Controller Synthesis and Verification for Markov Decision Processes with Qualitative Branching Time Objectives

Authors:
Tomáš Brázdil;Vojtěch Forejt;Antonín Kučera
Affiliations:
Faculty of Informatics, Masaryk University, Brno, Czech Republic 60200;Faculty of Informatics, Masaryk University, Brno, Czech Republic 60200;Faculty of Informatics, Masaryk University, Brno, Czech Republic 60200
Venue:
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Year:
2008

Citing 12
Cited 3

Temporal and modal logic

Handbook of theoretical computer science (vol. B)
Modal and temporal logics

Handbook of logic in computer science (vol. 2)
Competitive Markov decision processes

Competitive Markov decision processes
Introduction To Automata Theory, Languages, And Computation

Introduction To Automata Theory, Languages, And Computation
A Landscape with Games in the Background

LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Trading Memory for Randomness

QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Stochastic Games with Branching-Time Winning Objectives

LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Automatic verification of probabilistic concurrent finite state programs

SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Multi-objective model checking of Markov decision processes

TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Markov decision processes with multiple objectives

STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
On the controller synthesis for finite-state markov decision processes

FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Strategy synthesis for markov decision processes and branching-time logics

CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory

Quantitative multi-objective verification for probabilistic systems

TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
On Almost-Sure Properties of Probabilistic Discrete Event Systems

Fundamenta Informaticae - Theory that Counts: To Oscar Ibarra on His 70th Birthday
Extending a Synthesis-Centric Model-Based Systems Engineering Framework with Stochastic Model Checking

Electronic Notes in Theoretical Computer Science (ENTCS)

Quantified Score

Hi-index	0.01

Visualization

Abstract

We show that the controller synthesis and verification problems for Markov decision processes with qualitative PECTL*objectives are 2-EXPTIMEcomplete. More precisely, the algorithms are polynomialin the size of a given Markov decision process and doubly exponential in the size of a given qualitative PECTL*formula. Moreover, we show that if a given qualitative PECTL*objective is achievable by somestrategy, then it is also achievable by an effectively constructible one-counterstrategy, where the associated complexity bounds are essentially the same as above. For the fragment of qualitative PCTL objectives, we obtain EXPTIMEcompleteness and the algorithms are only singly exponential in the size of the formula.