Reference:

Tomáš Brázdil, Javier Esparza, and Stefan Kiefer. On the memory consumption of probabilistic pushdown automata. In Ravi Kannan and K. Narayan Kumar, editors, Proceedings of the IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), Leibniz International Proceedings in Informatics, pages 49–60, 2009.

Abstract:

We investigate the problem of evaluating memory consumption for systems modelled by probabilistic pushdown automata (pPDA). The space needed by a run of a pPDA is the maximal height reached by the stack during the run. The problem is motivated by the investigation of depth-first computations that play an important role for space-efficient schedulings of multithreaded programs. We study the computation of both the distribution of the memory consumption and its expectation. For the distribution, we show that a naive method incurs an exponential blow-up, and that it can be avoided using linear equation systems. We also suggest a possibly even faster approximation method. Given , these methods allow to compute bounds on the memory consumption that are exceeded with a probability of at most . For the expected memory consumption, we show that whether it is infinite can be decided in polynomial time for stateless pPDA (pBPA) and in polynomial space for pPDA. We also provide an iterative method for approximating the expectation. We show how to compute error bounds of our approximation method and analyze its convergence speed. We prove that our method converges linearly, i.e., the number of accurate bits of the approximation is a linear function of the number of iterations.

Suggested BibTeX entry:

@inproceedings{BEK09:fsttcs,
    author = {Tom\'{a}\v{s} Br\'{a}zdil and Javier Esparza and Stefan Kiefer},
    booktitle = {Proceedings of the IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)},
    editor = {Ravi Kannan and K.~Narayan Kumar},
    pages = {49--60},
    series = {Leibniz International Proceedings in Informatics},
    title = {On the Memory Consumption of Probabilistic Pushdown Automata},
    year = {2009}
}