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.

This paper studies the use of an equational variant of the modal /spl mu/-calculus as a unified framework for efficient temporal logic model checking. In particular we show how an expressive temporal logic, CTL*, may be efficiently translated into the /spl mu/-calculus. Using this translation, one may then employ /spl mu/-calculus model-checking techniques, including on-the-fly procedures, BDD-based algorithms and compositional model-checking approaches, to determine if systems satisfy formulas in CTL*.

This paper gives an on-the-fly algorithm for determining whether a finite-state system satisfies a formula in the temporal logic CTL. The time complexity of our algorithm matches that of the best existing "global algorithm" for model checking in this logic, and it performs as well as the best known global algorithms for the sublogics CTL and LTL. In contrast with these approaches, however, our routine constructs the state space of the system under consideration in a need-driven fashion and will therefore perform better in practice.