Adding Partial Orders to Linear Temporal Logic

Modeling execution as partial orders increases the flexibility in reasoning about concurrent programs by allowing the use of alternative, equivalent execution sequences. This is a desirable feature in specifying concurrent systems which allows formalizing frequently used arguments such as 'in an equivalent execution sequence', or 'in a consistent global state, not necessarily on the execution sequence' to be formalized. However, due to the addition of structure to the model, verification of partial order properties is non-trivial and sparse. We present here a new approach which allows expressing and verifying partial order properties. It is based on modeling an execution as a linear sequence of global states, where each state is equipped with its past partial-order history. The temporal logic BPLTL (for Branching Past Linear Temporal Logic) is introduced. We provide a sound and relatively complete proof system for the logic BPLTL over transitions programs. Our proof system augments an existing proof system for LTL.