L p distance and equivalence of probabilistic automata

Corinna Cortes, Mehryar Mohri, Ashish Rastogi

Research output: Contribution to journalArticlepeer-review


This paper presents an exhaustive analysis of the problem of computing the L p distance of two probabilistic automata. It gives efficient exact and approximate algorithms for computing these distances for p even and proves the problem to be NP-hard for all odd values of p, thereby completing previously known hardness results. It further proves the hardness of approximating the L p distance of two probabilistic automata for odd values of p. Similar techniques to those used for computing the L p distance also yield efficient algorithms for computing the Hellinger distance of two unambiguous probabilistic automata both exactly and approximately. A problem closely related to the computation of a distance between probabilistic automata is that of testing their equivalence. This paper also describes an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A 1 and A 2 in time O(|Σ| (|A 1| + |A 2|) 3), a significant improvement over the previously best reported algorithm for this problem.

Original languageEnglish (US)
Pages (from-to)761-779
Number of pages19
JournalInternational Journal of Foundations of Computer Science
Issue number4
StatePublished - Aug 2007

ASJC Scopus subject areas

  • Computer Science (miscellaneous)


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