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Regions Finite Partitioning of State Space

Regions Finite Partitioning of State Space. y. 2. 1. x. 1. 2. 3. An equivalence class (i.e. a region ) in fact there is only a finite number of regions!!. An Example Region Graph. Fischer’s Protocol. 2. ´. V. Criticial Section. X<10. X:=0. X>10. Init V=1. V := 1. V=1. A1.

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Regions Finite Partitioning of State Space

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  1. RegionsFinite Partitioning of State Space y 2 1 x 1 2 3 An equivalence class (i.e. a region) in fact there is only a finite number of regions!!

  2. An Example Region Graph

  3. Fischer’s Protocol 2 • ´ V Criticial Section X<10 X:=0 X>10 Init V=1 V:=1 V=1 A1 CS1 B1 Y<10 Y:=0 Y>10 V:=2 V=2 CS2 B2 A2

  4. X<1 X:=0 X>1 V:=1 V=1 A1 CS1 B1 Y>1 Y<1 Y:=0 V:=2 V=2 CS2 B2 A2 Fischer’s cont. Untimed case Timed case Partial Region Graph A1,A2,v=1 A1,A2,v=1 x=y=0 A1,A2,v=1 0 <x=y <1 A1,A2,v=1 x=y=1 A1,A2,v=1 1 <x,y A1,B2,v=2 A1,B2,v=2 0 <x<1 y=0 A1,B2,v=2 0 <y < x<1 A1,B2,v=2 0 <y < x=1 y=0 A1,B2,v=2 0 <y<1 1 <x A1,CS2,v=2 A1,B2,v=2 1 <x,y A1,B2,v=2 y=1 1 <x B1,CS2,v=1 A1,CS2,v=2 1 <x,y CS1,CS2,v=1 No further behaviour possible!!

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