A Note on the Complexity of Model-Checking Bounded Multi-Pushdown Systems
Abstract
In this note, we provide complexity characterizations of model checking multi-pushdown systems. Multi-pushdown systems model recursive concurrent programs in which any sequential process has a finite control. We consider three standard notions for boundedness: context boundedness, phase boundedness and stack ordering. The logical formalism is a linear-time temporal logic extending well-known logic CaRet but dedicated to multi-pushdown systems in which abstract operators (related to calls and returns) such as those for next-time and until are parameterized by stacks. We show that the problem is EXPTIME-complete for context-bounded runs and unary encoding of the number of context switches; we also prove that the problem is 2EXPTIME-complete for phase-bounded runs and unary encoding of the number of phase switches. In both cases, the value k is given as an input (whence it is not a constant of the model-checking problem), which makes a substantial difference in the complexity. In certain cases, our results improve previous complexity results.
Cite
@article{arxiv.1212.1485,
title = {A Note on the Complexity of Model-Checking Bounded Multi-Pushdown Systems},
author = {Kshitij Bansal and Stéphane Demri},
journal= {arXiv preprint arXiv:1212.1485},
year = {2012}
}