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Week-1: Introduction to model checking B. Srivathsan Chennai - - PowerPoint PPT Presentation

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Week-1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute NPTEL-course July - November 2015 1 / 30 Module 4: Modeling concurrent systems 2 / 30 Concurrent systems Independent Shared variables Shared actions 3 / 30

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Week-1: Introduction to model checking

  • B. Srivathsan

Chennai Mathematical Institute

NPTEL-course July - November 2015

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SLIDE 2

Module 4: Modeling concurrent systems

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SLIDE 3

Concurrent systems

Independent Shared variables Shared actions

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SLIDE 4

red green

TrLight1

red green

TrLight2

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SLIDE 5

red green

TrLight1

red green

TrLight2

What is the transition system for the joint behaviour?

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SLIDE 6

red green TrLight1 red green TrLight2

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SLIDE 7

red green TrLight1 red green TrLight2

red, red

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SLIDE 8

red green TrLight1 red green TrLight2

red, red green, red red, green

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SLIDE 9

red green TrLight1 red green TrLight2

red, red green, red red, green green, green

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SLIDE 10

red green TrLight1 red green TrLight2

red, red green, red red, green green, green

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SLIDE 11

red green TrLight1 red green TrLight2

red, red green, red red, green green, green

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SLIDE 12

red green TrLight1 red green TrLight2

red, red green, red red, green green, green

TrLight1 ||| TrLight2

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SLIDE 13

red green TrLight1 red green TrLight2

red, red green, red red, green green, green

TrLight1 ||| TrLight2 ||| : Interleaving operator

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SLIDE 14

x := x+1

...

l1 l2 x:= x+1

PG1 y := y-2

...

q1 q2 y:= y-2

PG2

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SLIDE 15

x := x+1

...

l1 l2 x:= x+1

PG1 y := y-2

...

q1 q2 y:= y-2

PG2

l1: x=0 l2: x=1 q1: y=7 q2: y=5

α β TS1

(initially x=0)

TS2

(initially y=7)

α β

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SLIDE 16

x := x+1

...

l1 l2 x:= x+1

PG1 y := y-2

...

q1 q2 y:= y-2

PG2

l1: x=0 l2: x=1 q1: y=7 q2: y=5 x=0, y=7 x=1, y=7 x=1, y=5 x=0, y=5

α β

α β β α

TS1

(initially x=0)

TS2

(initially y=7)

TS1 ||| TS2 α β

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SLIDE 17

l1 l2 l3 q1 q2

a b a a b

|||

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l1 l2 l3 q1 q2

a b a a b

|||

l1,q1 l2,q1 l3,q1 l1,q2 l2,q2 l3,q2

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SLIDE 19

l1 l2 l3 q1 q2

a b a a b

|||

l1,q1 l2,q1 l3,q1 l1,q2 l2,q2 l3,q2

a a

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SLIDE 20

l1 l2 l3 q1 q2

a b a a b

|||

l1,q1 l2,q1 l3,q1 l1,q2 l2,q2 l3,q2

a a b

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SLIDE 21

l1 l2 l3 q1 q2

a b a a b

|||

l1,q1 l2,q1 l3,q1 l1,q2 l2,q2 l3,q2

a a b a a

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SLIDE 22

l1 l2 l3 q1 q2

a b a a b

|||

l1,q1 l2,q1 l3,q1 l1,q2 l2,q2 l3,q2

a a b a a a

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SLIDE 23

l1 l2 l3 q1 q2

a b a a b

|||

l1,q1 l2,q1 l3,q1 l1,q2 l2,q2 l3,q2

a a b a a a b a b a b b

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SLIDE 24

Multiple systems

TS1 ||| TS2 ||| ... ||| TSn

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SLIDE 25

Multiple systems

TS1 ||| TS2 ||| ... ||| TSn

Exercise: Try out an example of interleaving three systems

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Concurrent systems

Independent

Interleaving TS1 ||| TS2 ||| ... ||| TSn

Shared variables Shared actions

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SLIDE 27

x:= 2·x

...

l1 l2 x := 2·x

PG1 x:= x+1

...

q1 q2 x:= x+1

PG2

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SLIDE 28

x:= 2·x

...

l1 l2 x := 2·x

PG1 x:= x+1

...

q1 q2 x:= x+1

PG2

l1: x=3 l2: x=6 q1: x=3 q2: x=4

α β TS1

(initially x=3)

TS2

(initially x=3)

