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Algorithmics on SLPcompressed strings: a survey,
 Groups Complex. Cryptol.
, 2012
"... Abstract Results on algorithmic problems on strings that are given in a compressed form via straightline programs are surveyed. A straightline program is a contextfree grammar that generates exactly one string. In this way, exponential compression rates can be achieved. Among others, we study pat ..."
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Cited by 10 (3 self)
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Abstract Results on algorithmic problems on strings that are given in a compressed form via straightline programs are surveyed. A straightline program is a contextfree grammar that generates exactly one string. In this way, exponential compression rates can be achieved. Among others, we study pattern matching for compressed strings, membership problems for compressed strings in various kinds of formal languages, and the problem of querying compressed strings. Applications in combinatorial group theory and computational topology and to the solution of word equations are discussed as well. Finally, extensions to compressed trees and pictures are considered.
Grammarbased tree compression
, 2004
"... Abstract. Grammarbased compression means to find a small grammar that generates a given object. Such a grammar reveals the structure of the object (according to the grammar formalism used); the main advantage of this compression method is that the resulting grammar can often be used in further comp ..."
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Cited by 7 (1 self)
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Abstract. Grammarbased compression means to find a small grammar that generates a given object. Such a grammar reveals the structure of the object (according to the grammar formalism used); the main advantage of this compression method is that the resulting grammar can often be used in further computations without prior decompression. A linear time bottomup algorithm is presented which transforms a tree into a particular contextfree tree grammar. For common XML documents the algorithm performs well, compressing the tree structure to about 5 % of the original size. The validation of an XML document against an XML type can be done without decompression, in linear time w.r.t. the size of the grammar (for a fixed type). While the involved grammars can be double exponentially smaller than the represented trees, testing them for equivalence can be done in polynomial space w.r.t. the sum of their sizes. 1
One Context Unification Problems Solvable in Polynomial Time
"... Abstract—One context unification extends firstorder unification by introducing a single context variable, possibly with multiple occurrences. One context unification is known to be in NP, but it is not known to be solvable in polynomial time. In this paper, we present a polynomial time algorithm f ..."
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Abstract—One context unification extends firstorder unification by introducing a single context variable, possibly with multiple occurrences. One context unification is known to be in NP, but it is not known to be solvable in polynomial time. In this paper, we present a polynomial time algorithm for certain interesting classes of the one context unification problem. Our algorithm is presented as an inference system that nontrivially extends the usual inference rules for firstorder unification. The algorithm is of independent value as it can be used, with slight modifications, to solve other problems, such as the firstorder unification problem that tolerates one clash. I.