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Asymptotic Complexity Estimates for Probabilistic Programs and Their VASS Abstractions

Authors Michal Ajdarów , Antonín Kučera

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Author Details

Michal Ajdarów
  • Masaryk University, Brno, Czech Republic
Antonín Kučera
  • Masaryk University, Brno, Czech Republic

Funding

The work is supported by the Czech Science Foundation, Grant No. 21-24711S.

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Michal Ajdarów and Antonín Kučera. Asymptotic Complexity Estimates for Probabilistic Programs and Their VASS Abstractions. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CONCUR.2023.12

Abstract

The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that this approach is not sufficiently robust, especially in situations when the expectations are infinite. We propose new estimates for the asymptotic analysis of probabilistic programs with non-deterministic choice that overcome this deficiency. Furthermore, we show how to efficiently compute/analyze these estimates for selected classes of programs represented as Markov decision processes over vector addition systems with states.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • Probabilistic programs
  • asymptotic complexity
  • vector addition systems

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References

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