Hard Counting Problems for Partial Words
In this paper we approach several decision and counting problems related to partial words, from a computational point of view. First we show that finding a full word that is not compatible with any word from a given list of partial words, all having the same length, is NP-complete; from this we derive that counting the number of words that are compatible with at least one word from a given list of partial words, all having the same length, is #P-complete. We continue by showing that some other related problems are also #P-complete; from these we mention here only two: counting all the distinct full words of a given length compatible with at least one factor of the given partial word, and counting all the distinct squares compatible with at least a factor of a given partial word.
KeywordsPartial Words NP-completeness #P Complexity Class #P-complete Problems Combinatorics on Words
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