Is an airplane's control software source code open (or to some extent) to external review?
I don't imagine it is open-sourced, but if it is completely a black box, how can we know that any accident is not due to weather, but system drawback?
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Any safety-critical software, of which aircraft fly-by-wire is an obvious example, must be written to the regulations regarding the SSIL (Software Safety Integrity Level).
At SSIL-4 (Defined as - if the software fails many people may die), it is legally required in most jurisdictions that the software is independently audited. So, the source code and full development process is made available to an outside party. This, of course, is a confidential process.
The exact regulations regarding this process vary between jurisdictions. For example in the USA the software must be validated under DO178C. In Europe and much of Asia, one of the CENELEC standards, e.g. BS EN50128 is used - the bane of my working life!.
So, is it a black box? Not necessarily. Can a fault be traced if an accident occurs? Yes, probably. All relevant standards mandate a mechanism for tracing the software processes in great detail. Even near-misses must be analyzed and faults corrected.