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Approximate Learning of Limit-Average Automata

Authors Jakub Michaliszyn , Jan Otop

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Author Details

Jakub Michaliszyn
  • University of Wrocław, Poland
Jan Otop
  • University of Wrocław, Poland

Funding

The National Science Centre (NCN), Poland under grant 2017/27/B/ST6/00299.

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Jakub Michaliszyn and Jan Otop. Approximate Learning of Limit-Average Automata. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CONCUR.2019.17

Abstract

Limit-average automata are weighted automata on infinite words that use average to aggregate the weights seen in infinite runs. We study approximate learning problems for limit-average automata in two settings: passive and active. In the passive learning case, we show that limit-average automata are not PAC-learnable as samples must be of exponential-size to provide (with good probability) enough details to learn an automaton. We also show that the problem of finding an automaton that fits a given sample is NP-complete. In the active learning case, we show that limit-average automata can be learned almost-exactly, i.e., we can learn in polynomial time an automaton that is consistent with the target automaton on almost all words. On the other hand, we show that the problem of learning an automaton that approximates the target automaton (with perhaps fewer states) is NP-complete. The abovementioned results are shown for the uniform distribution on words. We briefly discuss learning over different distributions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Quantitative automata
Keywords
  • weighted automata
  • learning
  • expected value

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