# Model Checking of Software

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1 Model Checking of Software Patrice Godefroid Bell Laboratories, Lucent Technologies SpecNCheck Page 1 August 2001

2 A Brief History of Model Checking Prehistory: transformational programs and theorem proving Early 80 s: foundations (the pioneers) Late 80 s: first tools (the first champions) Early 90 s: reality check: state spaces explode! (the engineers) Late 90 s: the boom then reality check (the entrepreneurs) Next: can model checking be applied to software? Challenges and approaches currently being investigated SpecNCheck Page 2 August 2001

3 Preliminaries: Formal Verification + Disclaimer What is Verification? 4 elements define a verification framework: Specification (what we want) Design Verification Implementation (what we get) Verification: to check if all possible behaviors of the implementation are compatible with the specification While testing can only find errors, verification can also prove their absence (=exhaustive testing). Disclaimer: emphasis on technical ideas, not references SpecNCheck Page 3 August 2001

4 Prehistory (70 s and before) Transformational programs: Most early computer programs were designed to compute something. Examples: accounting, scientific computing, etc. Transformation from initial to final state. Specification= pre-condition/post-condition Formal verification: Paper and pencil. Using Theorem Proving (first CAV tools) SpecNCheck Page 4 August 2001

5 Theorem Proving Goal: automate mathematical (logical) reasoning. Verification using theorem proving: Implementation represented by a logic formula I (ex: Hoare s logic). Specification represented by a logic formula S. Does I implies S hold? Proof is carried out at syntactic level. This approach is very general. Many programs and properties can be checked this way. However, most proofs are not fully automatic. A theorem prover is rather a proof assistant and a proof checker. SpecNCheck Page 5 August 2001

6 Early 80 s: Foundations (the pioneers) From transformational programs to reactive programs: A transformational program computes something. A reactive program controls something. Examples: telephone switch, airplane, ATM, power plant, pacemaker, etc. A reactive program continually interacts with its environment. Viewed as a FSM (automaton), called the state space. Behavior described in terms of sequences of states/transitions. Language for temporal properties: Temporal Logic [Pnueli, ] SpecNCheck Page 6 August 2001

7 Temporal Logic Model Checking Example: Linear-time Temporal Logic (LTL) Specify properties of infinite sequences of states (or transitions). Temporal operators include: G (always), F (eventually) and X (next). Example: G(p -> Fq) s0 p q Does M satisfy f? = model checking [Clarke, Emerson, Sifakis, ] For f in LTL, do all infinite computations of M satisfy f? For f in BTL, does the computation tree of M satisfy f? Algorithmic issues: efficient decision procedures exist Proof can be carried out at semantic level, via state-space exploration. Ex: for CTL, SAT is EXPTIME-complete, but model checking is linear! SpecNCheck Page 7 August 2001

8 First Model-Checking Frameworks 4 components define a model-checking framework: Implementation (program) = an FSM. Specification (property) = a temporal logic formula. Comparison Criteria = defined by semantics of the temporal logic. Algorithm = evaluates the formula against the FSM ( model-checking algorithm ) Model-Checking Research in the 80 s: Various temporal logics: linear-time, branching-time, Relationship between temporal logics and classes of automata (LTL and word automata; BTL and tree automata ) Classes of temporal properties (safety, liveness, ) Etc. Model checking is automatic but (essentially) restricted to finite-state systems. Many reactive systems can be modeled by FSMs! Let s build tools! SpecNCheck Page 8 August 2001

9 Late 80 s: First tools (the first champions) Examples: CAESAR, COSPAN, CWB, MURPHI, SPIN, etc. Differ by specification language, implementation language, comparison criterion, and/or verification algorithms, but all based on systematic state-space exploration. NOTE: using a temporal logic is not mandatory. Many model-checking tools do not support a full temporal logic. From now on, no distinction here between model checking and systematic statespace exploration. Logic is a powerful theoretical tool (characterizes classes of properties). Logic can be very useful in practice too (concise and expressive). First success stories in analyzing circuit designs, communication protocols, distributed algorithms! SpecNCheck Page 9 August 2001

