A Polynomial Time Match Test for Large Classes of Extended Regular Expressions

Reidenbach, Daniel; Schmid, Markus L.

doi:10.1007/978-3-642-18098-9_26

Cited by 13 publications

(15 citation statements)

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“…In [25][26][27], several possibilities are presented of how to restrict the structure of the source strings, such that StrMorph can be solved in polynomial time, and in [13], the N P-completeness of a large number of strongly restricted versions of StrMorph is shown.…”

Section: The Contribution Of This Papermentioning

confidence: 99%

On the Parameterised Complexity of String Morphism Problems

2015

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Given a source string u and a target string w, to decide whether w can be obtained by applying a string morphism on u (i. e., uniformly replacing the symbols in u by strings) constitutes an NP-complete problem. For example, the target string w := baaba can be obtained from the source string u := aba, by replacing a and b in u by the strings ba and a, respectively. In this paper, we contribute to the recently started investigation of the computational complexity of the string morphism problem by studying it in the framework of parameterised complexity. ACM Subject Classification IntroductionMany of the typical string problems are concerned with special kinds of string operations like, e. g., concatenating strings with each other, deleting symbols from or inserting symbols into a string or replacing symbols by other symbols or even by other strings. Among the most prominent of these string problems are string-to-string correction, sequence alignment as well as the longest common subsequence and shortest common supersequence problem. The complexity of these problems have been intensely studied, both in the classical sense as well as in the parameterised setting (see, e. g., [1,9]). In this work, we investigate string problems that arise from a less well-known operation on strings, i. e., mapping a source string u to a target string w by uniformly (i. e., by a mapping) replacing the symbols of u by strings. For example, we can turn the source string u := abba into the target string w := bbaaaaabba by replacing a and b of u by the strings bba and aa, respectively. On the other hand, w := abaaaaaabb cannot be obtained from u in a similar way. The string morphism problem (denoted by StrMorph) is to decide for two given strings u and w, whether or not w can be obtained from u by this kind of operation. Due to its simple definition, variants of this N P-complete problem can be found in many different areas of theoretical computer science. In fact, many respective results are scattered throughout the literature without pointers to each other and consulting the existing literature suggests that variants of the string morphism problem have emerged and have been investigated in different contexts without knowledge of other related work.

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Section: The Contribution Of This Papermentioning

confidence: 99%

On the Parameterised Complexity of String Morphism Problems

2015

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“…Nonetheless, there is a common core to these variants, which was first formalized by Aho [1], and later by Câmpeanu, Salomaa and Yu [5]. Still, theoretical investigation of extended regular expressions has been comparatively rare (in particular when compared to their more prominent subclass); see e. g., Larsen [20], Della Penna et al [12], Câmpeanu and Santean [6], Carle and Narendran [8], and Reidenbach and Schmid [22].…”

Section: Introductionmentioning

confidence: 99%

Extended Regular Expressions: Succinctness and Decidability

Freydenberger

2012

Theory Comput Syst

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Most modern implementations of regular expression engines allow the use of variables (also called back references). The resulting extended regular expressions (which, in the literature, are also called practical regular expressions, rewbr, or regex) are able to express non-regular languages.The present paper demonstrates that extended regular-expressions cannot be minimized effectively (neither with respect to length, nor number of variables), and that the tradeoff in size between extended and "classical" regular expressions is not bounded by any recursive function. In addition to this, we prove the undecidability of several decision problems (universality, equivalence, inclusion, regularity, and cofiniteness) for extended regular expressions. Furthermore, we show that all these results hold even if the extended regular expressions contain only a single variable.

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“…Thus, NBMCA can be used whenever classical multi-head automata can be applied, but due to their specific counters and nondeterminism they are particularly suitable algorithmic tools for recognising those languages that are characterised by the existence of a certain factorisation for their words, such as pattern languages (see [11]). …”

Section: Expressive Power Hierarchy and Decidabilitymentioning

confidence: 99%

“…These NBMCA are suitable algorithmic tools for recognising those languages that are characterised by the existence of a specific factorisation of their words, e. g., pattern languages, and are a generalisation of the Janus automata that have been introduced and applied in [11] in order to investigate the membership problem for pattern languages. In [11], NBMCA with exactly two input heads are used. In the present work we focus on NBMCA with only one head, since we can easily simulate several input heads by just a single one.…”

Section: Introductionmentioning

confidence: 99%

Automata with modulo counters and nondeterministic counter bounds

Reidenbach¹,

Schmid²

2014

Kybernetika

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Abstract. We introduce and investigate Nondeterministically Bounded Modulo Counter Automata (NBMCA), which are two-way one-head automata that comprise a constant number of modulo counters, where the counter bounds are nondeterministically guessed, and this is the only element of nondeterminism. NBMCA are tailored to recognising those languages that are characterised by the existence of a specific factorisation of their words, e. g., pattern languages. In this work, we subject NBMCA to a theoretically sound analysis.

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A Polynomial Time Match Test for Large Classes of Extended Regular Expressions

Cited by 13 publications

References 13 publications

On the Parameterised Complexity of String Morphism Problems

On the Parameterised Complexity of String Morphism Problems

Extended Regular Expressions: Succinctness and Decidability

Automata with modulo counters and nondeterministic counter bounds

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