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Games and Markov Decision Processes with Meanpayoff Parity and Energy Parity Objectives
"... In this paper we survey results of twoplayer games on graphs and Markov decision processes with parity, meanpayoff and energy objectives, and the combination of meanpayoff and energy objectives with parity objectives. These problems have applications in verification and synthesis of reactive syst ..."
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In this paper we survey results of twoplayer games on graphs and Markov decision processes with parity, meanpayoff and energy objectives, and the combination of meanpayoff and energy objectives with parity objectives. These problems have applications in verification and synthesis of reactive systems in resourceconstrained environments.
Solvency Markov Decision Processes with Interest
"... Abstract Solvency games, introduced by Berger et al., provide an abstract framework for modelling decisions of a riskaverse investor, whose goal is to avoid ever going broke. We study a new variant of this model, where, in addition to stochastic environment and fixed increments and decrements to t ..."
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Abstract Solvency games, introduced by Berger et al., provide an abstract framework for modelling decisions of a riskaverse investor, whose goal is to avoid ever going broke. We study a new variant of this model, where, in addition to stochastic environment and fixed increments and decrements to the investor's wealth, we introduce interest, which is earned or paid on the current level of savings or debt, respectively. We study problems related to the minimum initial wealth sufficient to avoid bankruptcy (i.e. steady decrease of the wealth) with probability at least p. We present an exponential time algorithm which approximates this minimum initial wealth, and show that a polynomial time approximation is not possible unless P = NP. For the qualitative case, i.e. p = 1, we show that the problem whether a given number is larger than or equal to the minimum initial wealth belongs to NP ∩ coNP, and show that a polynomial time algorithm would yield a polynomial time algorithm for meanpayoff games, existence of which is a longstanding open problem. We also identify some classes of solvency MDPs for which this problem is in P. In all above cases the algorithms also give corresponding bankruptcy avoiding strategies.
Mission Accomplished: An Introduction to Formal Methods in Mobile Robot Motion Planning and Control
"... A new trend in the robotic motion planning literature is to use formal methods, like model checking, reactive synthesis and supervisory ..."
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A new trend in the robotic motion planning literature is to use formal methods, like model checking, reactive synthesis and supervisory
Optimal Control of MDPs with Temporal Logic Constraints
"... Abstract — In this paper, we focus on formal synthesis of control policies for finite Markov decision processes with nonnegative realvalued costs. We develop an algorithm to automatically generate a policy that guarantees the satisfaction of a correctness specification expressed as a formula of Li ..."
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Abstract — In this paper, we focus on formal synthesis of control policies for finite Markov decision processes with nonnegative realvalued costs. We develop an algorithm to automatically generate a policy that guarantees the satisfaction of a correctness specification expressed as a formula of Linear Temporal Logic, while at the same time minimizing the expected average cost between two consecutive satisfactions of a desired property. The existing solutions to this problem are suboptimal. By leveraging ideas from automatabased model checking and game theory, we provide an optimal solution. We demonstrate the approach on an illustrative example. I.
PerfectInformation Stochastic MeanPayoff Parity Games ⋆,⋆⋆
"... Abstract The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 1 2player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other ..."
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Abstract The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 1 2player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other transitions are determined probabilistically. We consider 2 1player games where the objec2 tive of the System is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a meanpayoff condition). We establish that the problem of deciding whether the System can ensure that the probability to satisfy the meanpayoff parity objective is at least a given threshold is in NP∩coNP, matching the best known bound in the special case of 2player games (where all transitions are deterministic). We present an algorithm running in timeO(d·n 2d ·MeanGame) to compute the set of almostsure winning states from which the objective can be ensured with probability 1, where n is the number of states of the game, d the number of priorities of the parity objective, and MeanGame is the complexity to compute the set of almostsure winning states in 2 1 2player meanpayoff games. Our results are useful in the synthesis of stochastic reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective). 1