Theoretical and Experimental DNA Computation (Natural ...

4.10 The Translation Process 97
block Bk−1(i) correspond to the contents of memory location M[i] priorto
the execution of Ik by SA; Ck produces as its output r × S(n) Boolean values
arranged as S(n) r-bit blocks, the values in the i th block Bk(i) corresponding
to the contents of memory location M[i] after the execution of Ik by SA.
As a consequence of the translation just described, the programs corresponding
to the actions of each processor working in parallel at some stage
of the computation consist of identical (except for memory references) linear
control graphs. A typical linear graph consists of processing some values
stored in memory (using the accumulator), storing a value computed in memory,
and repeating this sequence until its computation is completed. We can
thus simulate this process by building a circuit which consists of several levels
–each level mimics the calculations performed in the program and ends with
either a halt instruction or a store instruction. What has to be ensured in the
circuit simulation is that the store and halt instructions have an effect only if
their controlling conditions evaluate to true. Thus, let L =< l1,l2,...,lt > be
a sequence of instructions such that lt has the form < conditional > HALT ,
< conditional > ST A, or< conditional > ST I, andlk(1 ≤ k