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Nondeterministic execution in BPJ model checking

In common processing event selection in BP is deterministic. However, in some cases it is desired to specify nondetermistic choices - e.g., when simulating environment behavior using b-threads as part of model checking. The BPJ model checking capability explores all possible execution paths defined by this nondeterminism. In fact, often, the only non-determinism in execution is in b-threads that simulate the environment.

Specifiying nondeterminism

  • In BP, event selection is deteremined by the unique priority of each b-thread, and by the order of events in the requested event set.
  • When the difference in priority of two b-threads is less than a given "epsilon" (a real number provided by the user), the two b-threads are considered of same priority. For example, to create 48 bthreads of the same priority, choose epsilon of 1.00 and create the set of these b-threads so that their priorities have the same whole part and differ only by fractional part. (e.g. priority values of 7.001 – 7.048). The value of "epsilon" is determined by the method call setBthreadEpsilon().
  • Additionally, during model checking if an event in a requested event set of any b-thread is selected (requested and not blocked, and non-deterministic execution actually selected it), then if the event was in a nested second-level set, then all other events in the same nested second-level set are considered to be of the same priority. For example, if the requested even set is R={{e1,e2},e3,{e4,e5,e6,e7},e8} - then if e5 was selected (say, all preceding events were blocked), then e6 and e7, and only them are considered of the same priority and will be explored in non-deterministic execution. This priority processing is relevant only to the first event selection in b-thread. Once the selected second-level set is exhausted, (or if the event was a first level in the first place), non-deterministic execution continues with the next b-thread of the "same" priority as the previous b-thread.

See execution below for more details.

Nondeterministic execution

When executing in model-checking mode, nondeterministic event selection is performed according to the following algorithm :

  • Scan b-threads in order of priority
  • Scan the requested event set of each b-thread in event order (the set is enumerable).
  • When the first event that is requested and not blocked is found it is remembered as one alternative.
  • If the selected event was in a second level event set (a set within a set), all its siblings in the same second level set that are not blocked are considered having the same priority, and are added as alternatives.
  • If the event is in a first level of the requested event set, this event is the only one from this b-thread.
  • After exploring all execution subtrees anchored at the alternatives from one b-thread go to the next b-thread of “same” priority as defined with epsilon, and repeat the above . At most one second-level set will be selected from the requested events of that b-thread, but not necessarily the first one.
  • When all alternatives in a given execution path are explored the execution returns to the next higher level in the nondeterministic execution path to select the next alternative at that level.
  • BPJ model checking uses the Java package javaflow to restore the stack of all b-threads in order to resume execution of another subtree at a previously visited synchronization point.

Programming Constraints

  • While in regular runs a b-thread can terminate, in a MC run A b-thread should not terminate, to allow BPJ model checking to backtrack. Precede/replace the return with bSync(none,none,none); In a regular run this will just terminate. In MC run it will allow the b-thread to backtrack from the end.