A temporal logic for the specification and verification of distributed behaviour

In this work we develop a temporal logic with fixpoints for distributed processes or distributed systems. Standard temporal logics refer to sequential processes (execution sequences) of distributed systems. Expressive temporal operators such as “Until” can be expressed as fixpoints of formulae involving only the simple “Next” modality. Fixpoint logics for sequential processes are known to be expressively equivalent to (Büchi) automata over infinite sequences. Thus, they represent the maximum in expressiveness in the range of “finite-state” methods. Here, we extend this approach to distributed processes, which represent the causal relation of events occurring in a run of a system as partial order. A key problem is the proper generalisation of the “Next” operator. Within a general framework we identify several syntactic subclasses of the logic. Both theoretical and pragmatic aspects of the resulting logics are investigated. The major theoretical result is the expressive equivalence of our fixpoint logic with Büchi asynchronous automata. This constructive result is based on mutual translations between formulae and asynchronous automata. On the other hand, asynchronous automata are known to be expressively equivalent with monadic second order logic over distributed processes. Thus, the main result establishes the theoretical robustness of our approach, which fully generalises known results from the sequential case. On the pragmatic side, we investigate automata based methods for the automatic verification of logical properties of finite state systems. We follow two paths, which base on translations of formulae to sequential automata recognising languages closed under Mazurkiewicz equivalence, and to asynchronous automata. The translation to sequential automata allows classical approaches to “model-checking with representatives”, which aim to reduce the system during its translation to a sequential automaton. The translation to asynchronous automata essentially reduces the verification to an emptiness test for asynchronous automata. Taking the view that automata are data structures, we develop optimised models of automata and constructions aimed on an efficient, stepwise transformation of asynchronous automata to sequential automata. If additionally heuristic, emptiness preserving reductions are applied during the stepwise transformation, the emptiness test gets dramatically cheaper in many cases.