Does anyone know if where i could learn more about the software safety standards for real time applications, such as for car and plane autopilots?
Both EU and US suggestions are very much wanted.
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The question is rather broad, only vaguely on-topic, and not a Q&A type of question...
However, I'll give it ago... and fortunately, the US and EU are reasonably well aligned.
The primary functional safety standard for the automotive world is ISO 26262... a massive standard of 13 parts, addressing the whole software and systems engineering lifecycle.
Associated with this, you have ISO/SAE 21434 which addresses the Cybersecurity side of things, and supersedes the longer standing SAE J3061.
As autonomy becomes a bigger issue, a number of parallel projects are ongoing, including UL4600 and several ISO-led works
In the aerospace domain, it's a little more complex and non-integrated... airborne software falls within DO-178C, while programmable electronics comes under DO-254
Work is ongoing to revise these for UAVs
At the software level, testing has been internationally standardised with ISO/IEC/IEEE 29119 (a multi part standard) which brought together a number of existing US and UK led standards in harmonised form... and has been further developed by an multi-national working group ISO/IEC JTC1/SC7/WG26.
Associated with this is the ISO/IEC 250xx SQuaRE family of standards which define quality measures.
Unfortunately, international standards are covered by copyright and are not freely available - hence no links in this answer. They can be sourced thorough the appropriate national body (eg BSI in the UK)
My day job revolves around a lot of these... I'm happy to discuss further (probably better offline... see profile)