Optimal algorithms for binomial ideals and commutative semigroups:
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| Format: | Book |
| Language: | English |
| Published: |
1997
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | München, Techn. Univ., Diss., 1997 |
| Physical Description: | VII, 141 S. |
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CONTENTS
V
CONTENTS
ABSTRACT I
ACKNOWLEDGMENTS - DANKSAGUNG III
CONTENTS V
1 INTRODUCTION 1
2 BASIC CONCEPTS AND NOTATIONS 5
2.1 SEMIGROUPS. 5
2.2 REDUCTION RELATIONS . 6
2.3 POLYNOMIAL RINGS, IDEALS, GROBNER BASES. 8
2.4 COMMUTATIVE THUE SYSTEMS, COMMUTATIVE SEMIGROUP PRESENTATIONS . 13
2.5 VECTOR ADDITION SYSTEMS, PETRI NETS . 15
2.6 UNIFORMLY SEMILINEAR SETS. 17
2.7 EXPONENTIAL SPACE .22
2.8 THE BASIC PROBLEMS, THEIR RELATIONSHIP AND THEIR COMPLEXITY
. 24
3 THE REDUCED GROBNER BASIS OF PURE DIFFERENCE BINOMIAL IDEALS 33
3.1 PREVIOUS WORK .33
3.2 THE STRUCTURE OF THE REDUCED GROBNER BASIS.35
3.3 AN OPTIMAL ALGORITHM FOR CONSTRUCTING THE REDUCED GROBNER BASIS . 36
3.4 FIRST APPLICATIONS.40
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/951118129
VI CONTENTS
3.4.1 TESTING FOR REDUCIBILITY .40
3.4.2 FINDING THE MINIMAL ELEMENT AND THE NORMAL FORM.41
4 THE REDUCED GROBNER BASIS OF BINOMIAL IDEALS 43
4.1 BASICS.43
4.2 AN OPTIMAL ALGORITHM FOR CONSTRUCTING THE REDUCED GROBNER BASIS . 55
5 THE COVERABILITY, FINITE ENUMERATION, AND BOUNDEDNESS PROBLEMS 59
5.1 DEFINITIONS, PREVIOUS WORK. 59
5.2 EXPONENTIAL SPACE ALGORITHMS.61
5.2.1 THE COVERABILITY PROBLEM.61
5.2.2 THE FINITE ENUMERATION PROBLEM.71
5.2.3 THE BOUNDEDNESS PROBLEM.76
5.3 EXPONENTIAL SPACE COMPLETENESS .77
5.4 THE FINITE CONTAINMENT AND FINITE EQUIVALENCE PROBLEMS .78
6 THE SUBWORD PROBLEM 81
6.1 PRELIMINARIES . 81
6.2 AN EXPONENTIAL SPACE ALGORITHM.83
6.3 EXPONENTIAL SPACE COMPLETENESS . 89
6.4 SOME APPLICATIONS. 89
6.4.1 THE BOUNDEDNESS PROBLEM.89
6.4.2 BOUNDED AND UNBOUNDED VARIABLES W.R.T. CONGRUENCE CLASSES 90
6.4.3 PERIODS OF A CONGRUENCE CLASS.92
7 THE CONTAINMENT AND EQUIVALENCE PROBLEMS 95
7.1 DEFINITION, PREVIOUS WORK. 95
7.2 AN EXPONENTIAL SPACE ALGORITHM. 96
7.3 EXPONENTIAL SPACE COMPLETENESS .104
CONTENTS VII
8 CONCLUSION 105
8.1 SUMMARY.105
8.2 OPEN PROBLEMS.106
A FURTHER EXAMPLES: BOUNDED CONGRUENCE CLASSES 109
A.L FIRST CONGRUENCE CLASS.I.109
A.1.1 BOUNDED VARIABLES.110
A. 1.2 ENUMERATING THE ELEMENTS.ILL
A. 2 SECOND CONGRUENCE CLASS.113
A.2.1 BOUNDED VARIABLES.113
A. 2.2 ENUMERATING THE ELEMENTS.DR.113
B FURTHER EXAMPLES: UNBOUNDED CONGRUENCE CLASSES 117
B. L FIRST CONGRUENCE CLASS.117
B. 1.1 BOUNDED AND UNBOUNDED VARIABLES, MINIMAL PERIODS.118
B.L.2 MINIMAL ELEMENTS.120
B.2 SECOND CONGRUENCE CLASS.122
B.2.1 BOUNDED AND UNBOUNDED VARIABLES, MINIMAL PERIODS.123
B.2.2 MINIMAL ELEMENTS.127
BIBLIOGRAPHY 131
INDEX
139 |
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| indexdate | 2024-10-09T16:08:11Z |
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| language | English |
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| spelling | Koppenhagen, Ulla Verfasser aut Optimal algorithms for binomial ideals and commutative semigroups Ulla Koppenhagen 1997 VII, 141 S. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 1997 Abelsche Halbgruppe (DE-588)4140989-9 gnd rswk-swf Gröbner-Basis (DE-588)4276378-2 gnd rswk-swf Polynomideal (DE-588)4175263-6 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Gröbner-Basis (DE-588)4276378-2 s Algorithmus (DE-588)4001183-5 s DE-604 Abelsche Halbgruppe (DE-588)4140989-9 s Polynomideal (DE-588)4175263-6 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007698397&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koppenhagen, Ulla Optimal algorithms for binomial ideals and commutative semigroups Abelsche Halbgruppe (DE-588)4140989-9 gnd Gröbner-Basis (DE-588)4276378-2 gnd Polynomideal (DE-588)4175263-6 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4140989-9 (DE-588)4276378-2 (DE-588)4175263-6 (DE-588)4001183-5 (DE-588)4113937-9 |
| title | Optimal algorithms for binomial ideals and commutative semigroups |
| title_auth | Optimal algorithms for binomial ideals and commutative semigroups |
| title_exact_search | Optimal algorithms for binomial ideals and commutative semigroups |
| title_full | Optimal algorithms for binomial ideals and commutative semigroups Ulla Koppenhagen |
| title_fullStr | Optimal algorithms for binomial ideals and commutative semigroups Ulla Koppenhagen |
| title_full_unstemmed | Optimal algorithms for binomial ideals and commutative semigroups Ulla Koppenhagen |
| title_short | Optimal algorithms for binomial ideals and commutative semigroups |
| title_sort | optimal algorithms for binomial ideals and commutative semigroups |
| topic | Abelsche Halbgruppe (DE-588)4140989-9 gnd Gröbner-Basis (DE-588)4276378-2 gnd Polynomideal (DE-588)4175263-6 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Abelsche Halbgruppe Gröbner-Basis Polynomideal Algorithmus Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007698397&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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