The Mortality Problem for Matrices of Low Dimensions

Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We s...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Bournez, O. [verfasserIn] Branicky, M.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2002

Schlagwörter:	Decision Problem Turing Machine Rational Entry Reachability Problem Composition Problem

Anmerkung:	© Springer-Verlag New York 2002

Übergeordnetes Werk:	Enthalten in: Theory of computing systems - New York, NY : Springer, 1997, 35(2002), 4 vom: 03. Juli, Seite 433-448
Übergeordnetes Werk:	volume:35 ; year:2002 ; number:4 ; day:03 ; month:07 ; pages:433-448

Links:	Volltext

DOI / URN:	10.1007/s00224-002-1010-5

Katalog-ID:	SPR002489996

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520			\|a Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results.
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650		4	\|a Turing Machine \|7 (dpeaa)DE-He213
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650		4	\|a Composition Problem \|7 (dpeaa)DE-He213
700	1		\|a Branicky, M. \|4 aut
773	0	8	\|i Enthalten in \|t Theory of computing systems \|d New York, NY : Springer, 1997 \|g 35(2002), 4 vom: 03. Juli, Seite 433-448 \|w (DE-627)254909728 \|w (DE-600)1463181-7 \|x 1433-0490 \|7 nnns
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912			\|a GBV_ILN_170
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912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_267
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912			\|a GBV_ILN_285
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912			\|a GBV_ILN_370
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912			\|a GBV_ILN_602
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912			\|a GBV_ILN_647
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2018
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2043
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912			\|a GBV_ILN_2048
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912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
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912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
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912			\|a GBV_ILN_2129
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912			\|a GBV_ILN_2147
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912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2193
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
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952			\|d 35 \|j 2002 \|e 4 \|b 03 \|c 07 \|h 433-448