10 Formal Verification vs. Testing Experiments with these tools show that model checking can be very useful! Main strength: model checking can detect subtle design errors. In practice, formal verification is actually testing because of approximations: when modeling the system, when modeling the environment, when specifying properties, when performing the verification. Therefore bug hunting is really the name of the game! Main goal: find errors that would be hard to find otherwise. SpecNCheck Page 10 August 2001

11 Early 90s: First Reality Check (the engineers) Model Checking is limited by the state explosion problem. X1=1 X2=1 Xn=1 2^n states! n! interleavings! FSM (=state space) can itself be the product of smaller FSMs Model checking is usually linear in the size of the state space, but the size of the state space is usually exponential (or worse) in the system description (program). State-space exploration is fundamentally hard (NP, PSPACE or worse). Engineering challenge: how to make model checking scalable? SpecNCheck Page 11 August 2001

12 Dealing with State Explosion Divide-and-conquer approaches: abstraction: hide/approximate details. compositionality: check first local properties of individual components, then combine these to prove correctness of the whole system. Algorithmic approaches: symbolic verification : represent state space differently (BDDs, ). state-space pruning techniques: avoid exploring parts of the state space (partial-order methods, symmetry methods, ). Techniques to tackle the effects of state explosion (bit-state hashing, statespace compression, caching, etc.). Etc. Several order of magnitudes gained! We are in business! SpecNCheck Page 12 August 2001

13 Late 90 s: the boom then reality check Industrial model-checking tools are developed and gain acceptance in industry Become routinely used for some applications in some companies. Mostly hardware: IBM, Intel, Lucent, Motorola, etc. Software designs too (with SDL (Telelogic), VFSM (Lucent), ) Several start-ups are trying to emerge! FormalCheck (now Cadence), Verisity, Verysys, Mentor Graphics, 0-in, Making money selling model-checking tools is hard! Scalability issues (state explosion ) Usability issues (requires training for specification and verification) SpecNCheck Page 13 August 2001

14 Applications: Hardware Hardware verification is an important application of model checking and related techniques. The finite-state assumption is not unrealistic for hardware. The cost of errors can be enormous (e.g., Pentium bug). The complexity of designs is increasing very rapidly (system on a chip). However, model checking still does not scale very well. Many designs and implementations are too big and complex. Hardware description languages (Verilog, VHDL, ) are very expressive. Using model checking properly requires experienced staff. Quid for Software? SpecNCheck Page 14 August 2001

15 Applications: Software Models Analysis of software models: (e.g., SPIN) Analysis of communication protocols, distributed algorithms. Models specified in extended FSM notation. Restricted to design. Analysis of software models that can be compiled: (e.g., SDL, VFSM) Same as above except that FSM can be compiled to generate the core of the implementation. More popular with software developers since reuse of model is possible. Analysis still restricted to FSM part of the implementation. SpecNCheck Page 15 August 2001

16 Model Checking of Software Challenge: how to apply model checking to analyze software? Real programming languages (e.g., C, C++, Java), Real size (e.g., 100,000 s lines of code). Two main approaches for software model checking: Modeling languages state-space exploration Model checking abstraction (Bandera, Feaver, JPF, SLAM, ) adaptation Programming languages state-space exploration Systematic testing (VeriSoft) SpecNCheck Page 16 August 2001

17 Approach: Systematic Testing (VeriSoft( VeriSoft) Control and observe the execution of concurrent processes of the system under test by intercepting system calls (communication, VS_toss(n), assertion violations, etc.). Systematically drive the system along all the paths (=scenarios) in its state space (=automatically generate, execute and evaluate many scenarios). From a given initial state, one can always guarantee a complete coverage of the state space up to some depth. VeriSoft s0 System Processes A B C deadlock SpecNCheck Page 17 August 2001

