Technical Reports

The report FIMU-RS-2005-07

Quantitative Analysis of Probabilistic Pushdown Automata: Expectations and Variances

by Javier Esparza, Antonín Kuèera, Richard Mayr, A full version of the paper presented at LICS 2005. July 2005, 26 pages.

FIMU-RS-2005-07. Available as Postscript, PDF.

Abstract:

Probabilistic pushdown automata (pPDA) have been identified as a natural model for probabilistic programs with recursive procedure calls. Previous works considered the decidability and complexity of the model-checking problem for pPDA and various probabilistic temporal logics. In this paper we concentrate on computing the expected values and variances of various random variables defined over runs of a given probabilistic pushdown automaton. In particular, we show how to compute the expected accumulated reward and the expected gain for certain classes of reward functions. Using these results, we show how to analyze various quantitative properties of pPDA that are not expressible in conventional probabilistic temporal logics.