An equational axiomatization of systolic systems

Abstract

The syntax of a systolic system is given by a systolic flowchart scheme. Systolic schemes differ from ordinary ones in their edges having a nonnegative integer, called the delay number associated with them. If the value of the delay number is d, then the edge is considered to be a buffer holding d data elements in each moment of the computation. The buffers are handled in a FIFO way, transmitting data between the corresponding i/o ports of two interconnected processors. The algebraic language which is used to express schemes is different from the most frequently used one, containing composition, pairing and iteration as basic operations. The present language contains sum and a new operation called the “feedback” beyond composition, and only five constants. The axiomatization is carried out in two steps. First we present a set of equational axioms for the class of loop-free schemes, which are called data flowchart schemes. This set of axioms is extended by further axioms describing the syntactic features of the feedback operation.