Decision procedures: an algorithmic point of view
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin <<[u.a.]>>
Springer
2010
|
| Schriftenreihe: | Texts in theoretical computer science
|
| Schlagworte: | |
| Online-Zugang: | http://d-nb.info/985166533/04 http://scans.hebis.de/HEBCGI/show.pl?23205520_kap-1.pdf http://scans.hebis.de/HEBCGI/show.pl?23205520_ein-1.pdf Inhaltsverzeichnis |
| Beschreibung: | XVI, 304 S. graph. Darst. |
| ISBN: | 9783642093449 |
Internformat
MARC
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| 020 | |a 9783642093449 |9 978-3-642-09344-9 | ||
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| 245 | 1 | 0 | |a Decision procedures |b an algorithmic point of view |c Daniel Kroening ; Ofer Strichman |
| 264 | 1 | |a Berlin <<[u.a.]>> |b Springer |c 2010 | |
| 300 | |a XVI, 304 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 856 | 4 | 2 | |m V:DE-576;X:springer |q application/pdf |u http://scans.hebis.de/HEBCGI/show.pl?23205520_kap-1.pdf |
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Datensatz im Suchindex
| _version_ | 1804149567531253760 |
|---|---|
| adam_text | Contents
Introduction
and Basic Concepts
.......................... 1
1.1
Two Approaches to Formal Reasoning
...................... 3
1.1.1
Proof by Deduction
................................ 3
1.1.2
Proof by Enumeration
............................. 4
1.1.3
Deduction and Enumeration
........................ 5
1.2
Basic Definitions
........................................ 5
1.3
Normal Forms and Some of Their Properties
................ 8
1.4
The Theoretical Point of View
............................ 14
1.4.1
The Problem We Solve
............................. 17
1.4.2
Our Presentation of Theories
....................... 17
1.5
Expressiveness vs. Decidability
............................ 18
1.6
Boolean Structure in Decision Problems
.................... 19
1.7
Problems
............................................... 21
1.8
Glossary
............................................... 23
Decision Procedures for Propositional Logic
............... 25
2.1
Propositional Logic
...................................... 25
2.1.1
Motivation
....................................... 25
2.2
SAT Solvers
............................................ 27
2.2.1
The Progress of SAT Solving
........................ 27
2.2.2
The DPLL Framework
............................. 28
2.2.3
BCP and the Implication Graph
.................... 30
2.2.4
Conflict Clauses and Resolution
..................... 35
2.2.5
Decision Heuristics
................................ 39
2.2.6
The Resolution Graph and the Unsatisfiable Core
..... 41
2.2.7
SAT Solvers: Summary
............................. 42
2.3
Binary Decision Diagrams
................................ 43
2.3.1
From Binary Decision Trees to ROBDDs
............. 43
2.3.2
Building BDDs from Formulas
...................... 46
2.4
Problems
............................................... 50
2.4.1
Warm-up Exercises
................................ 50
2.4.2
Modeling
......................................... 50
2.4.3
Complexity
....................................... 51 ,
2.4.4
DPLL SAT Solving
................................ 52
j
2.4.5
Related Problems
................................. 52
j
2.4.6
Binary Decision Diagrams
.......................... 53
|
2.5
Bibliographic Notes
...................................... 54 !
