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On the complexity of iterated shuffle

1984
*
Journal of computer and system sciences (Print)
*

It

doi:10.1016/0022-0000(84)90018-7
fatcat:wmw4u3zri5ep5ctfc6xsc3qgdu
*is*demonstrated that the following problems are*NP**complete*: (1) Given*words*w and w" wz ,..., w"*is*w in the shuffle of w" w 2,-r w,? (2) Given*words*w and v,*is*w in the iterated shuffle of v? ... From these results we show that the languages {%w$w": WE {*a*,b)*)@, lJ""",.(%w)@, (ab"cde'f: n > O}@, and {*a*""b"c"f": n 2 O)@ are*NP**complete*, where @ denotes the iterated shuffle. ... This problem remains*NP**complete*even if all*words*w,, We,..., w, are identical, which yields*a*second*NP**complete*problem: for*two**words*w and u, the problem of whether or not w*is*in the iterated shuffle ...##
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An Algebraic Framework for Schema Matching
[chapter]

2005
*
Lecture Notes in Computer Science
*

Then, we formulize SMP as

doi:10.1007/11563952_66
fatcat:eflycf3xffhchcudykentih2ii
*a*schema*homomorphism*problem, and prove that SMP*is*equivalent to*finding**a*semantic*homomorphism*from one schema to another. ... Thirdly, we show*a*classification of schema matching based on the algebraic framework. Finally, we discuss the relations*between*matching cardinality and subclasses of schema*homomorphism*. ... This paper*is*the extended version of WAIM 2005. We would like to thank the anonymous reviewers for their careful work in evaluating an earlier version of this paper. ...##
###
Extending SPARQL with regular expression patterns (for querying RDF)

2009
*
Journal of Web Semantics
*

We provide PRDF with

doi:10.1016/j.websem.2009.02.002
fatcat:nkjpsy2w6fafbb6ns6trgka7tq
*a*semantics extending that of RDF, and propose*a*correct and*complete*algorithm which, by computing*a*particular graph*homomorphism*, decides the consequence*between*an RDF graph and ... RDF*is**a*knowledge representation language dedicated to the annotation of resources within the framework of the semantic web. ...*A*similar proof to PRDF-GRDF*HOMOMORPHISM**between*G and σ(P ). Since PRDF-GRDF HOMO-MORPHISM*is**NP*-*complete*, then PSPARQL QUERY EVALUATION*is**NP*-*complete*for PRDF graphs. ...##
###
Extending SPARQL With Regular Expression Patterns: For Querying RDF

2009
*
Social Science Research Network
*

We provide PRDF with

doi:10.2139/ssrn.3199439
fatcat:xxqpmbiorjgi7c7duafnqamsk4
*a*semantics extending that of RDF, and propose*a*correct and*complete*algorithm which, by computing*a*particular graph*homomorphism*, decides the consequence*between*an RDF graph and ... RDF*is**a*knowledge representation language dedicated to the annotation of resources within the framework of the semantic web. ...*A*similar proof to PRDF-GRDF*HOMOMORPHISM**between*G and σ(P ). Since PRDF-GRDF HOMO-MORPHISM*is**NP*-*complete*, then PSPARQL QUERY EVALUATION*is**NP*-*complete*for PRDF graphs. ...##
###
Referentiality and incompletive reading in Mandarin

2018
*
Proceedings of the Linguistic Society of America
*

As an exception to Krifka's (1989) famous generalization that

doi:10.3765/plsa.v3i1.4338
fatcat:ju7t7srhcrbf7bvkibc2kjzd4e
*a*quantized incremental theme always induces an event-*homomorphic**completive*reading, Singh (1991, 1998) observes that in Hindi only the quantized ... mass noun phrases as the incremental theme entails*a**completive*reading, but unexpectedly quantized count nouns phrases can have an incompletive reading. ... event*is**homomorphic*to its direct object and the perfective aspect asserts the event*is**complete*. ...##
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INTERPRETING GRAPH COLORABILITY IN FINITE SEMIGROUPS

2006
*
International journal of algebra and computation
*

This problem

doi:10.1142/s0218196706002846
fatcat:tl2xcqfsnvcxvg62nwxycksepq
*is*known to be in co-*NP*and there are now*a*number of known semigroups for which this problem*is*co-*NP*-*complete*(such as B 1 2 ; see [14] and [8] ). ... Recall that the term-equivalence problem for an algebra*A**is*the problem of deciding for*two*terms s, t in the signature of*A*, if*A*|= s ≈ t. ... (*A*)*is**NP*-*complete*. ...##
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Locally constrained graph homomorphisms—structure, complexity, and applications

2008
*
Computer Science Review
*

*A*graph

*homomorphism*

*is*an edge preserving vertex mapping

*between*

*two*graphs. ... the neighborhood of its image in the target graph, the

*homomorphism*

*is*called locally bijective (injective, surjective, respectively). ... If the L-H-LInHom problem

*is*

*NP*-

*complete*, then the L-H -LInHom problem

*is*

*NP*-

*complete*as well. ...

