On a compact encoding of the swap automaton
نویسندگان
چکیده
Given a string P of length m over an alphabet Σ of size σ, 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 ′∈ΠP ΣP ′ (swap automaton for short), where ΠP 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 ΣP . 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 O(σ⌈k/w⌉) space and allows one to simulate the automaton on a string of length n in time O(n⌈k/w⌉), where ⌈m/σ⌉ ≤ k ≤ m.
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عنوان ژورنال:
- Inf. Process. Lett.
دوره 114 شماره
صفحات -
تاریخ انتشار 2014