A Binary Decision Tree. abstract domain. Functor. A Motivating Example. Precision Problem. Idea: The reduced cardinal power A2A1 A2 [CC79]

Size: px

Start display at page:

Download "A Binary Decision Tree. abstract domain. Functor. A Motivating Example. Precision Problem. Idea: The reduced cardinal power A2A1 A2 [CC79]"

Dylan Clinton Phelps
9 years ago
Views:

1 W k ) w _ ( 5 T > w < w w g x < g v ^ x x. B > 3 v ^ > ^ x + W ^ > x [. + 5 ] g P v > g ). x W S T w :: x ( ( k g x v ST v v x w ( k ) x ( ) q < E 5 v. T. T g k I I [4] w I g j g j I I v g v. T gg [4] w v g. v v g v / w g v / v g g k v g. I [4] w T k g. j. g x. T j g x k Iv [3] g [3] k v g. v g v. T gg vg g g g v w w g v g v. T v v. T k g g g g g v g. v g. g j g g. g v. T gg Ivv [3] g [3] [5] L wg x w. [8]: L g wg x w I v g v /. [3] g [3] Iv g. T. T j g x T. Iv [3] g [3] g j. g j Ex. vg x. Ex. vg x. g j v g g v g j. T v g / vw v g v v g. v g v / g j. T j g x. T x 3 L. T w j wg x w v. T j g x v g v g g / x ) { w (x >. g g g T j g x v g. Ex.++ ( 5> )vg { (w x < ) v x. v g. w ( > ) { L g g v wg x w [8 L ( x < 5 ) ++ Lg wg L x w v wg. ( x < 5 Ex ) ++ L x. x++. vg Ex. v 3 wg x w Ex. vg Ex x.. vg x x++ x Ex. vg x. w 3 5 ( > ) { 3 x++ 3 < 5 ) ++ 5 x (x 3 x x ( > ) x{ w ( > )3 w w ( > ) {( x < x++ x ( > ) { ( x < 5 w ) ++ ( x) < ( > { 5 ) ++ ( x < 5 ) ++ w x++ 5 ) ++ ( x < x++ W kw g v g ^ x ) _ x++ ( < x < 5x++ x++ Iv: ^ PRON (5 < x < 3^x+ Iv: ). W x w ^ 5 N O < R x P g ) <. ( g w v ) vx v v. H W ( ). k g ( ) x 5 g < k : (x ] v + x [ > 3 ^ g > 5 v ){ w B < ^ x + v ( x ^ > w g < x > v w (5 g { v k _ x. x ) w ^. B w W w g g x { > B B) x. ( / S. v g.. E w G g ) v T w. T. S w x x S P S. B ( E B w K w g g x. J x x S q k S g. :: B k.. / W w ). W ) ( ( v x x g ) q T ( S g S. w v ) G q g ( S ). w ) H v v... ( ) g g w B ( { g ) (S x v x B T w G ( q g ) G F K q v ( D J G g G w F ) (. T N { w Mvg Ex x B D T D F Jj Pk Nw Yk Uv ^ x ^ x + 5 Iv: x ^vx P: L ( )... vx P: ^ x q ^ x + 5 w x > ^x >^x+5 w L(v) ( ) q... > D ( ). Gv S k (vx ). B v D ( ). Gv S ( ) ( ) g. T (x < 5) v ( ) (S)( ) { ( ) S v ( ) (S) { S. q x g S. H w x k q g S. T w [79] ( ) 7 (( ) ). ( ) 7 (( ) )( ) () Gv S JPK g P (S{ JPK) S JPK () { ( ) B : B B w N. T B w v B LS : : ( ) \ S LJPK S JPK N ( ( ) \ S JPK) S JPK. Mv F B L w v : B ( ( F ) B B v )L\ Sw JPK) \ ( ( ) \ S JPK). E w ( v ( ) ( ) " S JPK g P. ( ) ( ) " w x w ( ( ) ) g ) I w g v g( w g ( ) ( ) ( ) [JM9] g v g w g x > ^ > SS 5 9 S 5 S M F J. & P SS 5 9 S 5 S M F P P J. & P I: v ( w ) j? N.g. G x (α v j) T : vx k w g w w g B g (( ) ) 7 (( ) ) B ) ) v. I w j v (( ) )) () 7(( { ( v () { ( g. H w ) J. & P 3 ` ((B ) ) 7 ((B ) \ D) B (( ) ) 7(( ) \) D) ` (D) { ` ( D ` 96 B (D) { ` ( ) D 4 T (H ). Gv : (X) {(x) x X (x) T (H ). Gv : 7 Y (Y ) {x G (X) {(x) x X : (Y ) {x (x) Y ` SS 5 9 S 5 S M F SS 5 9 S 5 S M F J. & P

2 Sx O S SS 5 9 S 5 S M F J. & P 5 S SS 5 9 S 5 S M F J. & P g > T q... Tq... w w w π v... g > x g > q... x x +... q... q... w w w q... w w w + w {" [ L... v... v " g v x x x g > x x E S JK { qx ql + ww w w k {" [ ++ L w {" [ S JkK {k E " g v.... v xe " g v. x [x S Jx EK {k : v] E ^v E S JK { E x x E S JK { S J K {( ) k E^ 8 S JkK + E {k k + L w {" [ S JkK {k E S J K ^ S J xe " g v. SS 5 9 S 5 S M F 6 J. & P 7 SS 5 9 S 5 S M F J. & P

