[PPT] - as * . . FFIMS Singapore ifip meeting September 2016 PowerPoint Presentation

SLIDE 1

ASSUME ADMISSIBLE SYNTHESIS

Jean

. Francois Raskin

Universit

'

Libre de Bruxelles

. .

FFIMS

Singapore

ifip

meeting

as

September

2016

*

SLIDE 2

REACTIVE

SYNTHESIS Classical setting

Sys

Enr ? t ¢

¢

is the winning

bjective for Sgs

EW is

adversarial

⇒ 2

player

zero

sum

game

Tinning strategy

=

Correct Sys

SLIDE 3

Sys

Enr ? t

¢

→ Env is completely adversarial

?

what if Ew =

Rational

user →

Sys

and /

r

Eno can be made

f several

components

, each with

their

wn
bjective

.

>

De need

a

richer

setting

SLIDE 4 N . players

turn

. based graph games Finite directed

graph

z

~ <

>

Vertices

are

partitioned

^

V=VsoV£ut

. .

.tk

(

=

|

vi.

verkasofployoei

>

Ee

V×V

SLIDE 5

Players

and

bjectives

Strategies 0=4,2

, ... ,w}

i

:V*.¥

V

Players

stand for : s.t.tt#.vev*.V.. ,

partofthegskmtodesqn

( visit

't .D)eE

parts of

the environment

;

*ma

s 2 ... W . .

N

"/\

. "

¢

.

¢2

¢

'

&

...

serofskakgiesof

KEV

Ployoei

.

SLIDE 6

Strategy profiles

and

utcomes

( %

, oz , ... ,

f )

E

{

sx

{

as x. . .x{w

Ei

€ { . i

profile

=

(

% , I all

strategies of

the

profile

broi

Qtr

(

f

, oz , . . . , %) = No Ns Ne . . . Nn . . . = T SE : . No = N

tj

> , ° : if

Tcj )

e

Vi

then

tcjts

)=%ftGjD

SLIDE 7

Running example

2 players

tv

5

3#

:

7 4

%

¢s=-

he

12=-17.43

= Players = Player 2

SLIDE 8

SYNTHESIS

RULES

SLIDE 9

Synthesis rules

WIN

Ew

Sys

s

2 ... W

0 .

{ &

...

% } ignored

=)

is

.

Voz

. . . . . How :

arcos

,r , ...

,or)÷

6 Can be inskakord =

2-

player zero

sum

case for

any

Players .

SLIDE 10

Running example

win

m

5 3 \

( ~ I

%

=-D a 4 >

µ

0/2 I D 43 4

hf

None

f the

players has

a

winning strategy

! \ }

Y

SLIDE 11

Running example

win

m

5 3 \

( ~

I

¢s=-

Da 4 >

µ

0/2 =-D 43 4

By playing

1

5 Players spoils

¢2±D<>3

SLIDE 12

Running example

win

m

5 3 \

( ~

I

¢s=-

Da 4 >

µ

0/2 ± D 43 4

By playing

2

2

Player 2 spoils

¢s±D<>4

SLIDE 13

Synthesis rules

WIN

. HYP Ew

Sys

1

2 ... W

Or

{ ok

Or }

. HYP

Foes

.

Voz

. . . . . How : Our ( os ,q , ... ,%) t

¢£^

. . .

^¢w

→

Or

%

Can be inskakard

HYP

for any Players .

SLIDE 14

Running example

WIN

. HYP

m

5 3 \

( ~ I

¢s=-

Da 4

>[g

0/2=-1343

li

,

Pts

wins

k
¢ .

with

a

5

th

\

> useless

solution !

SLIDE 15

ADMISSIBILITY

SLIDE 16

Dominated

strategy

is

dominated

by

l for E.

if

SLIDE 17

Dominated

strategy

is

dominated

by

l for E.

if @

tqi

EL . i : % Always as good

ark.

, %) t

¢

. ⇒

ONCE

. ' , a) t ¢ .

