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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
"... Abstract. We study the compressed word problem: a variant of the word problem for finitely generated groups where the input word is given by a contextfree grammar that generates exactly one string. We show that finite extensions and free products preserve the complexity of the compressed word probl ..."
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Cited by 3 (1 self)
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Abstract. We study the compressed word problem: a variant of the word problem for finitely generated groups where the input word is given by a contextfree grammar that generates exactly one string. We show that finite extensions and free products preserve the complexity of the compressed word problem. Also, the compressed word problem for a graph group can be solved in polynomial time. These results allow us to obtain new upper complexity bounds for the word problem for certain automorphism groups and group extensions. 1
Leaf languages and string compression
 In Proc. FSTTCS 2008
, 2008
"... Abstract. 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 th ..."
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Cited by 1 (1 self)
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Abstract. 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, it is shown that there exists a fixed linear visibly pushdown language for which the compressed membership problem is PSPACEcomplete. For XML languages, it is shown that the compressed membership problem is coNPcomplete. 1
unknown title
"... ABSTRACT. 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 iscompletefortheleaflanguageclassdefinedby L vialogspacemachines. Amoredifficult variant of the compressed ..."
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ABSTRACT. 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 iscompletefortheleaflanguageclassdefinedby L vialogspacemachines. Amoredifficult variant of the compressed membership problem for L is shown to be complete for the leaf language classdefinedby Lviapolynomialtimemachines. Asacorollary,afixedlinearvisiblypushdownlanguagewithaPSPACEcompletecompressedmembershipproblemisobtained. ForXMLlanguages, the compressed membership problem is shown tobe coNPcomplete. 1
Congruence Closure of Compressed Terms in Polynomial Time
"... Abstract. The wordproblem for a finite set of equational axioms between ground terms is the question whether for terms s, t the equation s = t is a consequence. We consider this problem under grammar based compression of terms, in particular compression with singleton tree grammars (STGs) and with ..."
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Abstract. The wordproblem for a finite set of equational axioms between ground terms is the question whether for terms s, t the equation s = t is a consequence. We consider this problem under grammar based compression of terms, in particular compression with singleton tree grammars (STGs) and with directed acyclic graphs (DAGs) as a special case. We show that given a DAGcompressed ground and reduced term rewriting system T, the Tnormal form of an STGcompressed term s can be computed in polynomial time, and hence the Tword problem can be solved in polynomial time. This implies that the word problem of STGcompressed terms w.r.t. a set of DAGcompressed ground equations can be decided in polynomial time. If the ground term rewriting system (gTRS) T is STGcompressed, we show NPhardness of Tnormalform computation. For compressed, reduced gTRSs we show a PSPACE upper bound on the complexity of the normal form computation of STGcompressed terms. Also special cases are considered and a prototypical implementation is presented.
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
Editors: R. Hariharan, M. Mukund, V. Vinay; pp Leaf languages and string compression ∗
"... ABSTRACT. 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 th ..."
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ABSTRACT. 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 problem is obtained. For XML languages, the compressed membership problem is shown to be coNPcomplete. 1
c ○ World Scientific Publishing Company COMPRESSED MEMBERSHIP PROBLEMS FOR REGULAR EXPRESSIONS AND HIERARCHICAL AUTOMATA ∗
"... Communicated by (xxxxxxxxxx) 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 differe ..."
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Communicated by (xxxxxxxxxx) 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.
Theory of Computing Systems manuscript No. (will
"... be inserted by the editor) Complexity of equations over sets of natural numbers ..."
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be inserted by the editor) Complexity of equations over sets of natural numbers
Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P) ∗
"... In this paper, a compressed membership problem for finite automata, both deterministic (DFAs) and nondeterministic (NFAs), with compressed transition labels is studied. The compression is represented by straightline programs (SLPs), i.e. contextfree grammars generating exactly one string. A novel ..."
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In this paper, a compressed membership problem for finite automata, both deterministic (DFAs) and nondeterministic (NFAs), with compressed transition labels is studied. The compression is represented by straightline programs (SLPs), i.e. contextfree grammars generating exactly one string. A novel technique of dealing with SLPs is introduced: the SLPs are recompressed, so that substrings of the input text are encoded in SLPs labelling the transitions of the NFA (DFA) in the same way, as in the SLP representing the input text. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. Furthermore, in order to reflect the recompression in the NFA, we need to modify it only a little, in particular its size stays polynomial in the input size. Using this technique it is shown that the compressed membership for NFA with compressed labels is in NP, thus confirming the conjecture of Plandowski and Rytter [21] and extending the partial result of Lohrey and Mathissen [14]; as this problem is known to be NPhard, we settle its exact computational complexity. Moreover, the same technique applied to the compressed membership for DFA with compressed labels yields that this problem is in P, and this problem is known to be Phard.