On a compact encoding of the swap automaton
Kimmo Fredriksson, Emanuele Giaquinta

TL;DR
This paper introduces a compact, bit-parallel encoding of the swap automaton for strings with local swaps, improving space and simulation efficiency by leveraging combinatorial properties and existing methods.
Contribution
It provides a novel theoretical analysis and a space-efficient encoding of the swap automaton using bit-parallel techniques, linking it to the automaton for the original string.
Findings
Space complexity is reduced to $O(\sigma^2 ext{ceil}(k/w))$
Simulation time is improved to $O(n ext{ceil}(k/w))$
The method exploits a combinatorial property connecting swap and original automata
Abstract
Given a string of length over an alphabet of size , a swapped version of is a string derived from 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 (swap automaton for short), where is the set of swapped versions of . 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 . By exploiting this property and the method presented by Cantone et al. (2010), we obtain a bit-parallel encoding of the swap automaton which takes space and allows one to simulate the automaton on a string of…
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Taxonomy
TopicsAlgorithms and Data Compression · semigroups and automata theory · DNA and Biological Computing
