On the memory consumption of probabilistic pushdown automata

Tomaš Brazdil, Javier Esparza, Stefan Kiefer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

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 ε > 0, these methods allow to compute bounds on the memory consumption that are exceeded with a probability of at most ε. 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.

Original languageEnglish
Title of host publicationFoundations of Software Technology and Theoretical Computer Science, FSTTCS 2009 - 29th Annual Conference, Proceedings
Pages49-60
Number of pages12
DOIs
StatePublished - 2009
Event29th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2009 - Kanpur, India
Duration: 15 Dec 200917 Dec 2009

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume4
ISSN (Print)1868-8969

Conference

Conference29th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2009
Country/TerritoryIndia
CityKanpur
Period15/12/0917/12/09

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