Theoretical Computer Science
Efficient parallel algorithms to test square-freeness and factorize strings
Information Processing Letters
An Optimal O(log log n)-Time Parallel Algorithm for Detecting all Squares in a String
SIAM Journal on Computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Efficient Algorithms for Lempel-Zip Encoding (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
An Improved Pattern Matching Algorithm for Strings in Terms of Straight-Line Programs
CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
Finding Maximal Repetitions in a Word in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Fully Compressed Pattern Matching Algorithm for Balanced Straight-Line Programs
SPIRE '00 Proceedings of the Seventh International Symposium on String Processing Information Retrieval (SPIRE'00)
Linear time algorithms for finding and representing all the tandem repeats in a string
Journal of Computer and System Sciences
Computing longest common substring and all palindromes from compressed strings
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
An efficient pattern matching algorithm on a subclass of context free grammars
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Processing compressed texts: a tractability border
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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In this paper we study the problem of deciding whether a given compressed string contains a square. A string x is called a square if x = zz and z = uk implies k = 1 and u = z. A string w is said to be square-free if no substrings of w are squares. Many efficient algorithms to test if a given string is square-free, have been developed so far. However, very little is known for testing square-freeness of a given compressed string. In this paper, we give an O(max(n2,n log2 N))-time O(n2)-space solution to test square-freeness of a given compressed string, where n and N are the size of a given compressed string and the corresponding decompressed string, respectively. Our input strings are compressed by balanced straight line program (BSLP). We remark that BSLP has exponential compression, that is, N = O(2n). Hence no decompress-then-test approaches can be better than our method in the worst case.