α β

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SLIDE 29

x:= 2·x

...

l1 l2 x := 2·x

PG1 x:= x+1

...

q1 q2 x:= x+1

PG2

l1: x=3 l2: x=6 q1: x=3 q2: x=4 x=3, x=3 x=6, x=3 x=6, x=4 x=3, x=4

α β

α β β α

TS1

(initially x=3)

TS2

(initially x=3)

TS1 ||| TS2 α β

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l1 l2 x := 2·x

PG1

q1 q2 x := x+1

PG2

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SLIDE 31

l1 l2 x := 2·x

PG1

q1 q2 x := x+1

PG2

l1,q1 l2,q2 l2,q1 l1,q2 x:=2·x x:=x+1 x:=x+1 x:=2·x

||| =

PG1 ||| PG2

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SLIDE 32

l1 l2 x := 2·x

PG1 α

q1 q2 x := x+1

PG2 β

l1,q1 l2,q2 l2,q1 l1,q2 x:=2·x x:=x+1 x:=x+1 x:=2·x

||| =

PG1 ||| PG2

l1,q1: x=3 l2,q1: x=6 l1,q2: x=4 l2,q2: x=7 l2,q2: x=8 α β β α

TS( PG1 ||| PG2 ):

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SLIDE 33

Concurrent systems

Independent

Interleaving TS1 ||| TS2 ||| ... ||| TSn

Shared variables

TS( PG1 ||| PG2 ||| ... ||| PGn )

Shared actions

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SLIDE 34

Coming next: Another example

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while x < 200 x := x+1 while x>0 x := x-1 while x=200 x := 0

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SLIDE 36

while x < 200 x := x+1 while x>0 x := x-1 while x=200 x := 0 Is the value of x always between 0 and 200?

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SLIDE 37

while x < 200 x := x+1

l1 l2 x < 200 x := x+1

while x>0 x := x-1

m1 m2 x > 0 x:=x-1

while x=200 x := 0

n1 n2 x = 200 x:=0

Is the value of x always between 0 and 200?

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SLIDE 38

l1,m1,n1 l2,m1,n1 l1,m2,n1 l1,m1,n2 l2,m2,n1 l2,m1,n2 l1,m2,n2 l2,m2,n2

x<200 x>0 x=200 x:=x+1 x:=x-1 x:=0 x>0 x:=x-1 x=200 x:=0 x<200 x:=x+1 x=200 x:=0 x<200 x:=x+1 x>0 x:=x-1 x=200 x:=0 x>0 x:=x-1 x<200 x:=x+1 15/30

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SLIDE 39

l1,m1,n1 l2,m1,n1 l1,m2,n1 l1,m1,n2 l2,m2,n1 l2,m1,n2 l1,m2,n2 l2,m2,n2

x<200 x>0 x=200 x:=x+1 x:=x-1 x:=0 x>0 x:=x-1 x=200 x:=0 x<200 x:=x+1 x=200 x:=0 x<200 x:=x+1 x>0 x:=x-1 x=200 x:=0 x>0 x:=x-1 x<200 x:=x+1 15/30

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SLIDE 40

l1,m1,n1 l2,m1,n1 l1,m2,n1 l1,m1,n2 l2,m2,n1 l2,m1,n2 l1,m2,n2 l2,m2,n2

x<200 x>0 x=200 x:=x+1 x:=x-1 x:=0 x>0 x:=x-1 x=200 x:=0 x<200 x:=x+1 x=200 x:=0 x<200 x:=x+1 x>0 x:=x-1 x=200 x:=0 x>0 x:=x-1 x<200 x:=x+1

Is the value of x always between 0 and 200? No

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Coming next: Mutual exclusion

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SHARED RESOURCE

P1 P2 Pn

...

(variable, printer, ...) Mutual Exclusion: No two processes can access the resource simultaneously

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Goal: Modeling the protocols used for mutual exclusion

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loop forever

. . .

request critical section release

. . .

end loop *non-critical actions* *non-critical actions*

P1

loop forever

. . .

request critical section release

. . .

end loop *non-critical actions* *non-critical actions*

P2

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loop forever

. . .

request critical section release

. . .

end loop *non-critical actions* *non-critical actions*

P1 PG1

noncrit1 wait1 crit1 loop forever

. . .

request critical section release

. . .

end loop *non-critical actions* *non-critical actions*

P2 PG2

noncrit2 wait2 crit2

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loop forever

. . .

