On a compact encoding of the swap automaton

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@?=