Complexity of Language Recognition Problems for Compressed Words

The compressed recognition problem consists in checking if an input word w is in a given language L, when we are only given a compressed representation of w. We present several new results related to language recognition problems for compressed texts. These problems are solvable in polynomial time for uncompressed words and some of them become NP-hard for compressed words.

[1]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[2]  Wojciech Plandowski,et al.  Application of Lempel-Ziv Encodings to the Solution of Words Equations , 1998, ICALP.

[3]  Wojciech Rytter,et al.  Almost-optimal fully LZW-compressed pattern matching , 1999, Proceedings DCC'99 Data Compression Conference (Cat. No. PR00096).

[4]  Gary Benson,et al.  Optimal Two-Dimensional Compressed Matching , 1994, J. Algorithms.

[5]  Gary Benson,et al.  Efficient two-dimensional compressed matching , 1992, Data Compression Conference, 1992..

[6]  M. Lothaire Combinatorics on words: Bibliography , 1997 .

[7]  Zvi Galil,et al.  Optimal Parallel Algorithms for Periods, Palindromes and Squares (Extended Abstract) , 1992, ICALP.

[8]  Wojciech Plandowski,et al.  Efficient algorithms for Lempel-Ziv encoding , 1996 .

[9]  Terry A. Welch,et al.  A Technique for High-Performance Data Compression , 1984, Computer.

[10]  Wojciech Rytter,et al.  Pattern-Matching for Strings with Short Descriptions , 1995, CPM.

[11]  Wojciech Plandowski,et al.  Randomized Efficient Algorithms for Compressed Strings: The Finger-Print Approach (Extended Abstract) , 1996, CPM.

[12]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[13]  Mikkel Thorup,et al.  String matching in Lempel-Ziv compressed strings , 1995, STOC '95.

[14]  Bogdan S. Chlebus,et al.  Optimal Pattern Matching on Meshes , 1994, STACS.

[15]  Wojciech Rytter,et al.  Text Algorithms , 1994 .

[16]  Wojciech Plandowski,et al.  On the Complexity of Pattern Matching for Highly Compressed Two-Dimensional Texts , 1997, CPM.

[17]  Abraham Lempel,et al.  On the Complexity of Finite Sequences , 1976, IEEE Trans. Inf. Theory.

[18]  Gary Benson,et al.  Let sleeping files lie: pattern matching in Z-compressed files , 1994, SODA '94.