Two Recursively Inseparable Problems for Probabilistic Automata

Fijalkow, Nathanaël; Gimbert, Hugo; Horn, Florian; Oualhadj, Youssouf

doi:10.1007/978-3-662-44522-8_23

Cited by 5 publications

(3 citation statements)

References 14 publications

(22 reference statements)

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“…Alternative semantics for probabilistic automata. It is very tempting to consider the limit case of infinitely many agents: the parameterised control question becomes the value 1 problem for probabilistic automata, which was proved undecidable in [GO10], and even in very restricted cases, see for instance [FGHO14]. Hence abstracting continuous distributions by a discrete population of arbitrary size can be seen as an approximation technique for probabilistic automata.…”

Section: Introductionmentioning

confidence: 99%

Controlling a random population

Colcombet¹,

Fijalkow²,

Ohlmann³

2021

Logical Methods in Computer Science

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Bertrand et al. introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all agents to a target state? They showed that the problem is decidable and EXPTIME-complete in the adversarial setting, and posed as an open problem the stochastic setting, where the agent is represented by a Markov decision process. In this paper, we show that the stochastic control problem is decidable. Our solution makes significant uses of well quasi orders, of the max-flow min-cut theorem, and of the theory of regular cost functions. We introduce an intermediate problem of independence interest called the sequential flow problem and study its complexity.

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Section: Introductionmentioning

confidence: 99%

Controlling a random population

Colcombet¹,

Fijalkow²,

Ohlmann³

2021

Logical Methods in Computer Science

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“…Alternative semantics for probabilistic automata. It is very tempting to consider the limit case of infinitely many agents: the parameterised control question becomes the value 1 problem for probabilistic automata, which was proved undecidable in Gimbert and Oualhadj (2010), and even in very restricted cases (Fijalkow et al (2014)). Hence abstracting continuous distributions by a discrete population of arbitrary size can be seen as an approximation technique for probabilistic automata.…”

Section: Introductionmentioning

confidence: 99%

Controlling a Random Population

Colcombet

Fijalkow

Ohlmann

2020

Lecture Notes in Computer Science

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Bertrand et al. (2017) introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all agents to a target state? They showed that the problem is decidable and EXPTIME-complete in the adversarial setting, and posed as an open problem the stochastic setting, where the agent is represented by a Markov decision process. In this paper, we show that the stochastic control problem is decidable. Our solution makes significant uses of well quasi orders, of the max-flow mincut theorem, and of the theory of regular cost functions.

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“…This work is also related to the widely studied model of interval MDPs, where the transition probabilities are given as intervals meant to model the uncertainty of the numerical values. Numberless MDPs [11] are a particular case of the latter in which values are only known to be zero or non-zero. In the context of numberless MDPs, a special case of the question we study can be simply rephrased as the comparison of the maximal reachability values of two given states.…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Graph-Based Reductions for Reachability in Markov Decision Processes

Roux

Pérez

2018

Lecture Notes in Computer Science

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We study the never-worse relation (NWR) for Markov decision processes with an infinite-horizon reachability objective. A state q is never worse than a state p if the maximal probability of reaching the target set of states from p is at most the same value from q, regardless of the probabilities labelling the transitions. Extremal-probability states, end components, and essential states are all special cases of the equivalence relation induced by the NWR. Using the NWR, states in the same equivalence class can be collapsed. Then, actions leading to sub-optimal states can be removed. We show that the natural decision problem associated to computing the NWR is coNP-complete. Finally, we extend a previously known incomplete polynomial-time iterative algorithm to underapproximate the NWR.

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Two Recursively Inseparable Problems for Probabilistic Automata

Cited by 5 publications

References 14 publications

Controlling a random population

Controlling a random population

Controlling a Random Population

The Complexity of Graph-Based Reductions for Reachability in Markov Decision Processes

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