2.6
Glossary
............................................... 57
j
Equality Logic and Uninterpreted Functions
............... 59
і
3.1
Introduction
............................................ 59
3.1.1
Complexity and Expressiveness
..................... 59
3.1.2
Boolean Variables
................................. 60
3.1.3
Removing the Constants: A Simplification
............ 60
3.2
Uninterpreted Functions
.................................. 60
3.2.1
How Uninterpreted Functions Are Used
.............. 61
3.2.2
An Example: Proving Equivalence of Programs
........ 63
3.3
From Uninterpreted Functions to Equality Logic
............ 64
3.3.1
Ackermann s Reduction
............................ 66
3.3.2
Bryant s Reduction
................................ 69
3.4
Functional Consistency Is Not Enough
..................... 72
3.5
Two Examples of the Use of Uninterpreted Functions
........ 74
3.5.1
Proving Equivalence of Circuits
..................... 75
3.5.2
Verifying a Compilation Process with Translation
Validation
........................................ 77
3.6
Problems
............................................... 78
3.6.1
Warm-up Exercises
................................ 78
3.6.2
Problems
......................................... 78
3.7
Glossary
............................................... 79
Decision Procedures for Equality Logic and Uninterpreted
Functions
.................................................. 81
4.1
Congruence Closure
...................................... 81
4.2
Basic Concepts
.......................................... 83
4.3
Simplifications of the Formula
............................. 85
4.4
A Graph-Based Reduction to Propositional Logic
............ 88
4.5
Equalities and Small-Domain Instantiations
................. 92
4.5.1
Some Simple Bounds
.............................. 93
4.5.2
Graph-Based Domain Allocation
.................... 94
4.5.3
The Domain Allocation Algorithm
................... 96
4.5.4
A Proof of Soundness
.............................. 98
4.5.5
Summary
......................................... 101
4.6
Ackermann s vs. Bryant s Reduction: Where Does It Matter?
. 101
4.7
Problems
............................................... 103
4.7.1
Conjunctions of Equalities and Uninterpreted Functions
103
4.7.2
Reductions
....................................... 104
4.7.3
Complexity
.......................................105
4.7.4
Domain Allocation
................................106
4.8
Bibliographic Notes
......................................106
4.9
Glossary
...............................................108
Linear Arithmetic
.........................................
Ill
5.1
Introduction
............................................
Ill
5.1.1
Solvers for Linear Arithmetic
.......................112
5.2
The Simplex Algorithm
..................................113
5.2.1
Decision Problems and Linear Programs
..............113
5.2.2
Basics of the Simplex Algorithm
.....................114
5.2.3
Simplex with Upper and Lower Bounds
..............116
5.2.4
Incremental Problems
..............................120
5.3
The Branch and Bound Method
...........................120
5.3.1
Cutting-Planes
....................................122
5.4
Fourier-Motzkin Variable Elimination
......................126
5.4.1
Equality Constraints
...............................126
5.4.2
Variable Elimination
...............................126
5.4.3
Complexity
.......................................129
5.5
The Omega Test
........................................129
5.5.1
Problem Description
...............................129
5.5.2
Equality Constraints
...............................130
5.5.3
Inequality Constraints
.............................132
5.6
Preprocessing
...........................................138
5.6.1
Preprocessing of Linear Systems
.....................138
5.6.2
Preprocessing of Integer Linear Systems
..............139
5.7
Difference Logic
.........................................140
5.7.1
Introduction
......................................140
5.7.2
A Decision Procedure for Difference Logic
............142
5.8
Problems
...............................................142
5.8.1
Warm-up Exercises
................................142
5.8.2
The Simplex Method
..............................143
5.8.3
Integer Linear Systems
.............................143
5.8.4
Omega Test
......................................144
5.8.5
Difference Logic
...................................145
5.9
Bibliographic Notes
......................................145
5.10
Glossary
...............................................146
Bit Vectors
................................................149
6.1
Bit-Vector Arithmetic
....................................149
6.1.1
Syntax
...........................................149
6.1.2
Notation
.........................................151
6.1.3
Semantics
........................................152
6.2
Deciding Bit-Vector Arithmetic with Flattening
.............156
6.2.1
Converting the Skeleton
............................156
6.2.2
Arithmetic Operators
..............................157
6.3
Incremental Bit Flattening
...............................160
