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# SPIN - PowerPoint PPT Presentation

SPIN. An explicit state model checker. Explict State Model Checker. Represents the system as an finite state machine Visits each reachable state (state space) explicitly Checks some property Property is satisfied Counterexample. DFS. DFS visit of the state space procedure DFS ( s )

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### SPIN

An explicit state model checker

• Represents the system as an finite state machine

• Visits each reachable state (state space) explicitly

• Checks some property

• Property is satisfied

• Counterexample

• DFS visit of the state space

procedureDFS(s)

visited = visited {s};

for each successor s’ of s

if s’visitedthen

DFS(s’);

end if

end for

end procedure

• How do we:

• Represent the transition relation

• Store the visited set

• Needs fast access (hash table)

• State space explosion

• Check properties

• Process Algebra

• An algebraic approach to the study of concurrent processes. Its tools are algebraical languages for the specification of processes and the formulation of statements about them, together with calculi for the verification of these statements. [Van Glabbeek, 1987]

• Describes the system in a way similar to a programming language

• Asynchronous composition of independent processes

• Communication using channels and global variables

• Non-deterministic choices and interleavings

T

C

An Example

mtype = { NONCRITICAL, TRYING, CRITICAL };

show mtype state[2];

proctype process(int id) {

beginning:

noncritical:

state[id] = NONCRITICAL;

if

:: goto noncritical;

:: true;

fi;

trying:

state[id] = TRYING;

if

:: goto trying;

:: true;

fi;

critical:

state[id] = CRITICAL;

if

:: goto critical;

:: true;

fi;

goto beginning;}

init { run process(0); run process(1); }

mtype = { NONCRITICAL, TRYING, CRITICAL };

show mtype state[2];

proctype process(int id) {

beginning:

noncritical:

state[id] = NONCRITICAL;

if

:: goto noncritical;

:: true;

fi;

trying:

state[id] = TRYING;

if

:: goto trying;

:: true;

fi;

critical:

state[id] = CRITICAL;

if

:: goto critical;

:: true;

fi;

goto beginning;}

init { run process(0); run process(1); }

mtype = { NONCRITICAL, TRYING, CRITICAL };

show mtype state[2];

proctype process(int id) {

beginning:

noncritical:

state[id] = NONCRITICAL;

if

:: goto noncritical;

:: true;

fi;

trying:

state[id] = TRYING;

if

:: goto trying;

:: true;

fi;

critical:

state[id] = CRITICAL;

if

:: goto critical;

:: true;

fi;

goto beginning;}

init { run process(0); run process(1); }

mtype = { NONCRITICAL, TRYING, CRITICAL };

show mtype state[2];

proctype process(int id) {

beginning:

noncritical:

state[id] = NONCRITICAL;

if

:: goto noncritical;

:: true;

fi;

trying:

state[id] = TRYING;

if

:: goto trying;

:: true;

fi;

critical:

state[id] = CRITICAL;

if

:: goto critical;

:: true;

fi;

goto beginning;}

init { run process(0); run process(1); }

mtype = { NONCRITICAL, TRYING, CRITICAL };

show mtype state[2];

proctype process(int id) {

beginning:

noncritical:

state[id] = NONCRITICAL;

if

:: goto noncritical;

:: true;

fi;

trying:

state[id] = TRYING;

if

:: goto trying;

:: true;

fi;

critical:

state[id] = CRITICAL;

if

:: goto critical;

:: true;

fi;

goto beginning;}

init { run process(0); run process(1); }

mtype = { NONCRITICAL, TRYING, CRITICAL };

show mtype state[2];

proctype process(int id) {

beginning:

noncritical:

state[id] = NONCRITICAL;

if

:: goto noncritical;

:: true;

fi;

trying:

state[id] = TRYING;

if

:: goto trying;

:: true;

fi;

critical:

state[id] = CRITICAL;

if

:: goto critical;

:: true;

fi;

goto beginning;}

init { run process(0); run process(1); }

NC

T

C

• A statement needs to be enabled for the process to be scheduled.

bool a, b;

proctype p1()

{

a = true;

a & b;

a = false;

}

proctype p2()

{

b = false;

a & b;

b = true;

}

init { a = false; b = false; run p1(); run p2(); }

• A statement needs to be enabled for the process to be scheduled.

bool a, b;

proctype p1()

{

a = true;

a & b;

a = false;

}

proctype p2()

{

b = false;

a & b;

b = true;

}

init { a = false; b = false; run p1(); run p2(); }

These statements are enabled only if both a and b are true.

• A statement needs to be enabled for the process to be scheduled.

bool a, b;

proctype p1()

{

a = true;

a & b;

a = false;

}

proctype p2()

{

b = false;

a & b;

b = true;

}

init { a = false; b = false; run p1(); run p2(); }

These statements are enabled only if both a and b are true.

In this case b is always false and therefore there is a deadlock.

