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A new type of recurrence equations called "indexed recurrences" (IR) is defined, in which the common notion of X i = opX i ; X i ,1 i = 1 : : : nis generalized to X gi = opX fi ; X h i f;g;h : f1: : : n g 7 ! f 1 : : : m g . This enables us to model sequential loops of the form for i = 1 to n do begin X gi := opX fi ;X h i ; as IR equations. Thus, a parallel algorithm that solves a set of IR equations is in fact a way to transform sequential loops into parallel ones. Note that the circuitdoi:10.1109/ipps.1997.580935 dblp:conf/ipps/HaberB97 fatcat:oz3ux6yfdzc5hf2vgts5xhwhc4