Asymptotic estimates for the number of solutions of the dualization problem and its generalizations
Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typi...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Djukova, E. V. [verfasserIn] Sotnezov, R. M. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Übergeordnetes Werk: |
Enthalten in: Computational mathematics and mathematical physics - Moscow : Maik Nauk/Interperiodica Publ., 1997, 51(2011), 8 vom: 17. Aug. |
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| Übergeordnetes Werk: |
volume:51 ; year:2011 ; number:8 ; day:17 ; month:08 |
| Links: |
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| DOI / URN: |
10.1134/S0965542511080069 |
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| Katalog-ID: |
SPR019924836 |
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| 100 | 1 | |a Djukova, E. V. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Asymptotic estimates for the number of solutions of the dualization problem and its generalizations |
| 264 | 1 | |c 2011 | |
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| 337 | |a Computermedien |b c |2 rdamedia | ||
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| 520 | |a Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed. | ||
| 650 | 4 | |a complexity of enumeration problems |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a dualization problem |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a maximal conjunction |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a irreducible covering of a Boolean matrix |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a irredundant covering of an integer matrix |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a complexity of search for irredundant coverings |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a metric properties of the set of coverings |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a metric properties of disjunctive normal forms |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a asymptotically optimal algorithm |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Sotnezov, R. M. |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Computational mathematics and mathematical physics |d Moscow : Maik Nauk/Interperiodica Publ., 1997 |g 51(2011), 8 vom: 17. Aug. |w (DE-627)26688265X |w (DE-600)1468110-9 |x 1555-6662 |7 nnns |
| 773 | 1 | 8 | |g volume:51 |g year:2011 |g number:8 |g day:17 |g month:08 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1134/S0965542511080069 |z lizenzpflichtig |3 Volltext |
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10.1134/S0965542511080069 doi (DE-627)SPR019924836 (SPR)S0965542511080069-e DE-627 ger DE-627 rakwb eng 510 ASE 33.06 bkl 31.76 bkl Djukova, E. V. verfasserin aut Asymptotic estimates for the number of solutions of the dualization problem and its generalizations 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed. complexity of enumeration problems (dpeaa)DE-He213 dualization problem (dpeaa)DE-He213 maximal conjunction (dpeaa)DE-He213 irreducible covering of a Boolean matrix (dpeaa)DE-He213 irredundant covering of an integer matrix (dpeaa)DE-He213 complexity of search for irredundant coverings (dpeaa)DE-He213 metric properties of the set of coverings (dpeaa)DE-He213 metric properties of disjunctive normal forms (dpeaa)DE-He213 asymptotically optimal algorithm (dpeaa)DE-He213 Sotnezov, R. M. verfasserin aut Enthalten in Computational mathematics and mathematical physics Moscow : Maik Nauk/Interperiodica Publ., 1997 51(2011), 8 vom: 17. Aug. (DE-627)26688265X (DE-600)1468110-9 1555-6662 nnns volume:51 year:2011 number:8 day:17 month:08 https://dx.doi.org/10.1134/S0965542511080069 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 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_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_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2188 GBV_ILN_2190 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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.06 ASE 31.76 ASE AR 51 2011 8 17 08 |
| spelling |
10.1134/S0965542511080069 doi (DE-627)SPR019924836 (SPR)S0965542511080069-e DE-627 ger DE-627 rakwb eng 510 ASE 33.06 bkl 31.76 bkl Djukova, E. V. verfasserin aut Asymptotic estimates for the number of solutions of the dualization problem and its generalizations 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed. complexity of enumeration problems (dpeaa)DE-He213 dualization problem (dpeaa)DE-He213 maximal conjunction (dpeaa)DE-He213 irreducible covering of a Boolean matrix (dpeaa)DE-He213 irredundant covering of an integer matrix (dpeaa)DE-He213 complexity of search for irredundant coverings (dpeaa)DE-He213 metric properties of the set of coverings (dpeaa)DE-He213 metric properties of disjunctive normal forms (dpeaa)DE-He213 asymptotically optimal algorithm (dpeaa)DE-He213 Sotnezov, R. M. verfasserin aut Enthalten in Computational mathematics and mathematical physics Moscow : Maik Nauk/Interperiodica Publ., 1997 51(2011), 8 vom: 17. Aug. (DE-627)26688265X (DE-600)1468110-9 1555-6662 nnns volume:51 year:2011 number:8 day:17 month:08 https://dx.doi.org/10.1134/S0965542511080069 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 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_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_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2188 GBV_ILN_2190 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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.06 ASE 31.76 ASE AR 51 2011 8 17 08 |
