Taming Infinity One Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F25%3A00144668" target="_blank" >RIV/00216224:14330/25:00144668 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2025.138" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ICALP.2025.138</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2025.138" target="_blank" >10.4230/LIPIcs.ICALP.2025.138</a>

Result language

angličtina

Original language name

Taming Infinity One Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs

Original language description

Markov decision processes (MDPs) are a canonical model to reason about decision making within a stochastic environment. We study a fundamental class of infinite MDPs: one-counter MDPs (OC-MDPs). They extend finite MDPs via an associated counter taking natural values, thus inducing an infinite MDP over the set of configurations (current state and counter value). We consider two characteristic objectives: reaching a target state (state-reachability), and reaching a target state with counter value zero (selective termination). The synthesis problem for the latter is not known to be decidable and connected to major open problems in number theory. Furthermore, even seemingly simple strategies (e.g., memoryless ones) in OC-MDPs might be impossible to build in practice (due to the underlying infinite configuration space): we need finite, and preferably small, representations. To overcome these obstacles, we introduce two natural classes of concisely represented strategies based on a (possibly infinite) partition of counter values in intervals. For both classes, and both objectives, we study the verification problem (does a given strategy ensure a high enough probability for the objective?), and two synthesis problems (does there exist such a strategy?): one where the interval partition is fixed as input, and one where it is only parameterized. We develop a generic approach based on a compression of the induced infinite MDP that yields decidability in all cases, with all complexities within PSPACE.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10200 - Computer and information sciences

Project

<a href="/en/project/GA23-06963S" target="_blank" >GA23-06963S: VESCAA: Verifiable and Efficient Synthesis of Controllers for Autonomous Agents</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

52nd International Colloquium on Automata, Languages, and Programming, ICALP 2025

ISBN

—

ISSN

1868-8969

e-ISSN

—

Number of pages

19

Pages from-to

„138:1“-„138:19“

Publisher name

Schloss Dagstuhl - Leibniz-Zentrum fur Informatik

Place of publication

Neuvedeno

Event location

Aarhus, Dánsko

Event date

Jan 1, 2025

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

001740139600138