Majority voting

Mehrdad Mahdavi

83206054

Winning an election

(strict majority)

(exists majority)

(conditional majority)

Predicates:

Abstract program :

A straightforward attempt

Disjunction inherent

using

(i)(ii)

First refinementIf there is no majority is a as i, then the only possible maj . In as (i+1) is as[i](i)

Introduction count c

A Second attemp is faster

Define variable

Refine…

Count c

Linear Time Code

Add variable d(State transformation)

Remove auxiliary c,j

Fast Code ………..

Merge alternationLaw 18.2 left-distribution of composition over alternation

.);(||;)(||

fiprogbranchGifprogfibranchGiif

ii

ii

Right-distribution of assignment over alternation

.);:]\[(||)(||;:

fibranchExExGiffibranchGiifEx

ii

ii

Simplify alternationLaw 18.4 remove false guard Law 18.5 remove alternation

Flatten nested alternationsLaw 18.6

.),(||

))(||(||

fibranchHGjif

fifibranchHjifGiif

ijji

ijji

Introduce invariant d>=0

Thanks