Open AccessJournal Article
Quasi-Birth-Death Processes, Tree-Like QBDs, Probabilistic 1-Counter Automata, and Pushdown Systems
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TLDR
It is observed that (discrete-time) Quasi-Birth-Death Processes (QBDs) are equivalent, in a precise sense, to probabilistic 1-Counter Automata (p1CAs).About:
This article is published in Performance Evaluation.The article was published on 2010-09-01 and is currently open access. It has received 12 citations till now. The article focuses on the topics: Tree (data structure).read more
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Reachability Games on Extended Vector Addition Systems with States
TL;DR: In this paper, the authors consider two-player turn-based games with zero reachability and zero safety objectives generated by extended vector addition systems with states and identify several decidable and even tractable subcases of this problem obtained by restricting the number of counters and/or the sets of target configurations.
Proceedings ArticleDOI
One-Counter Stochastic Games
TL;DR: Both qualitative limit problems and qualitative termination problems for OC-SSGs are already at least as hard as Condon's quantitative decision problem for finite-state SSGs.
Journal ArticleDOI
Recursive Markov Decision Processes and Recursive Stochastic Games
TL;DR: It is shown both problems are undecidable for multi-exit RMDPs, but are decidable for 1-RMDPs and 1-RSSGs, and more general model-checking problems with respect to linear-time temporal properties are undECidable even for a fixed property.
Journal ArticleDOI
Quasi-Birth-Death Processes, Tree-Like QBDs, Probabilistic 1-Counter Automata, and Pushdown Systems
TL;DR: The upper bound proof for QBDs combines several ingredients: a detailed analysis of the structure of 1-counter automata, an iterative application of a classic condition number bound for errors in linear systems, and a very recent constructive bound on the performance of Newton's method for monotone systems of polynomial equations.
Posted Content
Runtime Analysis of Probabilistic Programs with Unbounded Recursion
TL;DR: In this paper, the authors studied termination time and recurrence time in probabilistic pushdown automata (pPDA) and obtained bounds for the frequency of long request-service cycles.
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Book ChapterDOI
Reachability games on extended vector addition systems with states
TL;DR: Several decidable and even tractable subcases of this problem of deciding thewinner in two-player turn-based games with zero-reachability and zero-safety objectives obtained by restricting the number of counters and/or the sets of target configurations are identified.
Proceedings ArticleDOI
One-Counter Stochastic Games
TL;DR: Both qualitative limit problems and qualitative termination problems for OC-SSGs are already at least as hard as Condon's quantitative decision problem for finite-state SSGs.
Journal ArticleDOI
Recursive Markov Decision Processes and Recursive Stochastic Games
TL;DR: It is shown both problems are undecidable for multi-exit RMDPs, but are decidable for 1-RMDPs and 1-RSSGs, and more general model-checking problems with respect to linear-time temporal properties are undECidable even for a fixed property.
Journal ArticleDOI
Quasi-Birth-Death Processes, Tree-Like QBDs, Probabilistic 1-Counter Automata, and Pushdown Systems
TL;DR: The upper bound proof for QBDs combines several ingredients: a detailed analysis of the structure of 1-counter automata, an iterative application of a classic condition number bound for errors in linear systems, and a very recent constructive bound on the performance of Newton's method for monotone systems of polynomial equations.
Posted Content
Runtime Analysis of Probabilistic Programs with Unbounded Recursion
TL;DR: In this paper, the authors studied termination time and recurrence time in probabilistic pushdown automata (pPDA) and obtained bounds for the frequency of long request-service cycles.