The Complexity of Live Sequence Charts

We are interested in implementing a fully automated software development process starting from sequence charts, which have proven their naturalness and usefulness in industry. We show in this paper that even for the simplest variants of sequence charts, there are strong impediments to the implementability of this dream. In the case of a manual development, we have to check the final implementation (the model). We show that centralized model-checking is co-NP-complete. Unfortunately, this problem is of little interest to industry. The real problem is distributed model-checking, that we show PSPACE complete, as well as several simple but interesting verification problems. The dream itself relies on program synthesis, formally called realizability. We show that the industrially relevant problem, distributed realizability, is undecidable. The less interesting problems of centralized and constrained realizability are exponential and doubly-exponential complete, respectively.