No idea about ATC systems, either. Actual software that flies airplanes is certified under RTCA's DO-278, not IEC 61508. DO-278 recognizes 4 basic criticality levels:
Level D: virtually no testing required. Think inflight entertainment systems.
Level C: Annoyance if the software has bugs. Think maintenance monitoring software that may drive false maintenance actions.
Level B: Errors could degrade redundancy of on-board systems but can't, in and of itself, crash the plane. Errors could require significant pilot intervention/workload to manage. Think software that moves fuel around the airplane or controls the (multiple redundant) hydraulic systems.
Level A: The good stuff. Software works or people die. This requires "branch level" testing, where you prove that you have tested every single permutation of every possible path through the code. Uber expensive - takes banks of computers running 24/7 for 6-24 months (depending on code complexity) to get through all the test cases.