We consider turn-based stochastic games on infinite graphs induced by game probabilistic lossy channel systems (GPLCS), the game version of probabilistic lossy channel systems (PLCS). We study games with Buchi (repeated reachability) objectives and almost-sure winning conditions. These games are pure memoryless determined and, under the assumption that the target set is regular, a symbolic representation of the set of winning states for each player can be effectively constructed. Thus, turn-based stochastic games on GPLCS are decidable. This generalizes the decidability result for PLCS-induced Markov decision processes in [10].

/pdf/stochastic-games-with-lossy-channels-4lfbmxienp.pdf

Stochastic games with lossy channels

https://link.springer.com/content/pdf/10.1057%2Fjors.1996.159.pdf

Modeling and Analysis of Stochastic Systems

In this paper we develop a new algorithm for deciding the winner in parity games, and hence also for the modal μ-calculus model checking. The design and analysis of the algorithm is based on a notion of game progress measures: they are witnesses for winning strategies in parity games. We characterize game progress measures as pre-fixed points of certain monotone operators on a complete lattice. As a result we get the existence of the least game progress measures and a straightforward way to compute them. The worst-case running time of our algorithm matches the best worst-case running time bounds known so far for the problem, achieved by the algorithms due to Browne et al., and Seidl. Our algorithm has better space complexity: it works in small polynomial space; the other two algorithms have exponential worst-case space complexity.

Small progress measures for solving parity games

We survey several results and open problems related to synchronizing automata. In particular, we discuss some recent advances towards a solution of the Cerný conjecture.

/pdf/synchronizing-automata-and-the-cerny-conjecture-1lprq8wxe3.pdf

Synchronizing Automata and the Černý Conjecture

We study the problems of existence and construction of infinite schedules for finite weighted automata and one-clock weighted timed automata, subject to boundary constraints on the accumulated weight. More specifically, we consider automata equipped with positive and negative weights on transitions and locations, corresponding to the production and consumption of some resource (e.g.energy). We ask the question whether there exists an infinite path for which the accumulated weight for any finite prefix satisfies certain constraints (e.g.remains between 0 and some given upper-bound). We also consider a game version of the above, where certain transitions may be uncontrollable.

/pdf/infinite-runs-in-weighted-timed-automata-with-energy-2qsam52x73.pdf

Infinite Runs in Weighted Timed Automata with Energy Constraints

This chapter considers two fundamental problems for Mealy machines, i.e., finite-state machines with inputs and outputs. The machines will be used in subsequent chapters as models of a system or program to test. We repeat Definition 21.1 of Chapter 21 here: readers already familiar with Mealy machines can safely skip to Section 1.1.2.

Homing and synchronizing sequences

We suggest the first strongly subexponential and purely combinatorial algorithm for mean payoff games. It is based on solving a new controlled version of the shortest paths problem. By selecting exactly one outgoing edge in each of the controlled vertices we want to maximize the shortest distances to the unique sink. Mean payoff games easily reduce to this problem. To compute the longest shortest paths, player MAX selects a strategy (one edge in each controlled vertex) and player MIN responds by evaluating shortest paths to the sink in the remaining graph. Then MAX locally changes choices in controlled vertices, making attractive switches that seem to increase shortest paths (under the current evaluation). We show that this is a monotonic strategy improvement, and every locally optimal strategy is globally optimal. A careful choice of the next iterate results in a randomized algorithm of complexity min(poly(n).W, 2 o( √ n log n) ), which is simultaneously pseudopolynomial (W is the maximal absolute edge weight) and subexponential in the number of vertices n. All previous algorithms for mean payoff games were either exponential or pseudopolynomial (which is purely exponential for exponentially large edge weights).

A combinatorial strongly subexponential strategy improvement algorithm for mean Payoff games

We suggest a new randomized algorithm for solving parity games with worst case time complexity roughly min(O(n3 ? (n/k+ 1)k), 2O(?n log n), where n is the number of vertices and k the number of colors of the game. This is comparable with the previously known algorithms when the number of colors is small. However, the subexponential bound is an advantage when the number of colors is large, k = ?(n1/2+?).

A Discrete Subexponential Algorithm for Parity Games

http://www.dbai.tuwien.ac.at/staff/vorobyov/tcs-determinacy.pdf

Sven Sandberg

Papers

Stochastic games with lossy channels

Homing and synchronizing sequences

A combinatorial strongly subexponential strategy improvement algorithm for mean Payoff games

A Discrete Subexponential Algorithm for Parity Games

Memoryless determinacy of parity and mean payoff games: a simple proof