Decidability and complexity of infinite-state stochastic games

Bc. Václav Brožek, Ph.D.

Master's thesis

Abstract:

In this thesis we are concerned in 1 1/2-player stochastic games with infinitely many vertices. We are especially interested in games generated by pushdown automata (PDA) and stateless pushdown automata (BPA). We also define the extended reachability objective (ERO) and prove that for PDA games the reachability problem wrt. ERO is undecidable. On the other hand we give a polynomial-time algorithm to decide it for BPA games and we also present an application of our results to PCTL model checking of these games, which we show to be EXPTIME-complete. At the end we show the directions of possible future work, involving solving similar problems for 2 1/2-player games or generalizing ERO to Büchi winning objectives.

Keywords

infinite state stochastic games, Markov decision processes, probability theory, PDA, BPA, model checking, PCTL, reachability

Jazyk práce: English

Datum vytvoření / odevzdání či podání práce: 4. 1. 2007

Obhajoba závěrečné práce

• Obhajoba proběhla 13. 2. 2007
• Vedúci: doc. RNDr. Tomáš Brázdil, Ph.D.

Masaryk University

Faculty of Informatics

Master programme / odbor:
Informatics / Informatics