Deterministic polynomial identity testing in non-commutative models
Abstract. We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,···,xn and determines whether or not the output of the f...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Raz, Ran [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2005 |
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| Anmerkung: |
© Birkhäuser Verlag, Basel 2005 |
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| Übergeordnetes Werk: |
Enthalten in: Computational complexity - Birkhäuser-Verlag, 1991, 14(2005), 1 vom: Apr., Seite 1-19 |
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| Übergeordnetes Werk: |
volume:14 ; year:2005 ; number:1 ; month:04 ; pages:1-19 |
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| DOI / URN: |
10.1007/s00037-005-0188-8 |
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| 520 | |a Abstract. We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,···,xn and determines whether or not the output of the formula is identically 0 (as a formal expression).Pure arithmetic circuits: The algorithm gets as an input a pure set-multilinear arithmetic circuit (as defined by Nisan and Wigderson) in the variables x1,···,xn and determines whether or not the output of the circuit is identically 0 (as a formal expression). One application is a deterministic polynomial time identity testing for set-multilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for non-commutative algebraic branching programs as defined by Nisan. Finally, we obtain an exponential lower bound for the size of pure setmultilinear arithmetic circuits for the permanent and for the determinant. (Only lower bounds for the depth of pure circuits were previously known.) | ||
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10.1007/s00037-005-0188-8 doi (DE-627)OLC2071974573 (DE-He213)s00037-005-0188-8-p DE-627 ger DE-627 rakwb eng 510 VZ 004 VZ 17,1 ssgn Raz, Ran verfasserin aut Deterministic polynomial identity testing in non-commutative models 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2005 Abstract. We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,···,xn and determines whether or not the output of the formula is identically 0 (as a formal expression).Pure arithmetic circuits: The algorithm gets as an input a pure set-multilinear arithmetic circuit (as defined by Nisan and Wigderson) in the variables x1,···,xn and determines whether or not the output of the circuit is identically 0 (as a formal expression). One application is a deterministic polynomial time identity testing for set-multilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for non-commutative algebraic branching programs as defined by Nisan. Finally, we obtain an exponential lower bound for the size of pure setmultilinear arithmetic circuits for the permanent and for the determinant. (Only lower bounds for the depth of pure circuits were previously known.) Shpilka, Amir aut Enthalten in Computational complexity Birkhäuser-Verlag, 1991 14(2005), 1 vom: Apr., Seite 1-19 (DE-627)130982245 (DE-600)1076101-9 (DE-576)025197037 1016-3328 nnns volume:14 year:2005 number:1 month:04 pages:1-19 https://doi.org/10.1007/s00037-005-0188-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2010 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4318 AR 14 2005 1 04 1-19 |
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10.1007/s00037-005-0188-8 doi (DE-627)OLC2071974573 (DE-He213)s00037-005-0188-8-p DE-627 ger DE-627 rakwb eng 510 VZ 004 VZ 17,1 ssgn Raz, Ran verfasserin aut Deterministic polynomial identity testing in non-commutative models 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2005 Abstract. We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,···,xn and determines whether or not the output of the formula is identically 0 (as a formal expression).Pure arithmetic circuits: The algorithm gets as an input a pure set-multilinear arithmetic circuit (as defined by Nisan and Wigderson) in the variables x1,···,xn and determines whether or not the output of the circuit is identically 0 (as a formal expression). One application is a deterministic polynomial time identity testing for set-multilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for non-commutative algebraic branching programs as defined by Nisan. Finally, we obtain an exponential lower bound for the size of pure setmultilinear arithmetic circuits for the permanent and for the determinant. (Only lower bounds for the depth of pure circuits were previously known.) Shpilka, Amir aut Enthalten in Computational complexity Birkhäuser-Verlag, 1991 14(2005), 1 vom: Apr., Seite 1-19 (DE-627)130982245 (DE-600)1076101-9 (DE-576)025197037 1016-3328 nnns volume:14 year:2005 number:1 month:04 pages:1-19 https://doi.org/10.1007/s00037-005-0188-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2010 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4318 AR 14 2005 1 04 1-19 |
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Deterministic polynomial identity testing in non-commutative models |
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Abstract. We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,···,xn and determines whether or not the output of the formula is identically 0 (as a formal expression).Pure arithmetic circuits: The algorithm gets as an input a pure set-multilinear arithmetic circuit (as defined by Nisan and Wigderson) in the variables x1,···,xn and determines whether or not the output of the circuit is identically 0 (as a formal expression). One application is a deterministic polynomial time identity testing for set-multilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for non-commutative algebraic branching programs as defined by Nisan. Finally, we obtain an exponential lower bound for the size of pure setmultilinear arithmetic circuits for the permanent and for the determinant. (Only lower bounds for the depth of pure circuits were previously known.) © Birkhäuser Verlag, Basel 2005 |
| abstractGer |
Abstract. We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,···,xn and determines whether or not the output of the formula is identically 0 (as a formal expression).Pure arithmetic circuits: The algorithm gets as an input a pure set-multilinear arithmetic circuit (as defined by Nisan and Wigderson) in the variables x1,···,xn and determines whether or not the output of the circuit is identically 0 (as a formal expression). One application is a deterministic polynomial time identity testing for set-multilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for non-commutative algebraic branching programs as defined by Nisan. Finally, we obtain an exponential lower bound for the size of pure setmultilinear arithmetic circuits for the permanent and for the determinant. (Only lower bounds for the depth of pure circuits were previously known.) © Birkhäuser Verlag, Basel 2005 |
| abstract_unstemmed |
Abstract. We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,···,xn and determines whether or not the output of the formula is identically 0 (as a formal expression).Pure arithmetic circuits: The algorithm gets as an input a pure set-multilinear arithmetic circuit (as defined by Nisan and Wigderson) in the variables x1,···,xn and determines whether or not the output of the circuit is identically 0 (as a formal expression). One application is a deterministic polynomial time identity testing for set-multilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for non-commutative algebraic branching programs as defined by Nisan. Finally, we obtain an exponential lower bound for the size of pure setmultilinear arithmetic circuits for the permanent and for the determinant. (Only lower bounds for the depth of pure circuits were previously known.) © Birkhäuser Verlag, Basel 2005 |
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| title_short |
Deterministic polynomial identity testing in non-commutative models |
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https://doi.org/10.1007/s00037-005-0188-8 |
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| author2 |
Shpilka, Amir |
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10.1007/s00037-005-0188-8 |
| up_date |
2024-07-04T04:38:30.417Z |
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