English to Russian Tech/Engineering Computers: Software Процессоры, кэш-память

Контекст (искомый фрагмент в третьем предложении, встречается 2 раза):

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As an example and not by way of limitation, processor 242 may include one or more instruction caches, one or more data caches, and one or more translation lookaside buffers (TLBs).

Instructions in the instruction caches may be copies of instructions in memory 244 or storage 248 and the instruction caches may speed up retrieval of those instructions by processor 242.

Data in the data caches may be copies of data in memory 244 or storage 248 for instructions executing at processor 242 to operate on; the results of previous instructions executed at processor 242 for access by subsequent instructions executing at processor 242, or for writing to memory 244, or storage 248; or other suitable data.

The data caches may speed up read or write operations by processor 242.
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Никак не пойму: в первом случае "for" относится к "instructions" или "executing"? И почему "executing", а не "executed", как в середине этого предложения?