Deviation Detection in Clinical Pathways Based on Business Alignment

Algorithm 2

Synchronous composition algorithm.

	Input: process model Npm, log model Nlm;
	Output: synchronous composition model Ncm.
(1)	Pcm = Ppm ∪ Plm;
(2)	Fcm = Ø;
(3)	Tcm = Ø;
(4)	mi,cm = mi,pm ∪ mi,lm;
(5)	mf,cm = mf,pm ∪ mf,lm;
(6)	for all ∈ Tlmdo
(7)	//place transitions in Tcm according to Tlm;
(8)	Tcm = Tcm ∪ {(, ^≫)};
(9)	//set the related mapping functions and arc relations
(10)	αcm ((^≫, ty)) = αpm (ty);
(11)	Fcm = Fcm ∪ {(p, (^≫, ty))|p ∈ ^•ty ˄ ty ∈ Tpm} ∪ {((^≫, ty), p)|p ∈ ty^• ˄ ty ∈ Tpm};
(12)	end
(13)	for all ty ∈ Tpmdo
(14)	//place transitions in Tcm according to Tpm;
(15)	Tcm = Tcm ∪ {(^≫, ty)};
(16)	//set the related mapping functions and arc relationships
(17)	αcm ((^≫, ty)) = αpm (ty);
(18)	Fcm = Fcm ∪ {(p, (^≫, ty)) | p ∈ ^•ty ˄ ty ∈ Tpm} ∪ {((^≫, ty), p) | p ∈ ty^• ˄ ty ∈ Tpm};
(19)	end
(20)	for all ∈ Tlm ˄ ty ∈ Tpm ˄ αlm () == αpm (ty) do
(21)	//place synchronous transitions in Tcm;
(22)	Tcm = Tcm ∪ {(, ty)};
(23)	//remove log transitions and model transitions with the same labels;
(24)	αcm ((, ty)) = αcm (, ^≫);
(25)	Tcm = Tcm − {(, ^≫), (^≫, ty)};
(26)	//set the related mapping functions and arc relationships of the new transitions; remove the related arc relationships of the removed transitions of the deleted transitions
(27)	Fcm = Fcm ∪ {((, ty), p′)|p′ ∈ (, ^≫)^•} ∪ {(p′, (, ty))|p′ ∈ ^•(, ^≫)};
(28)	Fcm = Fcm – {((, ^≫), p′)|p′ ∈ (, ^≫)^•} – {(p′, (, ^≫))|p′ ∈ ^•(, ^≫)};
(29)	Fcm = Fcm ∪ {((, ty), p) | p ∈ (^≫, ty)^•} ∪ {(p, (, ty)) | p ∈ ^•(^≫, ty)};
(30)	Fcm = Fcm – {((^≫, ty), p) | p ∈ (^≫, ty)^•} – {(p, (^≫, ty)) | p ∈ ^•(^≫, ty)};
(31)	end
(32)	return Ncm = (Pcm, Tcm; Fcm, αcm, mi,cm, mf,cm);