Automatic Synthesis of New Behaviors from a Library of Available Behaviors

Transcription

1 Automti Synthesis of New Behviors from Lirry of Aville Behviors Giuseppe De Giomo Università di Rom L Spienz, Rom, Itly degiomo@dis.unirom1.it Sestin Srdin RMIT University, Melourne, Austrli ssrdin@s.rmit.edu.u

2 Behvior omposition Environment is similr to n tion theory! Behviors re similr to root progrms; pture possile exeutions Trget ehvior desription of the desired ehvior expressed in terms of virtul tions Environment desription of (virtul) tions, preoditions nd effets Aville ehviors desriptions of the ehvior of ville gents/devies expressed in terms virtul tions Atul ville ehviors Key points Ations re virtul Only ville ehviors provide tul tion exeution Must relize trget ehvior using frgments of ville ehviors Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 2

3 Behvior omposition: the setting studied Environment: Desrie preondition nd effet of tions (s n tion theory) Finite stte (to get omputiliy of the synthesis) Nondeterministi (devilish/don t t know nondeterminism) Represented s (finite) trnsition system (we re not onerned with representtion in this work) Aville ehviors: Desrie the pilities of the gent/devie Finite stte (to get omputility of the synthesis) Nondeterministi (devilish/don t t know nondeterminism) Cn ess the stte of the environment Cn not ess the stte of the other ville ehviors Represented s (finite) trnsition systems (with gurds to test the environment) Trget ehvior: As ville ehvior ut deterministi it s s spe of desired ehvior: we know wht we wnt! Prolem: synthesize sheduler tht relize the trget ehvior y suitly omposing the ville ehviors Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 3

4 Exmple trget ehvior (virtul!) ville ehvior 1 ville ehvior 2 sheduler Simplified se: ville ehviors re deterministi finite trnsition systems Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 4

5 Exmple trget ehvior ville ehvior 1 ville ehvior 2 sheduler A smple run tion request: sheduler response: Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 5

6 Exmple trget ehvior ville ehvior 1 ville ehvior 2 sheduler A smple run tion request: sheduler response:,1 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 6

7 Exmple trget ehvior ville ehvior 1 ville ehvior 2 sheduler A smple run tion request: sheduler response:,1,1 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 7

8 Exmple trget ehvior ville ehvior 1 ville ehvior 2 sheduler A smple run tion request: sheduler response:,1,1,2 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 8

9 Exmple trget ehvior ville ehvior 1 ville ehvior 2 sheduler A smple run tion request: sheduler response:,1,1,2,2 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 9

10 A sheduler progrm relizing the trget ehvior trget ehvior ville ehvior 1 sheduler progrm :1 :1 sheduler ville ehvior 2 :2 :2 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 10

11 Nondeterminism Nondeterministi environment Inomplete informtion on effets of tions Ation outome depends on externl (not modeled) events Nondeterministi ville ehviors Inomplete informtion on the tul ehvior Mismth etween ehvior desription (whih is in terms of the environment tions) nd tul ehvior of the gents/devies Deterministi trget ehvior Devilish (don t know)! it s s spe of desired ehvior: (devilish) nondeterminism is nned In generl, devilish nondeterminism diffiult to ope with eg. nondeterminism moves AI Plnning from PSPACE (lssil plnning) to EXPTIME (ontingent plnning with full oservility [Rintnen04]) Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 11

12 Exmple nondeterministi ehviors trget ehvior ehvior 1 S10 S11 sheduler ehvior 2 Devilish nondeterminism! S20 Aville ehviors represented s nondeterministi trnsition systems Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 12

13 Exmple nondeterministi ehviors trget ehvior ehvior 1 S10 S11 sheduler ehvior 2 S20 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 13

14 Exmple nondeterministi ehviors trget ehvior ehvior 1 S10 S11 sheduler ehvior 2 S20 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 14

15 Exmple nondeterministi ehviors trget ehvior ehvior 1 oserve the tul stte! S10 S11 sheduler ehvior 2 S20 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 15

16 Exmple nondeterministi ehviors trget ehvior ehvior 1 oserve the tul stte! S10 S11 sheduler ehvior 2 S20 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 16

17 Exmple: nondeterministi ehviors trget ehvior ehvior 1 oserve the tul stte! S10 S11 sheduler ehvior 2 S20 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 17

18 A sheduler progrm relizing the trget ehvior trget ehvior ehvior 1 S10 S11 sheduler progrm sheduler ehvior 2 S11::1 true::1 S20 S10::2 Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 18

19 Sheduler progrms Sheduler progrm is ny funtion P(h,) = i tht tkes history h nd n tion to exeute nd delgtes to the ville ehvior i A history is sequene of the form: (s 10,s 20,,s,s n0,e 0 ) 1 (s 11,s 21,,s,s n1,e 1 ) k (s k1,s 2k,,s,s nk,e k ) ontins ll the oservle informtion up the urrent sitution Oserve tht to tke deision P hs full ess to the pst,, ut no ess to the future Prolem: synthesize sheduler progrm P tht relizes the trget ehvior mking use of the ville ehviors Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 19

20 Tehnique: redution to PDL Bsi ide: A sheduler progrm P relizes the trget ehvior T iff: trnsition leled of the trget ehvior T n ville ehvior B i (the one hosen y P) ) whih n mke n -trnsition nd -trnsition of B i relizes the -trnsition of T Enoding in PDL: trnsition leled use rnhing n ville ehvior B i use underspeified predites ssigned through SAT -trnsition of B i : use rnhing gin Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 20

21 Struture of the PDL enoding = Init [u]( 0 i=1,,n i ux ) Initil sttes of ll ehviors PDL enoding of trget ehvior PDL enoding of the i-th ville ehvior + environment PDL dditionl dominindependent onditions PDL enoding is polynomil in the size of the trget ehvior, ville ehviors, nd environment Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 21

22 Tehnil results: theoretil Thm Cheking the existene of sheduler progrm relizing the trget ehvior is EXPTIME-omplete. EXPTIME-hrdness due to Musholl&Wlukiewiz05 for deterministi ehviors Thm If sheduler progrm exists there exists one tht is finite stte. Exploits the finite model property of PDL Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 22

23 Tehnil results: prtil Redution to PDL provides lso prtil sound nd omplete tehnique to ompute the sheduler progrm Use stte-of-the-rt tleux systems for OWL-DL for heking SAT of PDL formul If SAT, the tleu returns finite model of eg, Univ. Mrylnd exponentil in the size of the ehviors Projet wy irrelevnt predites from suh model, nd possily minimize polynomil in the size of the model The resulting struture is finite sheduler progrm tht relizes the trget ehvior Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 23

24 Conlusion Nondeterministi trget ehvior? loose speifition in lient request ngeli (don re) vs devilish (don t t know) nondeterminism see ICSOC 04 for ides Distriute the sheduler? Often entrlized sheduler is unrelisti: eg. Root Eologies too tight oordintion too muh ommunition sheduler nnot e emodied nywhere drop entrlized sheduler in fvor of independent ontrollers on single ville ehviors (exhnging messges) we re tively working on it Infinite sttes ehviors? Importnt for deling with dt/prmeters this is the single most diffiult issue to tkle first results: tions s DB updtes, see VLDB 05 literture on Astrtion in Verifition Automti Synthesis of New Behviors from Lirry of Aville Behviors IJCAI 07 - Jn 12, 2007 Hyderd, Indi Giuseppe De Giomo 24