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10.1134/S0965542511080069 doi (DE-627)SPR019924836 (SPR)S0965542511080069-e DE-627 ger DE-627 rakwb eng 510 ASE 33.06 bkl 31.76 bkl Djukova, E. V. verfasserin aut Asymptotic estimates for the number of solutions of the dualization problem and its generalizations 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed. complexity of enumeration problems (dpeaa)DE-He213 dualization problem (dpeaa)DE-He213 maximal conjunction (dpeaa)DE-He213 irreducible covering of a Boolean matrix (dpeaa)DE-He213 irredundant covering of an integer matrix (dpeaa)DE-He213 complexity of search for irredundant coverings (dpeaa)DE-He213 metric properties of the set of coverings (dpeaa)DE-He213 metric properties of disjunctive normal forms (dpeaa)DE-He213 asymptotically optimal algorithm (dpeaa)DE-He213 Sotnezov, R. M. verfasserin aut Enthalten in Computational mathematics and mathematical physics Moscow : Maik Nauk/Interperiodica Publ., 1997 51(2011), 8 vom: 17. Aug. (DE-627)26688265X (DE-600)1468110-9 1555-6662 nnns volume:51 year:2011 number:8 day:17 month:08 https://dx.doi.org/10.1134/S0965542511080069 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 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_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_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2188 GBV_ILN_2190 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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.06 ASE 31.76 ASE AR 51 2011 8 17 08 |
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10.1134/S0965542511080069 doi (DE-627)SPR019924836 (SPR)S0965542511080069-e DE-627 ger DE-627 rakwb eng 510 ASE 33.06 bkl 31.76 bkl Djukova, E. V. verfasserin aut Asymptotic estimates for the number of solutions of the dualization problem and its generalizations 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed. complexity of enumeration problems (dpeaa)DE-He213 dualization problem (dpeaa)DE-He213 maximal conjunction (dpeaa)DE-He213 irreducible covering of a Boolean matrix (dpeaa)DE-He213 irredundant covering of an integer matrix (dpeaa)DE-He213 complexity of search for irredundant coverings (dpeaa)DE-He213 metric properties of the set of coverings (dpeaa)DE-He213 metric properties of disjunctive normal forms (dpeaa)DE-He213 asymptotically optimal algorithm (dpeaa)DE-He213 Sotnezov, R. M. verfasserin aut Enthalten in Computational mathematics and mathematical physics Moscow : Maik Nauk/Interperiodica Publ., 1997 51(2011), 8 vom: 17. Aug. (DE-627)26688265X (DE-600)1468110-9 1555-6662 nnns volume:51 year:2011 number:8 day:17 month:08 https://dx.doi.org/10.1134/S0965542511080069 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 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_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_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2188 GBV_ILN_2190 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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.06 ASE 31.76 ASE AR 51 2011 8 17 08 |
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10.1134/S0965542511080069 doi (DE-627)SPR019924836 (SPR)S0965542511080069-e DE-627 ger DE-627 rakwb eng 510 ASE 33.06 bkl 31.76 bkl Djukova, E. V. verfasserin aut Asymptotic estimates for the number of solutions of the dualization problem and its generalizations 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed. complexity of enumeration problems (dpeaa)DE-He213 dualization problem (dpeaa)DE-He213 maximal conjunction (dpeaa)DE-He213 irreducible covering of a Boolean matrix (dpeaa)DE-He213 irredundant covering of an integer matrix (dpeaa)DE-He213 complexity of search for irredundant coverings (dpeaa)DE-He213 metric properties of the set of coverings (dpeaa)DE-He213 metric properties of disjunctive normal forms (dpeaa)DE-He213 asymptotically optimal algorithm (dpeaa)DE-He213 Sotnezov, R. M. verfasserin aut Enthalten in Computational mathematics and mathematical physics Moscow : Maik Nauk/Interperiodica Publ., 1997 51(2011), 8 vom: 17. Aug. (DE-627)26688265X (DE-600)1468110-9 1555-6662 nnns volume:51 year:2011 number:8 day:17 month:08 https://dx.doi.org/10.1134/S0965542511080069 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 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_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_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2188 GBV_ILN_2190 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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.06 ASE 31.76 ASE AR 51 2011 8 17 08 |
