Abstract
We survey several complexity issues related to algorithmic problems on words given in an implicit way: by a grammar, LZ-encoding or as a minimal solution of a word equation. We discuss the relation between two implicit representations, the role of word compression in solvability of word equations and compressed language recognition problems. The grammar compression is more convenient than LZ-encoding, its size differs from that of LZ-encoding by at most logarithmic factor, the constructive proof is based on the concept similar to balanced trees.
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Rytter, W. (2004). Grammar Compression, LZ-Encodings, and String Algorithms with Implicit Input. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_5
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DOI: https://doi.org/10.1007/978-3-540-27836-8_5
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