1. Computer Science 6/13/2015CPSC 433: Other Search Models and Processes 1 CPSC 433 - Artificial Intelligence Winter 2006 Search Paradigms: Search Summary Rob Kremer ICT 748 kremer@cpsc.ucalgary.ca http://pages.cpsc.ucalgary.ca/~kremer/

2. 6/13/2015CPSC 433: Other Search Models and Processes 2 TOC Search Models Search Processes Instances and Goals

3. 6/13/2015CPSC 433: Other Search Models and Processes 3 Search Models A:(S,T)Set-basedAnd-tree-basedOr-tree-based S:possible states S  2 F ; F:set of facts S   Atree; Atree: (pr, sol:{yes,?}, b 1 :Atree,…,b n :Atree), n  0 S   Otree; Otree: (pr, sol:{yes,?,no}, b 1 :Otree,…,b n :Otree), n  0 T:SxS = possible Transitions T: {(s,s') |  A  B  Ext  A  s  s'=(s-A)  B}; Ext  {A  B | A,B  F} T  = {(s 1 : S,s 2 : S ) | Erw  (s 1,s 2 )  Erw*  (s 2,s 1 )};  Erw  ((pr,?), (pr,yes));  Erw  ((pr,?), (pr,?,(pr 1,?),…,(pr n,?));    Erw  ((pr,?,b 1,…,b n ), (pr,?,b 1 ',…,b n '));  Erw*  ((pr,?,b 1,…,b n ), (pr,?,b 1 ',…,b n ')) T  = {(s 1,s 2 ) |s 1,s 2  S   Erw  (s 1,s 2 )};    Erw  ((pr,?), (pr,yes))  Erw  ((pr,?), (pr,no))  Erw  ((pr,?), (pr,?,(pr 1,?),..,(pr n,?)))  Erw  ((pr,?,b 1,…,b n ), (pr,?,b 1 ',…,b n '))

4. 6/13/2015CPSC 433: Other Search Models and Processes 4 Search Processes P:(A,Env,K)Set-basedAnd-tree- based Or-tree- based K:SxEnv  SK(s,e) = (s-A)  B Utility: SxSxEnv  Nat  A'  B'  Ext | A’  s  f Wert (A,B,e)  f Wert (A',B',e); f Wert : 2 F  2 F  Env  Nat f leaf Select: 2 SxS xEnv  SxS A  B = f select ({A'  B' |  A"  B"  Ext | A"  s  f Wert (A',B',e)  f Wert (A",B",e)},e); f select : 2 2F  2F  Env  2 F  2 F f trans

5. 6/13/2015CPSC 433: Other Search Models and Processes 5 Instances and Goals Set-basedAnd-tree-basedOr-tree-based Ins=(s 0,G) G: s  {yes,no} s goal  s  no more expansions possible s = (pr’, yes)  ((pr’, ?, b 1..b n ) ^ G ^ (b 1 )=..=G ^ (b n )=yes ^ the sols are compatable )  no more solutions s = (pr’, yes)  ((pr’, ?, b 1..b n ) ^ G ^ (b i )=yes )  can’t process any leaves