CSE 522UPPAAL – A Model Checking Tool

Computer Science & Engineering DepartmentArizona State University

Tempe, AZ 85287

Dr. Yann-Hang Leeyhlee@asu.edu(480) 727-7507

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UPPAAL -- Introduction

A tool for modeling, simulation and verification of real-time systems.

Appropriate for systems that can be modeled as a collection of non-deterministic processes with finite control

structure and real-valued clocks (i.e. timed automata) Networks of timed automata

communicate through channels and shared data structures. Modeling language

channels, and locations constants, data-variables (with bounded domains) and arrays guards and assignments templates with local clocks, data-variables, and constants C subset

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Tool Overview

System Editor Draw Automata: locations, edges, etc. Declare global and local constant, variables, and functions Create instances of system and processes

Simulator Traces (state transitions): next, prev, replay, open, save,

random Message sequences

Verifier A<> p : p will inevitable become true, the automaton is

guaranteed to eventually reach a state in which p is true.

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Example: Fischer’s Protocol (1)

A well-known mutual exclusion protocol a timed protocol where the concurrent processes check for both

a delay and their turn to enter the critical section using a shared variable id.

Protocol Starting from the initial location processes go to a request location, req, if id==0, which checks

that it is the turn for no process to enter the critical section. stay non-deterministically between 0 and k time units in req, go to the wait location and set id to their pid wait at least k time units, before entering the critical section CS if

it is its turn, i.e. id==pid.

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Example: Fischer’s Protocol (2)

id – shared variable, initialized 0 each process has it’s own timer (for delaying)

Process i:

while (true) {

<noncritical section>;

while id != -1 do {}

id := i;

delay K;

if (id = i) {

<critical section>;

id := -1;

}

}

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Example: Fischer’s Protocol

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Locations

Locations: to define the state of automaton. System state is defined by the locations of all automata, the

clock values, and the values of the discrete variables. Initial Locations

The beginning of the process. Each template must have exactly one initial location.

Urgent Locations Urgent locations freeze time. This forces the actual process to

always make a transition without any delay. Committed Locations

A committed state cannot delay and the next transition must involve an outgoing edge of at least one of the committed locations.

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Locations and Edges

Invariant, selection, guard, update, synchronization

n: int[0,5]

a!

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Channels in Uppaal

Used to synchronize two processes. binary synchronization and blocking an edge with synchronization label e! emits a signal on the

channel e and that the enabled edge with synchronization label e? will synchronize with the emitting process.

Urgent Channels synchronization via that channel has priority over normal

channels and the transition must be taken without delay. No clock guard allowed on edges using urgent channels.

Broadcast channel allows 1-to-many synchronization. sender is not blocked if there is no receiver.

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Declaration in Uppaal

Integer int num1, num2; // integer variables with default domain. int a[2][3]; // a multidimensional integer array. int[0,5] b=0; // with the range 0 to 5 initialized to 0.

Boolean bool yes = true; //a boolean variable “yes initialize to true. bool b[8], c[4]; // two boolean arrays b and c, with 8 and 4 elements

Const const int a = 1; // constant “a” with value 1 of type integer. const bool No = false; //constant “No” with value false

Clock clock x, y; //two clocks x and y.

Channel chan d; // a channel. urgent chan a, b ,c; //urgent channel.

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Verifying Properties (1)

E<> p: there exists a path where p eventually holds. A[] p: for all paths p always holds. E[] p: there exists a path where p always holds. A<> p: for all paths p will eventually hold. p --> q: whenever p holds q will eventually hold.

Name Property Equivalent toPossibly E<> p p is reachableInvariantly A[] p not E<> not p p is always truth

Potentially always E[] p

Eventually A<> p not E[] not p p is inevitable

Leads to p --> q A[] (p imply A<> q)whenever p holds eventually q will hold

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Verifying Properties (2)

E<>

A<>

A [ ]

E[ ]

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Verifying Properties (3)

Deadlock (state formula) A state is a deadlock state if there are no outgoing action transitions

neither from the state itself or any of its delay successors. Reachability

whether there exists a path starting at the initial state, such that a state formula is eventually satisfied (e.g. is it possible for a sender to send a message?)