SLIDE 18

Dominated

strategy

is

dominated

by

l for E.

if @

tqi

EL . i : % Always as good

ark

, %) t

¢

. ⇒

ONCE

. ' ,

.oDt¢

. 2 Z Ei E { . i : % Sometimes better

ON

i

, %) ¥ 0 , ^

ONCE .io

... ) t

¢

.

SLIDE 19

Dominated

strategy

is

dominated

by

l for E.

if @

tqi

EL . i : % Always as good

ark.

, %) t

¢

. ⇒

ONCE

. ' ,

.oDt&

2 =) Ei E { . i : % Sometimes better

ON

% , %) ¥ 0 , ^

ONCE .io

... ) t

¢

. → A

rational

player

avoids dominated

strategies

SLIDE 20

m

5 3 \ ,

¢s=

. Da 4

A;

4

Any strategy

that takes

r→5 is dominated by the

strategy

1→2 , 3 → 4

even

if

iris not a winning strategy

SLIDE 21

Admissible strategy

.

E.

E

{

i is

admissible

for ¢ ;

if

i

is not dominated

by any

E. ' E 4. for ¢ . . Adm , ( oh . ) c-

{

i is

the set of admissible

strategies of Player

i

for

¢i

.

Adm.

.

( oh

. ) =

the only { Festooned} strategies !

Adm

;

( ¢ ;)

= , t

fi

.

SLIDE 22

m

5 3 \ ✓

¢s=

. Da 4

( X;

4 1

2

, 3 → 4 9

{

is

admissible

a '

EE

' '

335L indents

SLIDE 23

Synthesis rules

ssune Admissible s 2 ... W

Or 02

0w

FK

,r , ... ,

r )

: @ % E Adm

( ¢ ; )

for

alli.rsisn@VoteAdm.iC4.D

:

Onto

.

,oI)k¢

.

Yach

q . is

winning against

all

admissible strategiesofthe others

SLIDE 24 ,

a

s

X

> 5 3 \

YYa3→4 ( ~

I

¢s=-

Da 4 >

y

42

=-D 43 4 GD n2→2

Claim

:

Hoi

e Adm~(oh) . Voze

Admz (

k

: Out (

r

,

r )

t

¢s^ $2

⇒ Assume Admissible

rule applies !

SLIDE 25

Assume Admissible

Synthesis

Theorem :

for

all

AA

profiles

(

r

, a. ... , %) : Our ( as , oos , . . ,

n)

t

¢n¢u

.

.ro/v

Theorem : the

ser of AA

profiles

is

rectangular

. = SIX ST x . . . x STW Sti =

{

i

E Adm (¢D|

Foe

e Adm. , ($ .D: Out ( q . ,%) taxi} ⇒ To need for synchronization ! ⇒

Compositionally

SLIDE 26

Theorem :

deciding if

AA

applies

is

Pspaa

C for

Safety

,

Reach ability

and Muller

bjectives

.

SLIDE 27

Theorem :

deciding if

AA

applies

is

Pspaa

C for

Safety

, Readability and Muller

bjectives

. State Space $2 =-D Safe Value is Value

Value
2

*

tu

XD Safe KKDD Safe TKRDD safe A player when playing admissible never decrease its value .

SLIDE 28

Theorem :

deciding if

AA

applies

is

Pspaa

. Cfa

Safety

, Readability and Muller

bjectives

. State Space $z=- Dsafe Values Valeo Value . z for

ther properties

#

Values

⇒ Win !

f

t

+ Value . ⇒ Win

n

ADD Safe KKDD Safe ' KRDD safe

Help !

⇒ The setofplays compatible A player when playing admissible

with admissible strategies

never decrease its value . is W .

regular

SLIDE 29

Conclusion

Assume

admissible

synthesis allows for

... compositional Synthesis in W . player non . zero

:

mm games .

:

"

Rectangular

sets of

solutions

. .

Jf

win

gives

a solution then AA gives a

solution

.

Jf

. Win

HYP

gives

a solution and ( (D)

¢z

then

AA

gives

a solution .