrain t close, open,move 0 1 open close 2 move close move open Property (0,0) (0,1) (1,1) {(1,1), (0,2)} (0,2) {(1,1), (0,viol)} {(1,viol), (0,2)} {(0,1)} {(0,1), (0,2)}

Laboratory for Advanced Software Engineering Research UMASS Some Observations: Data Flow Analysis Overall complexity is O(N 2 S) –N is the # nodes in the model –S is the number of states: property x constraints –Experimentally: performance subexponential Usually requires several iterations to determine needed constraints Constraints –Many automatically generated on request –Can be used to model other information

Laboratory for Advanced Software Engineering Research UMASS Experimental Comparisons All these approaches are: –very effective on some problems –disappointing on some problems Hard to predict how they will perform Experimental results –George S. Avrunin, James C. Corbett, Matthew B. Dwyer, Corina S. Pasareanu, and Stephen F. Siegel, Comparing Finite-State Verification Techniques for Concurrent Software Very Big Disclaimer!

Laboratory for Advanced Software Engineering Research UMASS url: laser.cs.umass.edu

Laboratory for Advanced Software Engineering Research UMASS Can we move beyond academic prototypes to practitioners’ tools? Yes, but there is more work to be done –Optimization, optimization, optimization –Process support –Better support for specifying properties –Better support for generating, selecting, visualizing counter example traces –Better approaches for dealing with dynamism –Full support for real languages –Full lifecycle support Integration with testing

Laboratory for Advanced Software Engineering Research UMASS Specifying Properties It is very hard to specify properties precisely –E.g., open and close file repeatedly Must file always be opened? Or, IF it is opened, then it must be closed? Can file be opened repeatedly before it is closed? Need notations that are easy to use –Specification patterns Need tools to help understand properties –need to test the properties

Laboratory for Advanced Software Engineering Research UMASS Counter Example Traces Want “short” but “useful” counter examples How to select the “next” counter example? How to incorporate user guidance? How to go from traces in the model to traces in the program?

Laboratory for Advanced Software Engineering Research UMASS Dynamism FSV is a static analysis approach that deals with static models –Must create a specific instance of the model E.g., N philosophers => 5 philosphers –Can not handle dynamic objects dynamic process creation Need hybrid techniques that integrate theorem proving with FSV

Laboratory for Advanced Software Engineering Research UMASS Support for Real Languages Many language features have not been addressed –Aliasing –Exception handling –Event based notification

Laboratory for Advanced Software Engineering Research UMASS Lifecycle-based Verification High-level architectural design –Extremely important for distributed systems Detect problems early –Need to support heterogeneous interaction models Low-level design –Additional detail leads to additional properties –Need to maintain consistency with the HLA

Laboratory for Advanced Software Engineering Research UMASS Lifecycle-based Verification (continued) Coding –Partial systems –Incremental, compositional development/verification Debugging –Hypothesize fault in terms of a property –FSV provides a counter example trace or invalidates hypothesis

Laboratory for Advanced Software Engineering Research UMASS Testing –Generalize test cases to their corresponding property –Test planning via requirements based property specification Regression testing –re-verify properties that should not have changed Need efficient re-verification techniques Lifecycle-based verification (continued)

Laboratory for Advanced Software Engineering Research UMASS Integrating Testing and Verification Testing and verification complement one another –verification makes assumptions that should be monitored dynamically –testing finds problems that should then be examined globally Need to develop integrated techniques

Laboratory for Advanced Software Engineering Research UMASS Synergy between Testing and Verification Properties Faults Testing Assumptions /constraints Counter examples Assertions Verification Test plans/cases

Laboratory for Advanced Software Engineering Research UMASS Conclusions Testing alone can not provide the assurance that is needed for many applications –especially distributed systems FSV a promising technology –Applicable to a wide range of properties –Applicable throughout the lifecycle –Initial empirical results promising

Laboratory for Advanced Software Engineering Research UMASSConclusion Finite State Verification is a major paradigm shift –More difficult than testing, but not that much more difficult –Cultural resistance to doing anything different Is the pain worth the gain? Grand challenge: Can we lower the obstacles to adoption?