One-Counter Stochastic Games

We study the computational complexity of basic decision problems for one-counter simple stochastic games (OC-SSGs), under various objectives. OC-SSGs are 2-player turn-based stochastic games played on the transition graph of classic one-counter automata. We study primarily the termination objective, where the goal of one player is to maximize the probability of reaching counter value 0, while the other player wishes to avoid this. Partly motivated by the goal of understanding termination objectives, we also study certain "limit" and "long run average" reward objectives that are closely related to some well-studied objectives for stochastic games with rewards. Examples of problems we address include: does player 1 have a strategy to ensure that the counter eventually hits 0, i.e., terminates, almost surely, regardless of what player 2 does? Or that the liminf (or limsup) counter value equals infinity with a desired probability? Or that the long run average reward is >0 with desired probability? We show that the qualitative termination problem for OC-SSGs is in NP intersection coNP, and is in P-time for 1-player OC-SSGs, or equivalently for one-counter Markov Decision Processes (OC-MDPs). Moreover, we show that quantitative limit problems for OC-SSGs are in NP intersection coNP, and are in P-time for 1-player OC-MDPs. 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.Comment: 20 pages, 1 figure. This is a full version of a paper accepted for publication in proceedings of FSTTCS 201

Qualitative Reachability in Stochastic BPA Games

We consider a class of infinite-state stochastic games generated by stateless pushdown automata (or, equivalently, 1-exit recursive state machines), where the winning objective is specified by a regular set of target configurations and a qualitative probability constraint `>0' or `=1'. The goal of one player is to maximize the probability of reaching the target set so that the constraint is satisfied, while the other player aims at the opposite. We show that the winner in such games can be determined in PTIME for the `>0' constraint, and both in NP and coNP for the `=1' constraint. Further, we prove that the winning regions for both players are regular, and we design algorithms which compute the associated finite-state automata. Finally, we show that winning strategies can be synthesized effectively.Comment: Submitted to Information and Computation. 48 pages, 3 figure

Optimal Strategies in Infinite-state Stochastic Reachability Games

We consider perfect-information reachability stochastic games for 2 players on infinite graphs. We identify a subclass of such games, and prove two interesting properties of it: first, Player Max always has optimal strategies in games from this subclass, and second, these games are strongly determined. The subclass is defined by the property that the set of all values can only have one accumulation point -- 0. Our results nicely mirror recent results for finitely-branching games, where, on the contrary, Player Min always has optimal strategies. However, our proof methods are substantially different, because the roles of the players are not symmetric. We also do not restrict the branching of the games. Finally, we apply our results in the context of recently studied One-Counter stochastic games

Approximating the termination value of one-counter MDPs and stochastic games

One-counter MDPs (OC-MDPs) and one-counter simple stochastic games (OC-SSGs) are 1-player, and 2-player turn-based zero-sum, stochastic games played on the transition graph of classic one-counter automata (equivalently, pushdown automata with a 1-letter stack alphabet). A key objective for the analysis and verification of these games is the termination objective, where the players aim to maximize (minimize, respectively) the probability of hitting counter value 0, starting at a given control state and given counter value. Recently, we studied qualitative decision problems ("is the optimal termination value equal to 1?") for OC-MDPs (and OC-SSGs) and showed them to be decidable in polynomial time (in NP intersection coNP, respectively). However, quantitative decision and approximation problems ("is the optimal termination value at least p", or "approximate the termination value within epsilon") are far more challenging. This is so in part because optimal strategies may not exist, and because even when they do exist they can have a highly non-trivial structure. It thus remained open even whether any of these quantitative termination problems are computable. In this paper we show that all quantitative approximation problems for the termination value for OC-MDPs and OC-SSGs are computable. Specifically, given an OC-SSG, and given epsilon>0, we can compute a value v that approximates the value of the OC-SSG termination game within additive error epsilon, and furthermore we can compute epsilon-optimal strategies for both players in the game. A key ingredient in our proofs is a subtle martingale, derived from solving certain linear programs that we can associate with a maximizing OC-MDP. An application of Azuma's inequality on these martingales yields a computable bound for the "wealth" at which a "rich person's strategy" becomes epsilon-optimal for OC-MDPs

Inovace Campbellova zrakového stimulátoru za použití tabletu

The article covers three fundamental themes: a) performance solutions using gaming to treat multiple eye defects; in particular - Amblyopia; b) an explanation of the issue and design of the software (including games) which is intended for therapeutic or health purposes; and c) highlighting the modern solutions and the power of software products for the needs of the health sector, in particular in the fields of diagnostics and rehabilitation. The reader can learn basic information about eye diseases and the principles of their treatment, and become acquainted with the reasons why computer games (and in particular video games) are appropriate for rehabilitation. Very important and beneficial for the reader is the section of the article which focuses on a) the differences in the design of standard software and software designed for the needs of the healthcare system, b) the high risks associated with defects of all software, or even the risk of side effects with the so-called „perfect“ software, c) the fact that a major part of software development does not comply with all of the standards. The article also discusses the advantages of the software solution over other methods of rehabilitation. Most of the paradigms are generally applicable. Familiarity with the principles of this application can thus be interesting even for developers in the relevant areas.Článek se zabývá třemi základními tématy, která zní: a) řešení výkon s použitím hraní her k léčbě roztroušené oční vady; zejména - amblyopií; b) vysvětlení problematiky a návrh software (včetně her), který je určen pro terapeutické nebo zdravotní účely; a c) zdůrazňování moderních řešení a sílu softwarových produktů pro potřeby zdravotnictví, a to zejména v oblastech diagnostiky a rehabilitace. Čtenář může dozvědět základní informace o očních chorob a principy jejich léčby, a seznámit se s důvody, proč jsou vhodné pro rehabilitaci počítačové hry (a zejména videoher)

Smart data flow control jako budoucnost mobilních sítí

Recent mobile networks have difficulties with the growth of traffic in data transferring. Trends of user preferences shows us, that there is growth of interest in mobile data, especially in multimedia. The future of the Internet in mobile devices is possible to predict, especially in technological synthesis of mobile networks and wireless networks, systems of unambiguous identification of authenticated users (e.g. via IPv6) and smart cooperation of systems. The article focuses mainly on the introduction of hybrid architecture, simple units and their function (private and public Wi-Fi, mobile networks, cloud), highlighting the advantages for users and specifies the changes which have to be made for extended usage.Současné mobilní sítě mají potíže s růstem trafficu v přenos dat. Trendy uživatelských preferencí nám ukazují, že existuje nárůst zájmu o mobilní data, a to zejména v multimédiích. Budoucnost internetu v mobilních zařízeních je možné předvídat, a to zejména v technologickém syntéze mobilních sítí a bezdrátových sítí, systémů jednoznačnou identifikaci ověřeným uživatelům (např. Přes IPv6) a inteligentní spolupráce systémů. Tento článek se zaměřuje především na zavedení hybridní architektury a její funkce (soukromé a veřejné Wi-Fi, mobilní sítě, cloud), zdůrazňují výhody pro uživatele. Článek také stanovuje změny, které mají být provedeny pro rozšířené použití metodiky

Stochastic Games with Branching-Time

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