Formal verification in Embedded System design Dr. Abhik Roychoudhury


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Formal verification in Embedded System design

  • Dr. Abhik Roychoudhury

  • School of Computing

  • abhik@comp.nus.edu.sg


Safety Critical Systems

  • Safety

    • Design invariants must always hold in all executions of the system.
  • Critical

  • Examples

    • Air traffic controller
    • Automobile parts.


Methodological view point

  • Inject higher reliability in design life cycle.

  • Safety critical systems often have a computer component.

  • This trend is increasing with growth of embedded applications.

  • What kind of computer systems are they ?



Reactive Systems

  • Continuously interacts with its environment.

  • Interaction with env. is asynchronous.

  • Often, its response to environment needs to obey time constraints.

  • Often consists of a concurrent composition of processes.

  • [Harel]



Why study them now ?

  • Embedded systems

    • Using a computer component as part of a bigger system becoming pervasive.
  • Many of them safety-critical

    • e.g. automobile parts
  • Difficulty in using Current verif. techniques

    • Lack of tool support for reliable modeling.
    • Perceived as intrusive to design process.


Validation Techniques

    • In circuit Emulator (ICE)
    • Logic Analyzer
    • Model based simulation
    • Formal verification techniques
      • Model Checking
      • Deduction
      • Combinations of the two


In circuit Emulator (ICE)

  • Used widely in industry for designs where a microproc. interacts with potpourri of peripherals.

  • ICE is a dedicated hardware for a particular processor which allows its internals to be read.

  • Response of processor (to environment) observed by physically replacing chip with ICE.



Logic Analyzer

  • Used for sampling many signals simultaneously in a complex design.

  • Can snoop on a bus to observe interactions of a microprocessor with its environment.

  • ICE and Logic Analyzer do not work when:

    • Processor, peripherals, bus all integrated in a chip.
    • System-on-Chip (SoC) – Current industry trend.


Model based simulation

  • Simulate and observe the behaviors of a system model, rather than the system itself.

  • Takes validation/debugging higher in the design life-cycle.

  • Since a model is validated, can take place prior to system integration

    • Hardware software co-simulation (POLIS)
    • [Earlier lecture]


Model Checking – What ?

  • Same as model based simulation except that you check all possible behaviors.

  • Needed for checking critical properties.

  • Can be used if model has finite states.

  • Many realistic systems are infinite-state

    • e.g. real-time systems.
  • For these systems, extensions of model checking.



Spec. and Impl.

  • Need a specification language (property to be verified).

  • Need an implementation language (system to be verified)

  • Such a language describes reactive system behaviors.

    • Temporal Logic
      • Linear - LTL
      • Branching - CTL
    • Process Algebra/Calculus
      • CCS (Milner 1989)
      • CSP (Hoare)
    • Finite state automata over infinite inputs.


Model Checking – How ?

  • Inputs:

    • finite state concurrent system (implementation as FSM)
    • Temporal logic formula (specification language)
  • Output:

    • True if the specification holds
    • A counterexample behavior if it does not
  • Technique:

    • Implementation FSM is a finite graph.
    • Unfold and search this finite graph to check all behaviors.


State space explosion

  • Model checking invariant properties = Reachability computation

  • Requires visiting reachable set of states (state space).

  • If a circuit has 100 latches, then maximum 2^100 states.

  • Visiting and enumerating all these states is inefficient

    • Space
    • Time also.
  • Explicit state model checking quickly runs out of MM.

  • Need a symbolic representation of the state space.



Symbolic representation

  • Any state s is an True/false assignment of boolean variables.

    • X1 = false , X2 = true, X3 = false
  • This induces a boolean function on these boolean vars.

    •  X1  X2   X3
  • Any set of states is also equivalent to a boolean function

    • ( X1  X2   X3)  ( X1  X2  X3)
  • A canonical representation of this boolean function implicitly encodes set of states (call it Binary Decision Diagram)

    •  X1  X2
  • A similar encoding can be obtained for transition relation also.

  • [McMillan et.al.]



BDD for two bit comparator



Model Checkers

  • FormalCheck (Commercialized by Cadence)

    • Synchronous input language
    • Based on  automata
  • Symbolic Model Verifier (CMU)

    • Internal representation : BDD
  • Mur (Stanford)

  • SPIN (Bell Labs)

    • Validation of Protocols/Software


Beyond finite state

  • Model Checking restricted to finite state systems.