##
###
Complexity of Conjugacy, Factoring and Embedding for Countable Sofic Shifts of Rank 2
[article]

2014
*
arXiv
*
pre-print

We prove that their conjugacy problem

arXiv:1408.6695v1
fatcat:kgp6akzvsrcyrguogomzxndzpu
*is**complete*for GI, the complexity class of graph isomorphism, and that the existence problems of block maps, factor maps and embeddings are*NP*-*complete*. ... Existence of embeddings*between*countable sofic shifts of Cantor-Bendixson rank at most 2*is**NP*-*complete*. ... For*two*graphs G and H, we show*a*correspondence*between*graph*homomorphisms*φ : G → H and block maps f : X G → X H . ...##
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Reasoning About Pattern-Based XML Queries
[chapter]

2013
*
Lecture Notes in Computer Science
*

As in the relational case, they can be viewed as both queries and incomplete documents, and thus static analysis problems can also be viewed as

doi:10.1007/978-3-642-39666-3_2
fatcat:oqgntk34j5aibdx6ceuw7gsv3e
*finding*certain answers of queries over such documents. ... We look at satisfiability of patterns under schemas, containment of queries for various features of XML used in queries,*finding*certain answers, and applications of pattern-based queries in reasoning ... Given*two*conjunctive queries Q 1 and Q 2 , we have Q 1 ⊆ Q 2 iff there*is**a**homomorphism*h : tab(Q 2 ) → tab(Q 1 ); this makes the problem*NP*-*complete*[13] . ...##
###
Complexity of Conjugacy, Factoring and Embedding for Countable Sofic Shifts of Rank 2
[chapter]

2015
*
Lecture Notes in Computer Science
*

We prove that their conjugacy problem

doi:10.1007/978-3-319-18812-6_10
fatcat:dms567z75rdo5ibamvmkpx2sg4
*is**complete*for GI, the complexity class of graph isomorphism, and that the existence problems of block maps, factor maps and embeddings are*NP*-*complete*. ... Existence of embeddings*between*countable sofic shifts of Cantor-Bendixson rank at most 2*is**NP*-*complete*. ... For*two*graphs G and H, we show*a*correspondence*between*graph*homomorphisms*φ : G → H and block maps f : X G → X H . ...##
###
Linear Index Coding via Graph Homomorphism
[article]

2014
*
arXiv
*
pre-print

In [4],

arXiv:1410.1371v1
fatcat:gwpnwevdifcxxndagtnoaok5bm
*a*direct connection*between*linear index coding problem and graph*homomorphism*problem*is*introduced. ... For digraphs, it*is*shown in [6] that for the binary alphabet, the decision problem for k=2*is**NP*-*complete*. We use graph*homomorphism*framework to extend this result to arbitrary alphabet. ...*A*. Rafiey for their invaluable comments. ...##
###
Exact Algorithm for Graph Homomorphism and Locally Injective Graph Homomorphism
[article]

2013
*
arXiv
*
pre-print

*A*

*homomorphism*

*is*locally injective if no

*two*vertices with

*a*common neighbor are mapped to

*a*single vertex in H. ... Many cases of graph

*homomorphism*and locally injective graph

*homomorphism*are

*NP*-

*complete*, so there

*is*little hope to design polynomial-time algorithms for them. ... The author

*is*sincerely grateful to Konstanty Junosza-Szaniawski for valuable discussion and advice. ...

##
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Authentication schemes from actions on graphs, groups, or rings

2010
*
Annals of Pure and Applied Logic
*

Then we give several concrete realizations of this general idea, and in particular, we describe several authentication schemes with long-term private keys where forgery (a.k.a. impersonation)

doi:10.1016/j.apal.2010.09.004
fatcat:ipmntlwb5vbmdk4fcs656hlzma
*is**NP*-hard ... We propose*a*couple of general ways of constructing authentication schemes from actions of*a*semigroup on*a*set, without exploiting any specific algebraic properties of the set acted upon. ... The first author*is*grateful to Max Planck Institut für Mathematik, Bonn for its hospitality during the work on this paper. ...##
###
The complexity of colouring symmetric relational systems

1994
*
Discrete Applied Mathematics
*

We show that H-COL

doi:10.1016/0166-218x(94)90203-8
fatcat:v3hckusmcbbynheuegpbwvjfoa
*is*polynomial when H*is**a*path and we show that trees exist such that H-COL*is**NP*-*complete*. ...*A*relational system, S,*is**a*set T with relations R" R" ,.., R, on T, denoted S = (T, R, , R" . , R,J We consider relational systems where all the relations are binary, symmetric and antireflexive. ... Alsof(gl)f(g2)~Ea(W) sincefis*a**homomorphism*. Therefore,at Step*NP*-*complete*trees We now prove that there exists*a*tree H such that H-COL*is**NP*-*complete*. ...##
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Computational Complexity of Synchronization under Sparse Regular Constraints
[article]

2021
*
arXiv
*
pre-print

With our previous result, we deduce

arXiv:2108.00081v1
fatcat:gzjnvyfrafbmjjhon3hgt3tv34
*a*full classification for these languages as well. In both cases, depending on the constraint language, our problem becomes*NP*-*complete*or polynomial time solvable. ... The constrained synchronization problem (CSP) asks for*a*synchronizing*word*of*a*given input automaton contained in*a*regular set of constraints. ... 1 In computer science the acronym CSP*is*usually used for the constraint satisfaction problem [35]. ...
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