18 VeriSoft State-Space Space Search Automatically searches for: (safety properties only!) deadlocks, assertion violations, divergences (a process does not communicate with the rest of the system during more than x seconds), livelocks (a process is blocked during x successive transitions). A scenario (path) is reported for each error found. How to efficiently explore state spaces without storing any state? States of arbitrary (OS) processes are too complex to be represented explicitly (no hash-tables, BDDs, ). For concurrent systems, need partial-order algorithms! [Godefroid, ] SpecNCheck Page 18 August 2001

19 The VeriSoft Simulator SpecNCheck Page 19 August 2001

20 VeriSoft Project Status Development of research prototype started in Examples of applications in Lucent Technologies: 4ESS Heart-Beat Monitor debugging and unit testing (Switching, switch maint.) WaveStar 40G R4 integration and system testing (Optical, network management) CDMA Call Processing Library testing (Wireless, call processing) VeriSoft 2.0 available outside Lucent since January 1999: 100 s of non-commercial licenses in 25+ countries; 10 s of commercial licenses; several industrial users (Lucent, Cisco, Motorola, Philips, ) Examples of related research issues: How to automatically close open reactive programs? [Colby, Godefroid, Jagadeesan,..] How to analyze effectively partial state-spaces? [Bruns, Godefroid, ] How to apply and optimize this approach to multi-threaded programs? [Stoller, ] SpecNCheck Page 20 August 2001

21 Approach: Automatic Abstraction Main ideas and issues: 1. Abstract: extract a model out of concrete program via static analysis. Which programming languages are supported? ((subset of) C, Java, Ada,DSL?) Additional assumptions? (Pointers? Recursion? Concurrency? ) What is the target modeling language? ((C)(E)FSMs, PDAs, ) Can/must the abstraction be guided by the user? How? 2. Model check the abstraction. What properties can be checked? (Safety? Liveness?, ) How to model the environment? (Closed or open system? ) Which model-checking algorithm? (New algorithms for PDAs, HSMs, ) Is the abstraction conservative? 3. Map abstract counter-examples back to code. Behaviors violating the property may have been introduced during Step 1. Hence, need to map scenarios leading to errors back to the code. HOW? SpecNCheck Page 21 August 2001

22 Active Area of Research Examples of tools: Bandera [Dwyer, Hatcliff, ]: Java to SPIN/SMV/* using user-guided abstraction mapping and slicing/abstract-interpretation/* SLAM [Ball, Rajamani, ]: C to Boolean programs (=CFG+boolean variables); automatic abstraction refinement using predicate abstraction JavaPathFinder [Havelund,Penix,Visser, ]: Java model-checking using special JVM and model-checker Feaver [Holzmann, ]: C to SPIN using user-specified abstraction mapping Etc! (Tools for Ada, static analysis of concurrent programs, ) Examples of frameworks: (automatic abstraction refinement) [Graf,Saidi, ], [Clarke,Grumberg,Jha, ], [Ball,Rajamani,Podelski, ], [Dill,Das, ], [Khurshan,Namjoshi, ], [Dwyer,Pasareanu,Visser, ], [Bruns,Godefroid,Huth,Jagadeesan,Schmidt ], [Henzinger, ], etc. SpecNCheck Page 22 August 2001

23 Summary: Two (Complementary) Approaches Systematic software testing: Idea: control the execution of concurrent processes by intercepting systems calls related to communication, and automatically drive the entire system through many scenarios. Flexible and scalable approach (code independent). Counterexamples arise from code execution (sound). Provide complete state-space coverage up to some depth only (incomplete). Static analysis for automatic model extraction: Idea: parse code to generate an abstract model which is then analyzed by model-checker; abstraction may/must be guided by the user. Coverage can be exhaustive (can be complete). Abstraction may cause spurious counterexamples (unsound) Technology less mature, active area of research. SpecNCheck Page 23 August 2001

24 Conclusions Model Checking is a very successful research area: New: original approach to check the correctness of reactive systems. Non-obvious: rich theory behind it. Useful: many applications and success stories, including in industry. From a business perspective, the success is mixed (!?!) Can model checking be applied to software? Hard problem (model checking + program analysis). Good for research! Bad for business? SpecNCheck Page 24 August 2001

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