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Approximating Probabilistic Automata by Regular Languages

Authors Rohit Chadha, A. Prasad Sistla, Mahesh Viswanathan



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Author Details

Rohit Chadha
  • University of Missouri, Columbia, USA
A. Prasad Sistla
  • University of Illinois, Chicago, Chicago, USA
Mahesh Viswanathan
  • University of Illinois, Urbana-Champaign, Urbana, USA

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Rohit Chadha, A. Prasad Sistla, and Mahesh Viswanathan. Approximating Probabilistic Automata by Regular Languages. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CSL.2018.14

Abstract

A probabilistic finite automaton (PFA) A is said to be regular-approximable with respect to (x,y), if there is a regular language that contains all words accepted by A with probability at least x+y, but does not contain any word accepted with probability at most x. We show that the problem of determining if a PFA A is regular-approximable with respect to (x,y) is not recursively enumerable. We then show that many tractable sub-classes of PFAs identified in the literature - hierarchical PFAs, polynomially ambiguous PFAs, and eventually weakly ergodic PFAs - are regular-approximable with respect to all (x,y). Establishing the regular-approximability of a PFA has the nice consequence that its value can be effectively approximated, and the emptiness problem can be decided under the assumption of isolation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Probabilistic computation
Keywords
  • Probabilistic Finite Automata
  • Regular Languages
  • Ambiguity

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