The computational complexity of logical theories:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1979
|
| Series: | Lecture notes in mathematics
718 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 243 S. |
| ISBN: | 3540095012 0387095012 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | TABLE OF CONTENTS
CHAPTER 1: Introduction and Background 1
1. Introduction 1
2. Basic Notation and Definitions 8
3. Automata Theory Background 11
4. Using Reducibi1ities to Prove Upper and
Lower Bounds 16
5. Logic Background and Notation 20
6. Practical Relevance of the Theoretical Results 25
CHAPTER 2: Ehrenfeucht Games and Decision Procedures 28
1. Ehrenfeucht Games 28
2. Complexity of Ehrenfeucht Games 43
CHAPTER 3: Integer Addition - An Example of an Ehrenfeucht
Game Decision Procedure 47
1. An Upper Bound for Integer Addition 47
CHAPTER 4: Some Additional Upper Bounds 55
1. Introduction 55
2. Upper Bounds for the Theory of a 1-1 Unary
Function 60
3. Upper Bounds for the Theory of a 1-1 Unary
Function with a Monadic Predicate 81
4. Upper Bounds for the Theory of Two Successors
and Equal Length 102
5. Upper Bounds for the Theories of N, ,
Lexicographical Order, and Well-order 112
6. Historical Remarks 127
CHAPTER 5: Direct Products of Theories 128
1. Weak Direct Powers and Ehrenfeucht Games 128
2. Upper Bounds for the Theories of Integer
Multiplication and Abelian Groups 135
X
TABLE OF CONTENTS (cont d)
3. The Complexity of Theories of Weak Direct Powers 141
4. Results about Other Kinds of Direct Products 144
CHAPTER 6: Lower Bound Preliminaries 148
1. Simple Turing Machines 148
2. Regular-like Expressions 152
CHATPER 7: A Technique for Writing Short Formulas
Defining Complicated Properties 153
CHAPTER 8: A Lower Bound on the Theories of Pairing Functions ... 162
1. Introduction 162
2. Some Undecidabi1ity Results 165
3. Construction of Formulas which Talk About
Large Sets 170
4. Using Formulas to Simulate Turing Machines 185
CHAPTER 9: Some Additional Lower Bounds 187
1. Lower Bounds for the Theory of One Successor 187
2. Lower Bounds for the Theory of One Successor
with a Monadic Predicate 201
3. Lower Bounds for the Theory of Two Successors 219
4. Lower Bounds for the Theory of a 1-1 Unary
Function 223
REFERENCES 234
Subject and Notation Index 239
TABLE 1: A Summary of Results 3
|
| any_adam_object | 1 |
| author | Ferrante, Jeanne Rackoff, Charles 1948- |
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| author_facet | Ferrante, Jeanne Rackoff, Charles 1948- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics 510 - Mathematics |
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| dewey-search | 511/.3 510/.8 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002260201 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:57Z |
| institution | BVB |
| isbn | 3540095012 0387095012 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001485344 |
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| physical | 243 S. |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Ferrante, Jeanne Verfasser aut The computational complexity of logical theories Jeanne Ferrante ; Charles W. Rackoff Berlin [u.a.] Springer 1979 243 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 718 Calcul des prédicats Complexité de calcul (Informatique) Computational complexity Predicate calculus Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Komplexität (DE-588)4135369-9 gnd rswk-swf Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Prädikatenlogik (DE-588)4046974-8 gnd rswk-swf Berechenbarkeit (DE-588)4138368-0 s Mathematische Logik (DE-588)4037951-6 s DE-604 Prädikatenlogik (DE-588)4046974-8 s Komplexität (DE-588)4135369-9 s Rackoff, Charles 1948- Verfasser (DE-588)1102140848 aut Lecture notes in mathematics 718 (DE-604)BV000676446 718 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001485344&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ferrante, Jeanne Rackoff, Charles 1948- The computational complexity of logical theories Lecture notes in mathematics Calcul des prédicats Complexité de calcul (Informatique) Computational complexity Predicate calculus Mathematische Logik (DE-588)4037951-6 gnd Komplexität (DE-588)4135369-9 gnd Berechenbarkeit (DE-588)4138368-0 gnd Prädikatenlogik (DE-588)4046974-8 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4135369-9 (DE-588)4138368-0 (DE-588)4046974-8 |
| title | The computational complexity of logical theories |
| title_auth | The computational complexity of logical theories |
| title_exact_search | The computational complexity of logical theories |
| title_full | The computational complexity of logical theories Jeanne Ferrante ; Charles W. Rackoff |
| title_fullStr | The computational complexity of logical theories Jeanne Ferrante ; Charles W. Rackoff |
| title_full_unstemmed | The computational complexity of logical theories Jeanne Ferrante ; Charles W. Rackoff |
| title_short | The computational complexity of logical theories |
| title_sort | the computational complexity of logical theories |
| topic | Calcul des prédicats Complexité de calcul (Informatique) Computational complexity Predicate calculus Mathematische Logik (DE-588)4037951-6 gnd Komplexität (DE-588)4135369-9 gnd Berechenbarkeit (DE-588)4138368-0 gnd Prädikatenlogik (DE-588)4046974-8 gnd |
| topic_facet | Calcul des prédicats Complexité de calcul (Informatique) Computational complexity Predicate calculus Mathematische Logik Komplexität Berechenbarkeit Prädikatenlogik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001485344&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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