Safety Something bad will never happen! (e.g. the temperature of the

engine is always (invariantly) under a certain threshold) (something good is invariantly true)

Liveness Something good will eventually happen! (e.g. when pressing the on

button, then eventually the television should turn on)

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System Model in Uppaal

System: a list of processes to define a network of timed automata, i.e.

concurrent processes. global declaration

Process: instantiated from a parameterized template.

Template: definition of a timed automaton can be parameterized, e.g., automata for 4 tasks have local declarations of variables, channels, and constants templates without parameters are instantiated into exactly one

process At a given time-point, transitions are enabled in the order

of the process priorities.

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Additional Features in Uppaal

Prioritychan priority a < b, c;

system P < Q, R; At a given time-point, local and synchronization transitions are

enabled in the order of process and channel priorities. User defined functions

C/C++/Java style no recursive call, evaluated atomically and must be deterministic compiled to byte-code, and executed at verification time on a

small embedded stack machine.

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Example: Train Crossing (1)

River

Crossing

Gate

Stopable

Area

[10,20]

[7,15]

Queue

[3,5]

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A railway control system which controls access to a bridge for several trains.

The bridge is a critical shared resource that may be accessed only by one train at a time.

A train can not be stopped instantly and restarting also takes time. When approaching, a train sends an appr! signal. Thereafter, it has 10

time units to receive a stop signal. This allows it to stop safely before the bridge.

After these 10 time units, it takes further 10 time units to reach the bridge if the train is not stopped.

If a train is stopped, it resumes its course when the controller sends a go! signal to it after a previous train has left the bridge and sent a leave! signal.

Example: Train Crossing (2)

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Example: Train Crossing (3)

channels for “appr”, “stop”, “go”, and “leave” Queries

A[] forall (i : id_t) forall (j : id_t) trains(i).Cross && trains(j).Cross imply i == j trains(1).Appr --> trains(1).Cross

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Example: Train Crossing (4)

Train automata Gate automata

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Labels in Edges (1)

Edges are annotated with guards, updates, synchronizations and selections

A guard is an expression which uses the variables and clocks of the model in order to indicate when the transition is enabled, i.e. may be fired. Note that several edges may be enabled at an specific time but

only one of them will be fired An update is an expression that is evaluated as soon as the

corresponding edge is fired. Selections non-deterministically bind a given identifier to a

value in a given range. The other three labels of an edge are within the scope of this binding.

(http://dmi.uib.es/~jproenza/SistEncTR/TheUppaalModelCheckerNEW.pdf)

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Labels in Edges (2)

Synchronization: the basic mechanism used to coordinate the action of two or more processes. models for instance the effect of messages causes two (or more)

processes to take a transition at the same time. Regular channel

fired between the processes paired with c! and c? for a channel c and when the guards of the edges are satisfied.

if there are several possible ways to have a pair c! and c?, one of them is non-deterministically chosen.

The update expression on an edge synchronizing on c! is executed first

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Committed Locations

Committed locations useful for creating atomic sequences a committed state cannot delay and the next transition must

involve an outgoing edge of at least one of the committed locations

if any process is in a committed location, the next transition must involve an edge from one of the committed locations

if several processes are in a committed location at the same time, then they will interleave.

a! and b! are atomic

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Delay Transition and Invariants (1)

Delay transitions model the passing of time without changing the current location.

a delay transition (L, v) --(d)--> (L, v'), where d is a non-negative real, if and only if: v' = v + d, where v+d is obtained by incrementing all clocks

with d. for all 0 <= d' <= d: v + d' satisfies Inv(L) L contains neither committed nor urgent locations no enabled edge with urgent synchronization

When will the reset synchronization happen?

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Delay Transition and Invariants (2)

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Delay Transition and Invariants (3)