  • Sources of non-finiteness in reactive emb. Sys.

    • Data values from unbounded domain - counters
    • Unbounded data paths
    • Real Variables, in particular timers
    • Unbounded number of similar components
    • Partial specification for some of the system components
  • How to verify such systems ?



Data Independence

  • If the control flow of the system is independent of data values

    • Data values need not blow up the state space.
    • Infinite number of data values clubbed to a single state.


Data abstraction



Data abstraction

  • Cannot collapse all data values into a single value.

  • Choose the abstract data domain based on the property

    • Data Delivery : { y, y}
    • Order Preservation : { x, y, {x, y} }
  • Such data abstractions are routine and can be automated from

    • System to be verified
    • Property to be verified (data delivery/ order preservation here)
  • Abstraction techniques for unbounded data paths

    • The Channel in this example could be unbounded.


Real time systems

  • Popular representation : timed automata [Alur et.al.]

    • Finite state automata
    • Augmented with finite set of real valued timers
    • Transitions in the automata occur in zero time.
    • Time can elapse in states : Delay transitions
  • State space of a timed automata is infinite.

  • Finite representation obtained by constructing “timer regions

  • Construct region graph where each node is a region.

  • Model Checking via searching this region graph.



Regions = Constraints



Parameterized systems

  • Infinite family of finite state systems

    • N process cache coherence protocol
    • N process distributed algorithm (for mutual exclusion)
    • A hardware arbiter for resource shared among N processes
  • Number of processes in the system to be verified is unbounded.

  • Non-finiteness is not due to data.

  • Verification is undecidable (no algorithm may exist).



That old trick !

  • A network of N similar processes.

  • Each process has the same finite state automata

    • { s0, s1, …, sk}
  • Define a finite vector cnt0, cnt1, …, cntk

    • Cnt0 = Number of processes in state s0
  • Such a vector defines a state of the entire network.

  • Constraints on cnt0, cnt1, …, cntk now define regions.

  • If the number of regions in your problem is finite,

    • Can construct and search finite region graph (Model Checking)


Induction

  • Example: System : n bit shift register

  • Initial state : Data fed at left end

  • property: F out (Data popped at right end)

  • Cannot construct a uniform proof ( for any n)

  • Natural to induct on the number of bits.

  • Induction on process structure (not just number of processes)

    • Tree networks (e.g. System Buses arranged hierarchically)
  • Combining limited induction with search (as in Model Checking).



FV for ES – The reality

  • Is it any different ?

    • Current verif. Techniques should scale up for ES Hardware.
    • Embodies hardware/software interaction: often real-time.
    • Reuse of vendor provided IP blocks
      • Implementation not known for Intellectual property reasons
    • No single person/team knows the entire design.


FV for ES – Consequences

  • Wealth of model checkers (with limited deduction) useful for ES hardware verification

    • Handle state-of-the-art superscalar processors with
      • Out-of-order execution
      • Speculative execution
  • ES component interaction is fairly detailed, low-level and often specified in hard-to-read manuals.

    • Real-time verification is not yet a mature technology.
    • Need to reliably model software-hardware interfaces.


FV for ES - Consequences

  • A realistic ES design typically consists of:

  • View an IP block as a hardware subroutine – Need REUSE.

  • Reuse IP blocks designed by others (and provided by vendors).

  • Each IP block comes with interface specification

    • Input and output signals
    • Some timing diagrams


FV for ES - Techniques

    • Model Checking (Not the panacea)
    • Abstraction
      • Data abstraction on integer counters useful
      • Routine control abstractions – based on symmetry etc.
      • A process of gradual refinement – not one shot.
    • Deduction
      • Routine inductions – without hypothesis strengthening
      • Integrate such reasoning with the search
    • Constraint solving
      • For real-time feature of ES.


FV for ES - Issues

  • Synthesizing component interfaces reliably.

    • Need high level modeling (UML).
    • Consistency of UML diagrams.
    • Synthesize executable description from high level models.
  • Still you might be using other’s components !!

    • Static verification of unknown components
      • Assume guarantee reasoning (Deduction)
      • Extract assumptions/guarantees from interface spec.


FV for ES - Issues

  • ES software subverts some of the problems of program verification.

    • Datatypes are often (arrays of) scalar types.
    • Develop specialized provers (with limited theorem proving)
    • ES software verification should look at both:
      • control intensive, reactive applications
      • Data intensive applications. Reasoning about:
        • Nested Loops.
        • Arrays.



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