3 T S T v x.... T Fw G SS 5 9 S 5 S M F J. & P 9 SS 5 9 S 5 S M F J. & P P L ( ) q... D ( ). Gv S ( ) ( ) (S) { ( ) S q x g S. Fw G w g (V E) g g: g g w. T FG (x) x : SS 5 9 S 5 S M F J. & P SS 5 9 S 5 S M F J. & P

4 P S FG T FG S: T SS 5 9 S 5 S M F J. & P 3 SS 5 9 S 5 S M F J. & P 4 P T B G (g w g) SS 5 9 S 5 S M F J. & P 5 SS 5 9 S 5 S M F J. & P 6

5 L E D E SS 5 9 S 5 S M F J. & P 7 SS 5 9 S 5 S M F J. & P 8 B P z SS 5 9 S 5 S M F J. & P 9 SS 5 9 S 5 S M F J. & P

6 B G Ex SS 5 9 S 5 S M F J. & P SS 5 9 S 5 S M F J. & P T S Pg T B D T Pk. S g. I S.S. Mk & N.D. J Pg Fw : T. g P-H I. Egw Nw J U.S SS 5 9 S 5 S M F J. & P 3 SS 5 9 S 5 S M F J. & P 4

7 B D T D. T(B D`) v B (w z `) D` (w z `) L M w D` B J B: K w B B ( ) g T(B \ D`) ( B B B \ v g B). J K P P J B : J B : L M L MK J B 3 : L 3 M L 4 MKK z B D 3. L v gg v (x)vx JK v x v z (L M) J `() w (J B: K) { JBK ) ( ) ^ JBK ) ( ) w. K L M SS 5 9 S 5 S M F L M B D T J K J K J K D F J. & P D 4. T(B D`)\ v? > O M w B D` w P Q... T(B D`)\ v T T {? > T(B D`) (8P T :? v P v > ) T T T j O M T T T wg wg 5 SS 5 9 S 5 S M F J. & P B D T D F T B w g. H g w. T D` v g g w v w. 6 SS 5 9 S 5 S M F J. & P 7 SS 5 9 S 5 S M F J. & P 8

8 B D T D F T B w g. H g w. T D` v g g w v w. v w vv g.g. (g ) I Eq T Gv w T(B D`) \{? > I : g (` `) v( )w ` ` B. v ` v` ` (` `) 6v w. Eq : v ^ v. I D` ` w. Pk R L Mg: S Sg D T D. E M P LNS 6 : SS 5 9 S 5 S M F J. & P 9 SS 5 9 S 5 S M F J. & P 3 M J Gv w T(B D`) \{? > M: (` `) v( )w` ` B. ` ` ` ` g ` D`. J: (` `) v( )w` ` B. D v v 5 >5 >5 ` (` ` `) ` D`( ) ` D`( ) `... ` D`( )w... D`( ) D` (w ` x D` w `( )). w j v v SS 5 9 S 5 S M F J. & P 3 SS 5 9 S 5 S M F J. & P 3

9 D v v D v v >5 >5 5 >5 > SS 5 9 S 5 S M F J. & P 33 SS 5 9 S 5 S M F J. & P 34 Wg Nwg Gv w T(B D`) \{? > v Wg O` : (` `) v( )w` ` B. ` (` O` `) ` D`( ) ` D`( ) `... ` D`( )w O` wg D`... D`( ) D`. w w v v Nwg M : (` `) v( ) w ` ` B. Nwg ` M ` M` ` g : wg (` `) v( M` ) w ` ` D`. B. ` ` M` ` g wg M` D`. R B D T P Gv T(B D`) w :?? > L M? L M L ` D`() M J B: K J B: D`(B) D`() D`( B) D`() K SS 5 9 S 5 S M F J. & P 35 SS 5 9 S 5 S M F J. & P 36

10 T T F g T F g v J J L M L MK J L M L MKK SS 5 9 S 5 S M F J. & P 37 SS 5 9 S 5 S M F J. & P 38 R Lv. g v {.... F... g. W ` (D`( ^ ^... ^ )). 3. F w ` `... `. B D T I - O g U g v v SS 5 9 S 5 S M F J. & P 39 SS 5 9 S 5 S M F J. & P 4

11 T Mgg B { B [ { B. Pk B.. E B (B B) B. 3. F JB : K v. 4. Ow xg. F (v) gg. W x w g v JB : K. x SS 5 9 S 5 S M F J. & P 4 SS 5 9 S 5 S M F J. & P 4 Ex j z wg z x v j w z wg vg SS 5 9 S 5 S M F J. & P 43 SS 5 9 S 5 S M F J. & P 44

12 W Fw G ( g ) B D T : Djv / j SS 5 9 S 5 S M F J. & P 45 SS 5 9 S 5 S M F J. & P 46 Tk & Q? SS 5 9 S 5 S M F J. & P 47

E. OZCEYLAN /International Journal of Lean Thinking Volume 1, Issue 1 (June 2010)

E. OZCEYLAN /International Journal of Lean Thinking Volume 1, Issue 1 (June 2010) I J L T k gv m1 I 1( J 2 0 1 0 ) LT k g. jmg: www. k g.m/ j AD S S m C m T M L g E Öz S ç ku D m I E g g C m 4 2 0 3 1 K T k z @ k.. ABSTRACT KEYWORDS L g m g m T m m m M m k g m m g g. F m T A m m x m