FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2173819663> ?p ?o ?g. }

• W2173819663 endingPage "88" @default.
• W2173819663 startingPage "80" @default.
• W2173819663 abstract "A nonnegative matrix A is called primitive if Ak is positive for some integer k>0. A generalization by Protasov and Voynov (2012) of this concept to finite sets of matrices is as follows: a set of matrices M={A1,A2,…,Am} is primitive if Ai1Ai2…Aik is positive for some indices i1,i2,...,ik. The concept of primitive sets of matrices comes up in a number of problems within the study of discrete-time switched systems. In this paper, we analyze the computational complexity of deciding if a given set of matrices is primitive and we derive bounds on the length of the shortest positive product. We show that while primitivity is algorithmically decidable, unless P=NP it is not possible to decide primitivity of a matrix set in polynomial time. Moreover, we show that the length of the shortest positive sequence can be superpolynomial in the dimension of the matrices. On the other hand, defining P to be the set of matrices with no zero rows or columns, we give a combinatorial proof of the Protasov–Voynov characterization (2012) of primitivity for matrices in P which can be tested in polynomial time. This latter observation is related to the well-known 1964 conjecture of Černý on synchronizing automata; in fact, any bound on the minimal length of a synchronizing word for synchronizing automata immediately translates into a bound on the length of the shortest positive product of a primitive set of matrices in P. In particular, any primitive set of n×n matrices in P has a positive product of length O(n3)." @default.
• W2173819663 created "2016-06-24" @default.
• W2173819663 creator A5005863931 @default.
• W2173819663 creator A5056625594 @default.
• W2173819663 creator A5073875709 @default.
• W2173819663 date "2015-11-01" @default.
• W2173819663 modified "2023-09-27" @default.
• W2173819663 title "On primitivity of sets of matrices" @default.
• W2173819663 cites W1972887674 @default.
• W2173819663 cites W1976631094 @default.
• W2173819663 cites W1978242229 @default.
• W2173819663 cites W1998692453 @default.
• W2173819663 cites W1999883305 @default.
• W2173819663 cites W2018800107 @default.
• W2173819663 cites W2032418100 @default.
• W2173819663 cites W2053583025 @default.
• W2173819663 cites W2055037223 @default.
• W2173819663 cites W2078126880 @default.
• W2173819663 cites W2084970142 @default.
• W2173819663 cites W2102194201 @default.
• W2173819663 cites W2108151339 @default.
• W2173819663 cites W2114403255 @default.
• W2173819663 cites W2124297048 @default.
• W2173819663 cites W2131370775 @default.
• W2173819663 cites W2133334438 @default.
• W2173819663 cites W2140147014 @default.
• W2173819663 cites W2154834860 @default.
• W2173819663 cites W2165744313 @default.
• W2173819663 cites W2296394888 @default.
• W2173819663 cites W2963669387 @default.
• W2173819663 doi "https://doi.org/10.1016/j.automatica.2015.07.026" @default.
• W2173819663 hasPublicationYear "2015" @default.
• W2173819663 type Work @default.
• W2173819663 sameAs 2173819663 @default.
• W2173819663 citedByCount "21" @default.
• W2173819663 countsByYear W21738196632015 @default.
• W2173819663 countsByYear W21738196632016 @default.
• W2173819663 countsByYear W21738196632017 @default.
• W2173819663 countsByYear W21738196632018 @default.
• W2173819663 countsByYear W21738196632019 @default.
• W2173819663 countsByYear W21738196632020 @default.
• W2173819663 countsByYear W21738196632021 @default.
• W2173819663 countsByYear W21738196632023 @default.
• W2173819663 crossrefType "journal-article" @default.
• W2173819663 hasAuthorship W2173819663A5005863931 @default.
• W2173819663 hasAuthorship W2173819663A5056625594 @default.
• W2173819663 hasAuthorship W2173819663A5073875709 @default.
• W2173819663 hasBestOaLocation W21738196632 @default.
• W2173819663 hasConcept C106487976 @default.
• W2173819663 hasConcept C114614502 @default.
• W2173819663 hasConcept C118615104 @default.
• W2173819663 hasConcept C121332964 @default.
• W2173819663 hasConcept C134306372 @default.
• W2173819663 hasConcept C139018669 @default.
• W2173819663 hasConcept C153269930 @default.
• W2173819663 hasConcept C158693339 @default.
• W2173819663 hasConcept C159985019 @default.
• W2173819663 hasConcept C177148314 @default.
• W2173819663 hasConcept C192562407 @default.
• W2173819663 hasConcept C199360897 @default.
• W2173819663 hasConcept C2524010 @default.
• W2173819663 hasConcept C33923547 @default.
• W2173819663 hasConcept C41008148 @default.
• W2173819663 hasConcept C54848796 @default.
• W2173819663 hasConcept C62520636 @default.
• W2173819663 hasConcept C62555958 @default.
• W2173819663 hasConcept C77553402 @default.
• W2173819663 hasConcept C90673727 @default.
• W2173819663 hasConcept C97137487 @default.
• W2173819663 hasConceptScore W2173819663C106487976 @default.
• W2173819663 hasConceptScore W2173819663C114614502 @default.
• W2173819663 hasConceptScore W2173819663C118615104 @default.
• W2173819663 hasConceptScore W2173819663C121332964 @default.
• W2173819663 hasConceptScore W2173819663C134306372 @default.
• W2173819663 hasConceptScore W2173819663C139018669 @default.
• W2173819663 hasConceptScore W2173819663C153269930 @default.
• W2173819663 hasConceptScore W2173819663C158693339 @default.
• W2173819663 hasConceptScore W2173819663C159985019 @default.
• W2173819663 hasConceptScore W2173819663C177148314 @default.
• W2173819663 hasConceptScore W2173819663C192562407 @default.
• W2173819663 hasConceptScore W2173819663C199360897 @default.
• W2173819663 hasConceptScore W2173819663C2524010 @default.
• W2173819663 hasConceptScore W2173819663C33923547 @default.
• W2173819663 hasConceptScore W2173819663C41008148 @default.
• W2173819663 hasConceptScore W2173819663C54848796 @default.
• W2173819663 hasConceptScore W2173819663C62520636 @default.
• W2173819663 hasConceptScore W2173819663C62555958 @default.
• W2173819663 hasConceptScore W2173819663C77553402 @default.
• W2173819663 hasConceptScore W2173819663C90673727 @default.
• W2173819663 hasConceptScore W2173819663C97137487 @default.
• W2173819663 hasLocation W21738196631 @default.
• W2173819663 hasLocation W21738196632 @default.
• W2173819663 hasLocation W21738196633 @default.
• W2173819663 hasOpenAccess W2173819663 @default.
• W2173819663 hasPrimaryLocation W21738196631 @default.
• W2173819663 hasRelatedWork W1503005706 @default.
• W2173819663 hasRelatedWork W1944957487 @default.
• W2173819663 hasRelatedWork W2053402117 @default.

• next