By selecting the POSIX FIFO scheduling policy, we can guarantee that no two threads of the same priority execute the critical section concurrently on a non-SMP system.
The FIFO scheduling policy dictates that all FIFO-scheduled threads in the system at the same priority will run, when scheduled, until they voluntarily release the processor to another thread.
This “release” can also occur when the thread blocks as part of requesting the service of another process, or when a signal occurs. The critical region must therefore be carefully coded and documented so that later maintenance of the code doesn't violate this condition.
In addition, higher-priority threads in that (or any other) process could still preempt these FIFO-scheduled threads. So, all the threads that could “collide” within the critical section must be FIFO-scheduled at the same priority. Having enforced this condition, the threads can then casually access this shared memory without having to first make explicit synchronization calls.