Counting with Probabilistic and Ultrametric Finite Automata

  • Kaspars BalodisEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8808)


We investigate the state complexity of probabilistic and ultrametric finite automata for the problem of counting, i.e. recognizing the one-word unary language \(C_n=\left\{ 1^n \right\} \). We also review the known results for other types of automata.

For one-way probabilistic automata, we construct a minimal \(3\)-state automaton for counting to \(n\) with isolated cutpoint (but with decreasing isolation radius as \(n\) increases). We construct a two-way probabilistic automaton that counts to \(n\) with a constant number of states. We also show a minimal \(2\)-state ultrametric automaton for counting.


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of ComputingUniversity of LatviaRigaLatvia

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