• Do loops

do

:: count = count + 1;

:: count = count - 1;

:: (count == 0) -> break

od

• Do loops

• Communication over channels

proctype sender(chan out)

{

int x;

if

::x=0;

::x=1;

fi

out ! x;

}

• Do loops

• Communication over channels

• Assertions

{

int value;

out ? value;

assert(value == 0 || value == 1)

}

• Do loops

• Communication over channels

• Assertions

• Atomic Steps

int value;

proctype increment()

{ atomic {

x = value;

x = x + 1;

value = x;

} }

• System is the asynchronous composition of processes

• The global transition relation is never build

• For each state the successor states are enumerated using the transition relation of each process

0

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On-The-Fly

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• Represents all the states that have been reached so far

• Will eventually become the set of all reachable state (state space)

• Test of presence of a state in the set must be efficient

• It is performed for each reached state

• procedure DFS(s)

• visited = visited {s};

• for each successor s’ of s

• if s’  visited then

• DFS(s’);

• end if

• end for

• end procedure

• Hash table

• Efficient for testing even if the number of elements in it is very big (≥ 106)

• Hash table

• Efficient for testing even if the number of elements in it is very big (≥ 106)

• Reduce memory usage

• Compress each state

When a transition is executed only a limited part of the state is modified

• Hash table

• Efficient for testing even if the number of elements in it is very big (≥ 106)

• Reduce memory usage

• Compress each state

• Reduce the number of states

• Partial Order Reduction

• Global variables

• Processes and local variables

• Queues

Processes

Global Variables

Queues

• Each transition changes only a small part of the state

• Assign a code to each element dynamically

• Encoded states + basic elements use considerably less spaces than the uncompressed states

3

2

2

1

1

0

0

0

Compression

i=0 j=0

P0

x=0

P0

x=1

Q0

{1}

P0

x=0

P1

y=0

0

0

1

0

0

2

3

2

P1

y=0

1

P0

x=1

i=0 j=0

P0

x=0

Q0

{1}

3

2

2

1

1

0

0

0

Compression

i=0 j=0

P0

x=0

P0

x=1

Q0

{1}

Q0

{}

P0

x=0

P0

x=1

P1

y=0

0

0

1

1

0

0

1

2

q ? x

3

2

P1

y=0

1

P0

x=1

Q0

{}

i=0 j=0

P0

x=0

Q0

{1}

• Uses a hashing function to store each state using only 2 bits

• Uses a hashing function to store each state using only 2 bits

• There is an non-zero probability that two states are mapped into the same bits

• Uses a hashing function to store each state using only 2 bits

• There is an non-zero probability that two states are mapped into the same bits

• If the number of states is quite smaller than the number of bits available there is a pretty good chance of not having conflicts

• Uses a hashing function to store each state using only 2 bits

• There is an non-zero probability that two states are mapped into the same bits

• If the number of states is quite smaller than the number of bits available there is a pretty good chance of not having conflicts

• The result is not (always) 100% correct!

• Turns the state in a sequence of integers

• Turns the state in a sequence of integers

• Constructs an automata which accepts the states in the visited set

• Turns the state in a sequence of integers

• Constructs an automata which accepts the states in the visited set

• Works like a BDD but on non-binary variables (MDD)

• Turns the state in a sequence of integers

• Constructs an automata which accepts the states in the visited set

• Works like a BDD but on non-binary variables (MDD)

• The variables are the components of the state

• Turns the state in a sequence of integers

• Constructs an automata which accepts the states in the visited set

• Works like a BDD but on non-binary variables (MDD)

• The variables are the components of the state

• The automata is the minimal automata

• Turns the state in a sequence of integers

• Constructs an automata which accepts the states in the visited set

• Works like a BDD but on non-binary variables (MDD)

• The variables are the components of the state

• The automata is the minimal automata

• The automata is updated efficiently

y=0

x=1

y=0

Partial Order Reduction

• Some interleavings of processes are equivalent

x=0

y=0

x++

y++

x=1

y=0

x=0

y=1

y++

x++

x=1

y=1

• Some interleavings of processes are equivalent

• Computing such interleavings and storing the intermediate states is expensive

• Some interleavings of processes are equivalent

• Computing such interleavings and storing the intermediate states is expensive

• Partial order reduction defines a reduced system which is equivalent to the original system but contains less states and transitions

Defines an equivalent relation between states and computes the quotient of the state transition graph to obtain a reduced state transition graph.

Properties are true of the reduced state transition graph if and only if are true of the original graph.

• Optimal partial order reduction is as difficult as model checking!

• Optimal partial order reduction is as difficult as model checking!

• Compute an approximation based on syntactical information

Send on exclusive send-access queues

• Optimal partial order reduction is as difficult as model checking!

• Compute an approximation based on syntactical information

• Independent

• Invisible

• Check (at run-time) for actions postponed at infinitum

Not mentioned in the property

So called stack proviso

• Safety properties

• Properties of states

• Liveness properties

• Something good eventually happens

• Properties of paths

Reachability is sufficient

We need something more complex to check liveness properties

• Liveness properties are expressed in LTL

• Subset of CTL* of the form:

• A f

where f is a path formula with does not contain any quantifiers

• The quantifier A is usually omitted.

• G is substituted by  (always or box)

• F is substituted by  (eventually or diamond)

• X is substituted by  (next)

• Always eventually p:   p

AGFp in CTL*

AG AF p in CTL

• Always after p there is eventually q:  ( p (  q ) )

AG(pFq) in CTL*

AG(p AFq) in CTL

• Fairness:

(   p ) 

(AGF p)   in CTL*

Can’t express it in CTL

• http://spinroot.com/

• Design and Validation of Computer Protocols by Gerard Holzmann

• The Spin Model Checker by Gerard Holzmann

• An automata-theoretic approach to automatic program verification, by Moshe Y. Vardi, and Pierre Wolper

• An analysis of bitstate hashing, by G.J. Holzmann

• An Improvement in Formal Verification, by G.J. Holzmann and D. Peled

• Simple on-the-fly automatic verification of linear temporal logic, by Rob Gerth, Doron Peled, Moshe Vardi, and Pierre Wolper

• A Minimized automaton representation of reachable states, by A. Puri and G.J. Holzmann