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Querying and Embedding Compressed Texts
, 2005
"... Abstract. In this work the computational complexity of two simple string problems on compressed input strings is considered: the querying problem (What is the symbol at a given position in a given input string?) and the embedding problem (Can the first input string embedded into the second input str ..."
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Abstract. In this work the computational complexity of two simple string problems on compressed input strings is considered: the querying problem (What is the symbol at a given position in a given input string?) and the embedding problem (Can the first input string embedded into the second input string?). Straightline programs are used for text compression. It is shown that the querying problem becomes Pcomplete for compressed strings, while the embedding problem becomes hard for the complexity class Θ p 2. 1
Efficient computation in groups via compression
 In Proc. CSR 2007, LNCS 4649
, 2007
"... Abstract. A compressed variant of the word problem for finitely generated groups, where the input word is given by a contextfree grammar that generates exactly one string (also called a straightline program), is studied. It is shown that finite extensions and free products preserve the complexity ..."
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Abstract. A compressed variant of the word problem for finitely generated groups, where the input word is given by a contextfree grammar that generates exactly one string (also called a straightline program), is studied. It is shown that finite extensions and free products preserve the complexity of the compressed word problem and that the compressed word problem for a graph group can be solved in polynomial time. Using these results together with connections between the compressed word problem and the (classical) word problem allows to obtain new upper complexity bounds for certain automorphism groups and group extensions. 1
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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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.
Leaf languages and string compression
, 2008
"... Tight connections between leafs languages and strings compressed via straightline programs (SLPs) are established. It is shown that the compressed membership problem for a language L is complete for the leaf language class defined by L via logspace machines. A more difficult variant of the compress ..."
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Cited by 6 (4 self)
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Tight connections between leafs languages and strings compressed via straightline programs (SLPs) are established. It is shown that the compressed membership problem for a language L is complete for the leaf language class defined by L via logspace machines. A more difficult variant of the compressed membership problem for L is shown to be complete for the leaf language class defined by L via polynomial time machines. As a corollary, a fixed linear visibly pushdown language with a PSPACEcomplete compressed membership problemis obtained. For XML languages, the compressed membership problem is shown to be coNPcomplete.
COMPRESSED MEMBERSHIP PROBLEMS FOR REGULAR EXPRESSIONS AND HIERARCHICAL AUTOMATA
, 2010
"... Membership problems for compressed strings in regular languages are investigated. Strings are represented by straightline programs, i.e., contextfree grammars that generate exactly one string. For the representation of regular languages, various formalisms with different degrees of succinctness ..."
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Cited by 6 (2 self)
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Membership problems for compressed strings in regular languages are investigated. Strings are represented by straightline programs, i.e., contextfree grammars that generate exactly one string. For the representation of regular languages, various formalisms with different degrees of succinctness (e.g., suitably extended regular expressions, hierarchical automata) are considered. Precise complexity bounds are derived. Among other results, it is shown that the compressed membership problem for regular expressions with intersection is PSPACEcomplete. This solves an open problem of Plandowski and Rytter.
Compressed membership in automata with compressed labels
 CSR, volume 6651 of LNCS
, 2011
"... Abstract. The algorithmic problem of whether a compressed string is accepted by a (nondeterministic) finite state automaton with compressed transition labels is investigated. For string compression, straightline programs (SLPs), i.e., contextfree grammars that generate exactly one string, are used ..."
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Abstract. The algorithmic problem of whether a compressed string is accepted by a (nondeterministic) finite state automaton with compressed transition labels is investigated. For string compression, straightline programs (SLPs), i.e., contextfree grammars that generate exactly one string, are used. Two algorithms for this problem are presented. The first one works in polynomial time, if all transition labels are nonperiodic strings (or more generally, the word length divided by the period is bounded polynomially in the input size). This answers a question of Plandowski and Rytter. The second (nondeterministic) algorithm is an NPalgorithm under the assumption that for each transition label the period is bounded polynomially in the input size. This generalizes the NP upper bound for the case of a unary alphabet, shown by Plandowski and Rytter. 1
Efficient algorithms for highly compressed data: The Word Problem in Higman’s group is in P
"... Power circuits are data structures which support efficient algorithms for highly compressed integers. Using this new data structure it has been shown recently by Myasnikov, Ushakov and Won that the Word Problem of the onerelator Baumslag group is is decidable in polynomial time. Before that the bes ..."
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Power circuits are data structures which support efficient algorithms for highly compressed integers. Using this new data structure it has been shown recently by Myasnikov, Ushakov and Won that the Word Problem of the onerelator Baumslag group is is decidable in polynomial time. Before that the best known upper bound was nonelementary. In the present paper we provide new results for power circuits and we give new applications in algorithmic group theory: 1. We define a modified reduction procedure on power circuits which runs in quadratic time thereby improving the known cubic time complexity. 2. We improve the complexity of the Word Problem for the Baumslag group to cubic time thereby providing the first practical algorithm for that problem. 3. The Word Problem of Higman’s group is decidable in polynomial time. It is due to the last result that we were forced to advance the theory of power circuits.
Automata for Positive Core XPath Queries on Compressed Documents
 In Proceedings of LPAR’06
, 2006
"... Abstract. Given any dag t representing a fully or partially compressed XML document, we present a method for evaluating any positive unary query expressed in terms of Core XPath axes, on t, without unfolding t into a tree. To each Core XPath query of a certain basic type, we associate a word automa ..."
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Abstract. Given any dag t representing a fully or partially compressed XML document, we present a method for evaluating any positive unary query expressed in terms of Core XPath axes, on t, without unfolding t into a tree. To each Core XPath query of a certain basic type, we associate a word automaton; these automata run on the graph of dependency between the nonterminals of the straightline regular tree grammar associated to the given dag, or along complete sibling chains in this grammar. Any given Core XPath query can be decomposed into queries of the basic type, and the answer to the query, on the dag t, can then be expressed as a subdag of t suitably labeled under the runs of such automata.
Matching of Compressed Patterns with CharacterVariables
, 2012
"... We consider the problem of finding an instance of a stringpattern s in a given string under compression by straight line programs (SLP). The variables of the string pattern can be instantiated by single characters. This is a generalisation of the fully compressed pattern match, which is the task of ..."
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We consider the problem of finding an instance of a stringpattern s in a given string under compression by straight line programs (SLP). The variables of the string pattern can be instantiated by single characters. This is a generalisation of the fully compressed pattern match, which is the task of finding a compressed string in another compressed string, which is known to have a polynomial time algorithm. We mainly investigate patterns s that are linear in the variables, i.e. variables occur at most once in s, also known as partial words. We show that fully compressed pattern matching with linear patterns can be performed in polynomial time. A polynomialsized representation of all matches and all substitutions is also computed. Also, a related algorithm is given that computes all periods of a compressed linear pattern in polynomial time. A technical key result on the structure of partial words shows that an overlap of h + 2 copies of a partial word w with at most h holes implies that w is strongly periodic.
Compressed word problems in HNNextensions and amalgamated products
, 811
"... Abstract. It is shown that the compressed word problem for an HNNextension 〈H,t  t −1 at = ϕ(a)(a ∈ A) 〉 with A finite is polynomial time Turingreducible to the compressed word problem for the base group H. An analogous result for amalgamated free products is shown as well. 1 ..."
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Abstract. It is shown that the compressed word problem for an HNNextension 〈H,t  t −1 at = ϕ(a)(a ∈ A) 〉 with A finite is polynomial time Turingreducible to the compressed word problem for the base group H. An analogous result for amalgamated free products is shown as well. 1