Refining the hierarchy of blind multicounter languages and twist-closed trios

  • Authors:

  • Matthias Jantzen;Alexy Kurganskyy

  • Affiliations:

  • Universität Hamburg FB Informatik, Universität Hamburg, Vogt-Kölln-Straße 30, 22527 Hamburg, Germany;Universität Hamburg FB Informatik, Universität Hamburg, Vogt-Kölln-Straße 30, 22527 Hamburg, Germany

  • Venue:
  • Information and Computation
  • Year:
  • 2003

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Abstract

We introduce the new families (k, r)-RBC of languages accepted in quasi-realtime by one-way counter automata having k blind counters, of which at least r are reversal-bounded. It is proved, that these families form a strict and linear hierarchy of semi-AFLs within the the family BLIND = M∩(C1) of blind multicounter languages with generator C1 = {w ∈ {a1, b1}* | |w|a1= |w|b1}. This thereby combines the families BLIND and RBC from [13] to one strict hierarchy and generalizes and sharpens Greibachs results. The strict inclusions between the k-counter families (k, r)-RBC are proved using linear algebra techniques. We also study the language theoretic monadic operation twist [18,20], in connection with the semi-AFLs of languages accepted by multicounter and multipushdown acceptors, all restricted to reversal-bounded behavior. It is verified, that the family (k, r)-RBC is twist-closed if and only if r = 0, in which case (k, 0)-RBC = M(Ck), Ck being the k-fold shuffle of disjoint copies of C1. We characterize the family M∩(PAL) of languages accepted in quasi-realtime by nondeterministic one-way reversal-bounded multipushdown acceptors as the least twist-closed trio Mtwist(PAL) generated by the set of palindromes PAL = {w ∈ {a, b}* | w = wrev}.