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On the complexity of iterated shuffle

Manfred K. Warmuth, David Haussler
1984 Journal of computer and system sciences (Print)  
It 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  ... 
doi:10.1016/0022-0000(84)90018-7 fatcat:wmw4u3zri5ep5ctfc6xsc3qgdu

An Algebraic Framework for Schema Matching [chapter]

Zhi Zhang, Haoyang Che, Pengfei Shi, Yong Sun, Jun Gu
2005 Lecture Notes in Computer Science  
Then, we formulize SMP as 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.  ... 
doi:10.1007/11563952_66 fatcat:eflycf3xffhchcudykentih2ii

Extending SPARQL with regular expression patterns (for querying RDF)

Faisal Alkhateeb, Jean-François Baget, Jérôme Euzenat
2009 Journal of Web Semantics  
We provide PRDF with 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.  ... 
doi:10.1016/j.websem.2009.02.002 fatcat:nkjpsy2w6fafbb6ns6trgka7tq

Extending SPARQL With Regular Expression Patterns: For Querying RDF

Faisal Alkhateeb, Jean-Frannois Baget, JJrrme Euzenat
2009 Social Science Research Network  
We provide PRDF with 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.  ... 
doi:10.2139/ssrn.3199439 fatcat:xxqpmbiorjgi7c7duafnqamsk4

Referentiality and incompletive reading in Mandarin

Anqi Zhang
2018 Proceedings of the Linguistic Society of America  
As an exception to Krifka's (1989) famous generalization that 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.  ... 
doi:10.3765/plsa.v3i1.4338 fatcat:ju7t7srhcrbf7bvkibc2kjzd4e

INTERPRETING GRAPH COLORABILITY IN FINITE SEMIGROUPS

MARCEL JACKSON, RALPH McKENZIE
2006 International journal of algebra and computation  
This problem 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.  ... 
doi:10.1142/s0218196706002846 fatcat:tl2xcqfsnvcxvg62nwxycksepq

Locally constrained graph homomorphisms—structure, complexity, and applications

Jiří Fiala, Jan Kratochvíl
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.  ... 
doi:10.1016/j.cosrev.2008.06.001 fatcat:p57dezmpfjhzpf5xahy4f7rtga

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

Ville Salo, Ilkka Törmä
2014 arXiv   pre-print
We prove that their conjugacy problem 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 .  ... 
arXiv:1408.6695v1 fatcat:kgp6akzvsrcyrguogomzxndzpu

Reasoning About Pattern-Based XML Queries [chapter]

Amélie Gheerbrant, Leonid Libkin, Cristina Sirangelo
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 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] .  ... 
doi:10.1007/978-3-642-39666-3_2 fatcat:oqgntk34j5aibdx6ceuw7gsv3e

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

Ville Salo, Ilkka Törmä
2015 Lecture Notes in Computer Science  
We prove that their conjugacy problem 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 .  ... 
doi:10.1007/978-3-319-18812-6_10 fatcat:dms567z75rdo5ibamvmkpx2sg4

Linear Index Coding via Graph Homomorphism [article]

Javad B. Ebrahimi, Mahdi Jafari Siavoshani
2014 arXiv   pre-print
In [4], 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.  ... 
arXiv:1410.1371v1 fatcat:gwpnwevdifcxxndagtnoaok5bm

Exact Algorithm for Graph Homomorphism and Locally Injective Graph Homomorphism [article]

Paweł Rzążewski
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.  ... 
arXiv:1310.3341v1 fatcat:ngzxlbpa35bmnkkr564aywafla

Authentication schemes from actions on graphs, groups, or rings

Dima Grigoriev, Vladimir Shpilrain
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) 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.  ... 
doi:10.1016/j.apal.2010.09.004 fatcat:ipmntlwb5vbmdk4fcs656hlzma

The complexity of colouring symmetric relational systems

Richard Brewster
1994 Discrete Applied Mathematics  
We show that H-COL 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.  ... 
doi:10.1016/0166-218x(94)90203-8 fatcat:v3hckusmcbbynheuegpbwvjfoa

Computational Complexity of Synchronization under Sparse Regular Constraints [article]

Stefan Hoffmann
2021 arXiv   pre-print
With our previous result, we deduce 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].  ... 
arXiv:2108.00081v1 fatcat:gzjnvyfrafbmjjhon3hgt3tv34
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