Compressed Membership Problems for Regular Expressions and Hierarchical Automata

Lohrey, Markus

doi:10.1142/s012905411000757x

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…Several algorithmic problems for SLP-compressed input strings were considered in the past, e.g. equivalence and pattern matching [5,12], word problems for certain groups and monoids [8,9,11,14], and membership problems for various language classes [3,7,9,13]. In this paper, we study the membership problem for compressed words in automata with compressed labels.…”

Section: Introductionmentioning

confidence: 99%

Compressed Membership in Automata with Compressed Labels

Lohrey

Mathissen

2011

Computer Science – Theory and Applications

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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, straight-line 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 NP-algorithm 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.

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Section: Introductionmentioning

confidence: 99%

Compressed Membership in Automata with Compressed Labels

Lohrey

Mathissen

2011

Computer Science – Theory and Applications

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“…PSPACEhardness for ¹ ; [; :º is shown in [85] by a reduction from the quantified boolean satisfiability problem; the reduction is mainly taken from [98], where it was shown that model checking the temporal logic LTL on SLP-compressed strings is PSPACE-complete. PSPACE-hardness for ¹ ; [; 2 º and ¹ ; [; ; \º is shown by generic reductions from the acceptance problem for a polynomial space bounded machine.…”

Section: Compressed Membership For Regular Expressionsmentioning

confidence: 99%

Algorithmics on SLP-compressed strings: A survey

Lohrey

2012

Groups - Complexity - Cryptology

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Results on algorithmic problems on strings that are given in a compressed form via straight-line programs are surveyed. A straight-line program is a context-free 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.

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“…In years to come, the compressed membership problem was investigated for various language classes [15,20,21,27,28,39]. Compressed word problem for groups and monoids [27,31,32], which can be seen as a generalisation of membership problem, was also considered.…”

Section: Membership Problemmentioning

confidence: 99%

The Complexity of Compressed Membership Problems for Finite Automata

Jeż

2013

Theory Comput Syst

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In this paper, a compressed membership problem for finite automata, both deterministic (DFAs) and non-deterministic (NFAs), with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is employed: the SLPs are recompressed, so that substrings of the input word 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

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Compressed Membership Problems for Regular Expressions and Hierarchical Automata

Cited by 9 publications

References 26 publications

Compressed Membership in Automata with Compressed Labels

Compressed Membership in Automata with Compressed Labels

Algorithmics on SLP-compressed strings: A survey

The Complexity of Compressed Membership Problems for Finite Automata

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