powerdomain
The powerdomain of a domain D is a domain containing some of the subsets of D. Due to the asymmetry condition in the definition of a partial order (and therefore of a domain) the powerdomain cannot contain all the subsets of D. This is because there may be different sets X and Y such that X <= Y and Y <= X which, by the asymmetry condition would have to be considered equal. There are at least three possible orderings of the subsets of a powerdomain: Egli-Milner: X <= Y iff for all x in X, exists y in Y: x <= y and for all y in Y, exists x in X: x <= y ("The other domain always contains a related element"). Hoare or Partial Correctness or Safety: X <= Y iff for all x in X, exists y in Y: x <= y ("The bigger domain always contains a bigger element"). Smyth or Total Correctness or Liveness: X <= Y iff for all y in Y, exists x in X: x <= y ("The smaller domain always contains a smaller element"). If a powerdomain represents the result of an {abstract interpretation} in which a bigger value is a safe approximation to a smaller value then the Hoare powerdomain is appropriate because the safe approximation Y to the powerdomain X contains a safe approximation to each point in X. ("<=" is written in LaTeX as sqsubseteq). (1995-02-03) In addition suitable contents:
[ 2 ] [ = ] [ abstract interpretation ] [ af ] [ ai ] [ al ] [ am ] [ an ] [ app ] [ ar ] [ arc ] [ as ] [ at ] [ au ] [ av ] [ b ] [ be ] [ bi ] [ bs ] [ by ] [ C ] [ ca ] [ ch ] [ co ] [ con ] [ cons ] [ D ] [ de ] [ diff ] [ do ] [ domain ] [ du ] [ E ] [ ec ] [ ed ] [ ee ] [ element ] [ er ] [ es ] [ et ] [ fi ] [ file ] [ fo ] [ for ] [ ge ] [ gl ] [ gs ] [ h ] [ hat ] [ Hoare powerdomain ] [ hr ] [ id ] [ iff ] [ il ] [ in ] [ int ] [ io ] [ is ] [ it ] [ la ] [ LaTeX ] [ ld ] [ Lex ] [ li ] [ lt ] [ lu ] [ M ] [ ma ] [ mall ] [ mm ] [ mo ] [ mod ] [ module ] [ my ] [ na ] [ ne ] [ ng ] [ ni ] [ nn ] [ no ] [ ns ] [ om ] [ op ] [ ordering ] [ pa ] [ ph ] [ point ] [ pr ] [ query ] [ rc ] [ re ] [ ro ] [ S ] [ sa ] [ safe ] [ se ] [ set ] [ si ] [ sm ] [ so ] [ sqsubseteq ] [ st ] [ su ] [ subseteq ] [ sy ] [ T ] [ th ] [ theory ] [ tn ] [ to ] [ tr ] [ tt ] [ ua ] [ us ] [ va ] [ value ] [ ve ] [ X ] [ Y ] [ yt ]
[ Go Back ]
Free On-line Dictionary of Computing Copyright © by OnlineWoerterBuecher.de - (3664 Reads) |
