Efficient Model Checking for LTL with Partial Order Snapshots

Abstract

Abstract. Certain behavioral properties of distributed systems are difficult to express in interleaving semantics, whereas they are naturally expressed in terms of partial orders of events or, equivalently, Mazurkiewicz traces. Examples of such properties are serializability of a database or snapshots. Recently, a modest extension for LTL by an operator that expresses snapshots has been proposed. It combines the ease of linear (interleaving) specification with this useful partial order concept. The new construct allows one to assert that a global snapshot (also called a slice or a cut) was passed, perhaps not in the observed (interleaved) execution sequence, but possibly in a (trace) equivalent one. A model checking algorithm was suggested for a subset of this logic, with PSPACE complexity in the size of the system and the checked formula. For the whole logic, a solution that is in EXSPACE in the size of the system (PSPACE in the number of its global states) was given.In this paper, we provide a model checking algorithm in PSPACE in the size of a system of communicating sequential processes when restricting snapshots to boolean combinations of local properties of each process. Concerning size of the formula, it is PSPACE for the case of snapshot properties expressed in DNF, and EXPSPACE where a translation to DNF is necessary.

Testing Distributed Systems Through Symbolic Model Checking

“…A Mazurkiewicz trace [20], over an alphabet Σ with a independence relation I, can be defined as a Σ-labelled partial order set of events with special properties not explained here. For Mazurkiewicz traces, local [21,22] and global [23,24,25] trace logics have been defined. However, in our case, the trace 1 is an abstraction of a distributed execution (or of a scenario) and models a set of possible interleavings of events the distributed system may have had.…”