On a compact encoding of the swap automaton

  • Authors:
  • Kimmo Fredriksson;Emanuele Giaquinta

  • Affiliations:
  • School of Computing, University of Eastern Finland, P.O. Box 1627, FI-70211 Kuopio, Finland;Department of Computer Science, University of Helsinki, Finland

  • Venue:
  • Information Processing Letters
  • Year:
  • 2014

Quantified Score

Hi-index 0.89

Visualization

Abstract

Given a string P of length m over an alphabet @S of size @s, a swapped version of P is a string derived from P by a series of local swaps, i.e., swaps of adjacent symbols, such that each symbol can participate in at most one swap. We present a theoretical analysis of the nondeterministic finite automaton for the language @?"P"^"'"@?"@P"""P@S^@?P^' (swap automaton, for short), where @P"P is the set of swapped versions of P. Our study is based on the bit-parallel simulation of the same automaton due to Fredriksson, and reveals an interesting combinatorial property that links the automaton to the one for the language @S^@?P. By exploiting this property and the method presented by Cantone et al. (2012), we obtain a bit-parallel encoding of the swap automaton which takes O(@s^2@?k/w@?) space and allows one to simulate the automaton on a string of length n in time O(n@?k/w@?), where @?m/@s@?=