6.3.1
Some Operators Are Hard
..........................160
6.3.2
Enforcing Functional Consistency
...................162
6.4
Using Solvers for Linear Arithmetic
........................163
6.4.1
Motivation
.......................................163
6.4.2
Integer Linear Arithmetic for Bit Vectors
.............163
6.5
Fixed-Point Arithmetic
...................................165
6.5.1
Semantics
........................................165
6.5.2
Flattening
........................................167
6.6
Problems
...............................................167
6.6.1
Semantics
........................................167
6.6.2
Bit-Level Encodings of Bit-Vector Arithmetic
.........168
6.6.3
Using Solvers for Linear Arithmetic
..................169
6.7
Bibliographic Notes
......................................169
6.8
Glossary
...............................................170
Arrays
.....................................................171
7.1
Introduction
............................................171
7.2
Arrays as Uninterpreted Functions
.........................172
7.3
A Reduction Algorithm for Array Logic
....................175
7.3.1
Array Properties
..................................175
7.3.2
A Reduction Algorithm
............................176
7.4
Problems
...............................................178
7.5
Bibliographic Notes
......................................178
7.6
Glossary
...............................................179
Pointer Logic
..............................................181
8.1
Introduction
............................................181
8.1.1
Pointers and Their Applications
.....................181
8.1.2
Dynamic Memory Allocation
........................182
8.1.3
Analysis of Programs with Pointers
..................184
8.2
A Simple Pointer Logic
...................................185
8.2.1
Syntax
...........................................185
8.2.2
Semantics
........................................187
8.2.3
Axiomatization of the Memory Model
................188
8.2.4
Adding Structure Types
............................189
8.3
Modeling Heap-Allocated Data Structures
..................190
8.3.1
Lists
.............................................190
8.3.2
Trees
............................................191
8.4
A Decision Procedure
....................................193
8.4.1
Applying the Semantic Translation
..................193
8.4.2
Pure Variables
....................................195
8.4.3
Partitioning the Memory
...........................196
8.5
Rule-Based Decision Procedures
...........................197
8.5.1
A Reachability Predicate for Linked Structures
........198
8.5.2
Deciding Reachability Predicate Formulas
............199
8.6
Problems
...............................................202
8.6.1
Pointer Formulas
..................................202
8.6.2
Reachability Predicates
............................203
8.7
Bibliographic Notes
......................................204
8.8
Glossary
...............................................206
9
Quantified Formulas
.......................................207
9.1
Introduction
............................................207
9.1.1
Example: Quantified Boolean Formulas
...............209
9.1.2
Example: Quantified Disjunctive Linear Arithmetic
.... 211
9.2
Quantifier Elimination
...................................211
9.2.1
Prenex Normal Form
..............................211
9.2.2
Quantifier Elimination Algorithms
...................213
9.2.3
Quantifier Elimination for Quantified Boolean Formulas
214
9.2.4
Quantifier Elimination for Quantified Disjunctive
Linear Arithmetic
.................................217
9.3
Search-Based Algorithms for QBF
.........................218
9.4
Problems
...............................................220
9.4.1
Warm-up Exercises
................................220
9.4.2
QBF
.............................................220
9.5
Bibliographic Notes
......................................223
9.6
Glossary
...............................................224
10
Deciding a Combination of Theories
.......................225
10.1
Introduction
............................................225
10.2
Preliminaries
............................................225
10.3
The Nelson-Oppen Combination Procedure
.................227
10.3.1
Combining Convex Theories
........................227
10.3.2
Combining Nonconvex Theories
.....................230
10.3.3
Proof of Correctness of the Nelson-Oppen Procedure
.. 233
10.4
Problems
...............................................236
10.5
Bibliographic Notes
......................................236
10.6
Glossary
...............................................239
11
Propositional Encodings
...................................241
11.1
Overview
...............................................241
11.2
Lazy Encodings
.........................................244
11.2.1
Definitions and Notations
..........................244
11.2.2
Building Propositional Encodings
....................245
11.2.3
Integration into DPLL
.............................246
11.2.4
Theory Propagation and the DPLL(T) Framework
.... 246