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matchkey_str	article:14330490:2002----::hmraiyrbefrarcsf
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publishDate	2002
allfields	10.1007/s00224-002-1010-5 doi (DE-627)SPR002489996 (SPR)s00224-002-1010-5-e DE-627 ger DE-627 rakwb eng Bournez, O. verfasserin aut The Mortality Problem for Matrices of Low Dimensions 2002 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York 2002 Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results. Decision Problem (dpeaa)DE-He213 Turing Machine (dpeaa)DE-He213 Rational Entry (dpeaa)DE-He213 Reachability Problem (dpeaa)DE-He213 Composition Problem (dpeaa)DE-He213 Branicky, M. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 35(2002), 4 vom: 03. Juli, Seite 433-448 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:35 year:2002 number:4 day:03 month:07 pages:433-448 https://dx.doi.org/10.1007/s00224-002-1010-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 35 2002 4 03 07 433-448
spelling	10.1007/s00224-002-1010-5 doi (DE-627)SPR002489996 (SPR)s00224-002-1010-5-e DE-627 ger DE-627 rakwb eng Bournez, O. verfasserin aut The Mortality Problem for Matrices of Low Dimensions 2002 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York 2002 Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results. Decision Problem (dpeaa)DE-He213 Turing Machine (dpeaa)DE-He213 Rational Entry (dpeaa)DE-He213 Reachability Problem (dpeaa)DE-He213 Composition Problem (dpeaa)DE-He213 Branicky, M. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 35(2002), 4 vom: 03. Juli, Seite 433-448 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:35 year:2002 number:4 day:03 month:07 pages:433-448 https://dx.doi.org/10.1007/s00224-002-1010-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 35 2002 4 03 07 433-448
allfields_unstemmed	10.1007/s00224-002-1010-5 doi (DE-627)SPR002489996 (SPR)s00224-002-1010-5-e DE-627 ger DE-627 rakwb eng Bournez, O. verfasserin aut The Mortality Problem for Matrices of Low Dimensions 2002 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York 2002 Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results. Decision Problem (dpeaa)DE-He213 Turing Machine (dpeaa)DE-He213 Rational Entry (dpeaa)DE-He213 Reachability Problem (dpeaa)DE-He213 Composition Problem (dpeaa)DE-He213 Branicky, M. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 35(2002), 4 vom: 03. Juli, Seite 433-448 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:35 year:2002 number:4 day:03 month:07 pages:433-448 https://dx.doi.org/10.1007/s00224-002-1010-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 35 2002 4 03 07 433-448
allfieldsGer	10.1007/s00224-002-1010-5 doi (DE-627)SPR002489996 (SPR)s00224-002-1010-5-e DE-627 ger DE-627 rakwb eng Bournez, O. verfasserin aut The Mortality Problem for Matrices of Low Dimensions 2002 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York 2002 Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results. Decision Problem (dpeaa)DE-He213 Turing Machine (dpeaa)DE-He213 Rational Entry (dpeaa)DE-He213 Reachability Problem (dpeaa)DE-He213 Composition Problem (dpeaa)DE-He213 Branicky, M. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 35(2002), 4 vom: 03. Juli, Seite 433-448 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:35 year:2002 number:4 day:03 month:07 pages:433-448 https://dx.doi.org/10.1007/s00224-002-1010-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 35 2002 4 03 07 433-448
allfieldsSound	10.1007/s00224-002-1010-5 doi (DE-627)SPR002489996 (SPR)s00224-002-1010-5-e DE-627 ger DE-627 rakwb eng Bournez, O. verfasserin aut The Mortality Problem for Matrices of Low Dimensions 2002 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York 2002 Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results. Decision Problem (dpeaa)DE-He213 Turing Machine (dpeaa)DE-He213 Rational Entry (dpeaa)DE-He213 Reachability Problem (dpeaa)DE-He213 Composition Problem (dpeaa)DE-He213 Branicky, M. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 35(2002), 4 vom: 03. Juli, Seite 433-448 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:35 year:2002 number:4 day:03 month:07 pages:433-448 https://dx.doi.org/10.1007/s00224-002-1010-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 35 2002 4 03 07 433-448
language	English
source	Enthalten in Theory of computing systems 35(2002), 4 vom: 03. Juli, Seite 433-448 volume:35 year:2002 number:4 day:03 month:07 pages:433-448
sourceStr	Enthalten in Theory of computing systems 35(2002), 4 vom: 03. Juli, Seite 433-448 volume:35 year:2002 number:4 day:03 month:07 pages:433-448
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Decision Problem Turing Machine Rational Entry Reachability Problem Composition Problem
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container_title	Theory of computing systems
authorswithroles_txt_mv	Bournez, O. @@aut@@ Branicky, M. @@aut@@
publishDateDaySort_date	2002-07-03T00:00:00Z
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author	Bournez, O.
spellingShingle	Bournez, O. misc Decision Problem misc Turing Machine misc Rational Entry misc Reachability Problem misc Composition Problem The Mortality Problem for Matrices of Low Dimensions
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topic_title	The Mortality Problem for Matrices of Low Dimensions Decision Problem (dpeaa)DE-He213 Turing Machine (dpeaa)DE-He213 Rational Entry (dpeaa)DE-He213 Reachability Problem (dpeaa)DE-He213 Composition Problem (dpeaa)DE-He213
topic	misc Decision Problem misc Turing Machine misc Rational Entry misc Reachability Problem misc Composition Problem
topic_unstemmed	misc Decision Problem misc Turing Machine misc Rational Entry misc Reachability Problem misc Composition Problem
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doi_str_mv	10.1007/s00224-002-1010-5
title_sort	mortality problem for matrices of low dimensions
title_auth	The Mortality Problem for Matrices of Low Dimensions
abstract	Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results. © Springer-Verlag New York 2002
abstractGer	Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results. © Springer-Verlag New York 2002
abstract_unstemmed	Abstract In this paper we discuss the existence of an algorithm to decide if a given set of 2 \times 2 matrices is mortal. A set F={A1,\ldots,Am} of square matrices is said to be mortal if there exist an integer k \geq 1 and some integers i1,i2,\ldots,ik ∈ {1, \ldots, m} with Ai1 Ai2 ⋅s Aik=0 . We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results. © Springer-Verlag New York 2002
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title_short	The Mortality Problem for Matrices of Low Dimensions
url	https://dx.doi.org/10.1007/s00224-002-1010-5
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author2	Branicky, M.
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doi_str	10.1007/s00224-002-1010-5
up_date	2024-07-04T03:12:07.875Z
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