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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
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
Complexity Results on Balanced ContextFree Languages
 FOSSACS'07
, 2007
"... Abstract. Some decision problems related to balanced contextfree languages are important for their application to the static analysis of programs generating XML strings. One such problem is the balancedness problem which decides whether or not the language of a given contextfree grammar (CFG) over ..."
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Abstract. Some decision problems related to balanced contextfree languages are important for their application to the static analysis of programs generating XML strings. One such problem is the balancedness problem which decides whether or not the language of a given contextfree grammar (CFG) over a paired alphabet is balanced. Another important problem is the validation problem which decides whether or not the language of a CFG is contained by that of a regular hedge grammar (RHG). This paper gives two new results; (1) the balancedness problem is in PTIME; and (2) the CFGRHG containment problem is 2EXPTIMEcomplete. 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.
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