critical section

. . .

end loop *non-critical actions* *non-critical actions*

*request* *release*

〈 if y>0: y:=y-1 〉 y:=y+1

P1 PG1

noncrit1 wait1 crit1 y>0:y:=y-1 y:= y+1 loop forever

. . .

critical section

. . .

end loop *non-critical actions* *non-critical actions*

*request* *release*

〈 if y>0: y:=y-1 〉 y:=y+1

P2 PG2

noncrit2 wait2 crit2 y>0:y:=y-1 y:= y+1

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SLIDE 47

loop forever

. . .

critical section

. . .

end loop *non-critical actions* *non-critical actions*

*request* *release*

〈 if y>0: y:=y-1 〉 y:=y+1

P1 PG1

noncrit1 wait1 crit1 y>0:y:=y-1 y:= y+1 loop forever

. . .

critical section

. . .

end loop *non-critical actions* *non-critical actions*

*request* *release*

〈 if y>0: y:=y-1 〉 y:=y+1

P2 PG2

noncrit2 wait2 crit2 y>0:y:=y-1 y:= y+1

atomic

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noncrit1, noncrit2 wait1, noncrit2 noncrit1, wait2 crit1, noncrit2 wait1, wait2 noncrit1, crit2 crit1, wait2 wait1, crit2 crit1, crit2 y:=y+1 y:=y+1 y:=y+1 y:=y+1 y:=y+1 y>0: y:=y-1 y>0: y:=y-1 y>0: y:=y-1

PG1 ||| PG2

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n1, n2, y=1 w1, n2, y=1 n1, w2, y=1 c1, n2, y=0 w1, w2, y=1 n1, c2, y=0 c1, w2, y=0 w1, c2, y=0

TS( PG1 ||| PG2 )

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SLIDE 50

n1, n2, y=1 w1, n2, y=1 n1, w2, y=1 c1, n2, y=0 w1, w2, y=1 n1, c2, y=0 c1, w2, y=0 w1, c2, y=0

TS( PG1 ||| PG2 ) Both processes cannot be in critical section simultaneously

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SLIDE 51

Concurrent systems

Independent

Interleaving TS1 ||| TS2 ||| ... ||| TSn

Shared variables

TS( PG1 ||| PG2 ||| ... ||| PGn )

Mutual Exclusion

Shared actions

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Coming next: Book-keeping system in a supermarket

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1 1 1 scan check_price check_price print_cmd print_cmd print Bar-Code Reader (BCR) Booking Program (BP) Printer (P)

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1 1 1 scan check_price check_price print_cmd print_cmd print Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 000

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1 1 1 scan check_price check_price print_cmd print_cmd print Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 100 000 scan

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1 1 1 scan check_price check_price print_cmd print_cmd print Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 100 000 010 scan check_price

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1 1 1 scan check_price check_price print_cmd print_cmd print Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 100 000 001 010 scan check_price prt_cmd

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1 1 1 scan check_price check_price print_cmd print_cmd print Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 100 000 001 110 111 011 101 010 print scan scan print print scan prt_cmd check_price check_price prt_cmd scan print

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SLIDE 59

1 1 1 scan check_price check_price print_cmd print_cmd print Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 100 000 001 110 111 011 101 010 print scan scan print print scan prt_cmd check_price check_price prt_cmd scan print BCR || BP || P

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1 1 1 scan check_price check_price print_cmd print_cmd print Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 100 000 001 110 111 011 101 010 print scan scan print print scan prt_cmd check_price check_price prt_cmd scan print BCR || BP || P check_price, print_cmd: Shared actions (also called handshaking actions)

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Next example: Train-Gate-Controller

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TRAIN GATE

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TRAIN GATE far near in 1 2 3 up down approach enter exit approach lower exit raise lower raise

Train Controller Gate

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far near in 1 2 3 up down approach enter exit approach lower exit raise lower raise

Train Controller Gate

far, 0, up near, 1, up near, 2, down in, 1, up in, 2, down far, 3, down approach lower enter enter exit lower raise Train || Controller || Gate

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|| : Handshake operator

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Independent

Interleaving TS1 ||| TS2 ||| ... ||| TSn

Shared variables

TS( PG1 ||| PG2 ||| ... ||| PGn )

Mutual Exclusion

Shared actions

TS1 || TS2

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SLIDE 67

Reference: Principles of Model Checking, Baier and Katoen, MIT Press (2008) Pages 35 - 53

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