As modern software would utilize error checking I'd say no random mutation would occur on its own. A single bit flipped due to whatever reason could cause fatal results or do basically nothing to a machine/software. "Physical" measurements like ECC memory, and software solutions like checksums are commonplace.

I see two options here:

1. They are designed to evolve.

I'm no expert on AI technology so I'm ignorant about AIs limitations but as we are not even close to creating evolving nanobots with modern technology and AI technology is in its infancy it would not be too much of a stretch to simply say that your nanobots do utilize AI to determine new 'evolutionary' paths.

2. Nanobots have to fight other nanobots

In a full out warfare against other nanobots I could imagine some errors to accumulate. Nanobots would probably have reasons to change their combat strategy on a physical level (prompting them to change) but they would also engage on a software level trying to hack each other. With a limit on time (security measures take some time), a constant physical and software barrage of enemies trying to utilize every weakness and certain random events (radiation, rapid changing magnetic fields, etc) I could definitely see the nanobots undergoing a DNA like change over time.

As modern software would utilize error checking I'd say no random mutation would occur on its own. A single bit flipped due to whatever reason could cause fatal results or do basically nothing to a machine/software. "Physical" measures like ECC memory, and software solutions like checksums are commonplace.

I see two options here:

1. They are designed to evolve.

I'm no expert on AI technology so I'm ignorant about AIs limitations but as we are not even close to creating evolving nanobots with modern technology and AI technology is in its infancy it would not be too much of a stretch to simply say that your nanobots do utilize AI to determine new 'evolutionary' paths.

2. Nanobots have to fight other nanobots

In a full out warfare against other nanobots I could imagine some errors accumulating. Nanobots would probably have reasons to change their combat strategy on a physical level (prompting them to change) but they would also engage on a software level trying to hack each other. With a limit on time (security measures take some time), a constant physical and software barrage of enemies trying to utilize every weakness and certain random events (radiation, rapid changing magnetic fields, etc) I could definitely see the nanobots undergoing a DNA like change over time.