# Systolic Computations by M. A. Frumkin (auth.)

By M. A. Frumkin (auth.)

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Definition 1. A nonbranching program with S registers (NBPR) is an NBP with the following instruction set: R. (Zl'z 1 1 . 1 ), zl'z . 1 1 1 is one of r. 1 S E {X 1 , ••• ,x n ,R 1 , ••• ,Rs }, i=l, ... ,T, x 1 , ••• ,x n are input variables, h. : X x X ~ X. In 1 1 a natural way to the left side of each instruction of NBPR we can assign an element of the set X. NBPR computes a function f:X n ~ xm if for each j E [l,m) there exists an where R. r. registers, instruction which the left side considered as a function of inputs is equal to the jth component of f.

Definition 1. A nonbranching program with S registers (NBPR) is an NBP with the following instruction set: R. (Zl'z 1 1 . 1 ), zl'z . 1 1 1 is one of r. 1 S E {X 1 , ••• ,x n ,R 1 , ••• ,Rs }, i=l, ... ,T, x 1 , ••• ,x n are input variables, h. : X x X ~ X. In 1 1 a natural way to the left side of each instruction of NBPR we can assign an element of the set X. NBPR computes a function f:X n ~ xm if for each j E [l,m) there exists an where R. r. registers, instruction which the left side considered as a function of inputs is equal to the jth component of f.

Definition 15. A block RB-game of the order B on an acyclic directed graph is a game vith the folloving rules: 1. At each moment ve can remove an arbitrary number of pebbles. 2. Input. At the initial moment all input nodes contain blue pebbles. 3. Store the results in the main memory. Each node must be pebbled by a blue pebble. 4. Computation. A red pebble can be placed vith all predecessors pebbled by red pebble from a node to a successive slide and pebbling are alloved. pebbles. node 5. Block exchange betveen memories.