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Enthalten in Computational mathematics and mathematical physics 51(2011), 8 vom: 17. Aug. volume:51 year:2011 number:8 day:17 month:08 |
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V.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Asymptotic estimates for the number of solutions of the dualization problem and its generalizations</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). 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Djukova, E. V. |
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Djukova, E. V. ddc 510 bkl 33.06 bkl 31.76 misc complexity of enumeration problems misc dualization problem misc maximal conjunction misc irreducible covering of a Boolean matrix misc irredundant covering of an integer matrix misc complexity of search for irredundant coverings misc metric properties of the set of coverings misc metric properties of disjunctive normal forms misc asymptotically optimal algorithm Asymptotic estimates for the number of solutions of the dualization problem and its generalizations |
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510 ASE 33.06 bkl 31.76 bkl Asymptotic estimates for the number of solutions of the dualization problem and its generalizations complexity of enumeration problems (dpeaa)DE-He213 dualization problem (dpeaa)DE-He213 maximal conjunction (dpeaa)DE-He213 irreducible covering of a Boolean matrix (dpeaa)DE-He213 irredundant covering of an integer matrix (dpeaa)DE-He213 complexity of search for irredundant coverings (dpeaa)DE-He213 metric properties of the set of coverings (dpeaa)DE-He213 metric properties of disjunctive normal forms (dpeaa)DE-He213 asymptotically optimal algorithm (dpeaa)DE-He213 |
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ddc 510 bkl 33.06 bkl 31.76 misc complexity of enumeration problems misc dualization problem misc maximal conjunction misc irreducible covering of a Boolean matrix misc irredundant covering of an integer matrix misc complexity of search for irredundant coverings misc metric properties of the set of coverings misc metric properties of disjunctive normal forms misc asymptotically optimal algorithm |
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ddc 510 bkl 33.06 bkl 31.76 misc complexity of enumeration problems misc dualization problem misc maximal conjunction misc irreducible covering of a Boolean matrix misc irredundant covering of an integer matrix misc complexity of search for irredundant coverings misc metric properties of the set of coverings misc metric properties of disjunctive normal forms misc asymptotically optimal algorithm |
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ddc 510 bkl 33.06 bkl 31.76 misc complexity of enumeration problems misc dualization problem misc maximal conjunction misc irreducible covering of a Boolean matrix misc irredundant covering of an integer matrix misc complexity of search for irredundant coverings misc metric properties of the set of coverings misc metric properties of disjunctive normal forms misc asymptotically optimal algorithm |
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Asymptotic estimates for the number of solutions of the dualization problem and its generalizations |
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Asymptotic estimates for the number of solutions of the dualization problem and its generalizations |
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asymptotic estimates for the number of solutions of the dualization problem and its generalizations |
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Asymptotic estimates for the number of solutions of the dualization problem and its generalizations |
| abstract |
Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed. |
| abstractGer |
Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed. |
| abstract_unstemmed |
Abstract Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed. |
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8 |
| title_short |
Asymptotic estimates for the number of solutions of the dualization problem and its generalizations |
| url |
https://dx.doi.org/10.1134/S0965542511080069 |
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| author2 |
Sotnezov, R. M. |
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| doi_str |
10.1134/S0965542511080069 |
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2024-07-04T03:21:05.055Z |
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| score |
7.4006376 |