Theoretical Computer Science
Handbook of formal languages, vol. 1
Efficient string matching: an aid to bibliographic search
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Crucial words and the complexity of some extremal problems for sets of prohibited words
Journal of Combinatorial Theory Series A
Combinatorial Enumeration
Simple deterministic wildcard matching
Information Processing Letters
Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)
Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)
Note: Testing avoidability on sets of partial words is hard
Theoretical Computer Science
Unavoidable Sets of Partial Words
Theory of Computing Systems - Special Issue: Symposium on Parallelism in Algorithms and Architectures 2006; Guest Editors: Robert Kleinberg and Christian Scheideler
On the Complexity of Deciding Avoidability of Sets of Partial Words
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Number of holes in unavoidable sets of partial words II
Journal of Discrete Algorithms
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Blanchet-Sadri et al. have shown that Avoidability, or the problem of deciding the avoidability of a finite set of partial words over an alphabet of size k=2, is NP-hard [F. Blanchet-Sadri, R. Jungers, J. Palumbo, Testing avoidability on sets of partial words is hard, Theoret. Comput. Sci. 410 (2009) 968-972]. Building on their work, we analyze in this paper the complexity of natural variations on the problem. While some of them are NP-hard, others are shown to be efficiently decidable. Using some combinatorial properties of de Bruijn graphs, we establish a correspondence between lengths of cycles in such graphs and periods of avoiding words, resulting in a tight bound for periods of avoiding words. We also prove that Avoidability can be solved in polynomial space, and reduces in polynomial time to the problem of deciding the avoidability of a finite set of partial words of equal length over the binary alphabet. We give a polynomial bound on the period of an infinite avoiding word, in the case of sets of full words, in terms of two parameters: the length and the number of words in the set. We give a polynomial space algorithm to decide if a finite set of partial words is avoided by a non-ultimately periodic infinite word. The same algorithm also decides if the number of words of length n avoiding a given finite set of partial words grows polynomially or exponentially with n.