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Stochastic Analysis of Minimal Automata Growth for Generalized Strings

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  • Ian G. Char

    (University of Colorado)

  • Manuel E. Lladser

    (University of Colorado)

Abstract

Generalized strings describe various biological motifs that arise in molecular and computational biology. In this manuscript, we introduce an alternative but efficient algorithm to construct the minimal deterministic finite automaton (DFA) associated with any generalized string. We exploit this construction to characterize the typical growth of the minimal DFA (i.e., with the least number of states) associated with a random generalized string of increasing length. Even though the worst-case growth may be exponential, we characterize a point in the construction of the minimal DFA when it starts to grow linearly and conclude it has at most a polynomial number of states with asymptotically certain probability. We conjecture that this number is linear.

Suggested Citation

  • Ian G. Char & Manuel E. Lladser, 2020. "Stochastic Analysis of Minimal Automata Growth for Generalized Strings," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 329-347, March.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:1:d:10.1007_s11009-019-09706-8
    DOI: 10.1007/s11009-019-09706-8
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    1. Nuria Flames & Oliver Hobert, 2009. "Gene regulatory logic of dopamine neuron differentiation," Nature, Nature, vol. 458(7240), pages 885-889, April.
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