11.2.5
Some Implementation Details of DPLL(T)
............250
11.3
Propositional Encodings with Proofs (Advanced)
............253
11.3.1
Encoding Proofs
..................................254
11.3.2
Complete Proofs
..................................255
11.3.3
Eager Encodings
..................................257
11.3.4
Criteria for Complete Proofs
........................258
11.3.5
Algorithms for Generating Complete Proofs
..........259
11.4
Problems
...............................................263
11.5
Bibliographic Notes
......................................264
11.6
Glossary
...............................................267
A The SMT-LIB Initiative
...................................269
В
A
C++
Library for Developing Decision Procedures
.......271
B.I Introduction
............................................271
B.2 Graphs and Trees
.......................................272
B.2.1 Adding Payload
.................................274
B.3 Parsing
................................................274
B.3.1 A Grammar for First-Order Logic
...................274
B.3.2 The Problem File Format
..........................276
B.3.3 A Class for Storing Identifiers
.......................277
B.3.4 The Parse Tree
....................................277
B.4 CNF and SAT
..........................................278
B.4.1 Generating CNF
..................................278
B.4.2 Converting the Propositional Skeleton
................281
B.5 A Template for a Lazy Decision Procedure
..................281
References
.....................................................285
Index
..........................................................299
|
| any_adam_object | 1 |
| author | Kroening, Daniel Strichman, Ofer |
| author_GND | (DE-588)135831431 |
| author_facet | Kroening, Daniel Strichman, Ofer |
| author_role | aut aut |
| author_sort | Kroening, Daniel |
| author_variant | d k dk o s os |
| building | Verbundindex |
| bvnumber | BV040500182 |
| classification_rvk | ST 125 ST 134 |
| classification_tum | DAT 530f |
| ctrlnum | (OCoLC)704907244 (DE-599)HEB232055203 |
| dewey-full | 004.015113 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 004 - Computer science |
| dewey-raw | 004.015113 |
| dewey-search | 004.015113 |
| dewey-sort | 14.015113 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV040500182 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:25:05Z |
| institution | BVB |
| isbn | 9783642093449 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025346971 |
| oclc_num | 704907244 |
| open_access_boolean | |
| owner | DE-739 DE-91G DE-BY-TUM DE-526 |
| owner_facet | DE-739 DE-91G DE-BY-TUM DE-526 |
| physical | XVI, 304 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts in theoretical computer science |
| spelling | Kroening, Daniel Verfasser (DE-588)135831431 aut Decision procedures an algorithmic point of view Daniel Kroening ; Ofer Strichman Berlin <<[u.a.]>> Springer 2010 XVI, 304 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science Algorithmus (DE-588)4001183-5 gnd rswk-swf Entscheidungsverfahren (DE-588)4637781-5 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Entscheidungsverfahren (DE-588)4637781-5 s Mathematische Logik (DE-588)4037951-6 s Algorithmus (DE-588)4001183-5 s 1\p DE-604 Strichman, Ofer Verfasser aut B:DE-101 application/pdf http://d-nb.info/985166533/04 V:DE-576;X:springer application/pdf http://scans.hebis.de/HEBCGI/show.pl?23205520_kap-1.pdf V:DE-576;X:springer application/pdf http://scans.hebis.de/HEBCGI/show.pl?23205520_ein-1.pdf Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025346971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kroening, Daniel Strichman, Ofer Decision procedures an algorithmic point of view Algorithmus (DE-588)4001183-5 gnd Entscheidungsverfahren (DE-588)4637781-5 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4637781-5 (DE-588)4037951-6 |
| title | Decision procedures an algorithmic point of view |
| title_auth | Decision procedures an algorithmic point of view |
| title_exact_search | Decision procedures an algorithmic point of view |
| title_full | Decision procedures an algorithmic point of view Daniel Kroening ; Ofer Strichman |
| title_fullStr | Decision procedures an algorithmic point of view Daniel Kroening ; Ofer Strichman |
| title_full_unstemmed | Decision procedures an algorithmic point of view Daniel Kroening ; Ofer Strichman |
| title_short | Decision procedures |
| title_sort | decision procedures an algorithmic point of view |
| title_sub | an algorithmic point of view |
| topic | Algorithmus (DE-588)4001183-5 gnd Entscheidungsverfahren (DE-588)4637781-5 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Algorithmus Entscheidungsverfahren Mathematische Logik |
| url | http://d-nb.info/985166533/04 http://scans.hebis.de/HEBCGI/show.pl?23205520_kap-1.pdf http://scans.hebis.de/HEBCGI/show.pl?23205520_ein-1.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025346971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kroeningdaniel decisionproceduresanalgorithmicpointofview AT strichmanofer decisionproceduresanalgorithmicpointofview |