automated reasoning ss08 christoph weidenbach texpoint fonts used in emf. read the texpoint manual...
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![Page 1: Automated Reasoning SS08 Christoph Weidenbach TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A](https://reader036.vdocument.in/reader036/viewer/2022062314/56649ed05503460f94bde125/html5/thumbnails/1.jpg)
Automated Reasoning SS08
Christoph Weidenbach
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Christoph Weidenbach Automated Reasoning SS08
Content
Propositional Logic DPLL 2-Watch, Learning
Propositional Logic+
TheoriesDPLL(T) Coupling
First-Order Logic SuperpositionIndexing, Sharing,
Filtering
First-Order Logic+
TheoriesSUP(T) Coupling
LinearArithmetic
Logic Calculus Algorithms
![Page 3: Automated Reasoning SS08 Christoph Weidenbach TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A](https://reader036.vdocument.in/reader036/viewer/2022062314/56649ed05503460f94bde125/html5/thumbnails/3.jpg)
Christoph Weidenbach Automated Reasoning SS08
Propositional Logic
&
&
1
1PQ
R
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Christoph Weidenbach Automated Reasoning SS08
Hardware
• Industrial Processor Verification: 14-cycle Model Checking
• 1Mio Variables, 10 Mio Literals, 4 Mio Clauses
• 3 hours run time (2004)
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Christoph Weidenbach Automated Reasoning SS08
SUDOKU
1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
7
8
9
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Christoph Weidenbach Automated Reasoning SS08
Summary
• propositional logic is suitable to represent finite domains
• software: restrict all variables to finite domain
• hardware: restrict number of cycles
• suitable to test problems with thousands of variables
• Limits: infinite domains or “calculations”, i.e.,
mathematical structure
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Christoph Weidenbach Automated Reasoning SS08
Propositional Logic + T
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Christoph Weidenbach Automated Reasoning SS08
Dutch Soccer League
• if Eindhoven and Amsterdam play on the same day the TV income is x
• If Eindhoven and Amsterdam play on two different days, the income is 2x
• if a team plays on Wednesday champions league it doesn’t play on Friday
• there are at most 3 plays on Friday
• ….. in sum several thousand constraints over LP and Boolean variables
• League is modelled by the Barcelogic tool
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Christoph Weidenbach Automated Reasoning SS08
Transition Systems
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Christoph Weidenbach Automated Reasoning SS08
Summary
• propositional logic + T can also represent aspects of infinite theories
• for the “meta algorithm” for the theory often “nice” properties are needed
• bottleneck often the solver for T
• Limits: quantification and “free” structures beyond boolean combinations
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Christoph Weidenbach Automated Reasoning SS08
First-Order Logic
All professors love squeezing all students.Chris is a professor.
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Christoph Weidenbach Automated Reasoning SS08
SUDOKU
2, 3, 4
95
1, 4, 6, 8
7
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Christoph Weidenbach Automated Reasoning SS08
SUDOKU
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Christoph Weidenbach Automated Reasoning SS08
SUDOKU
7
1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
7
8
9
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Christoph Weidenbach Automated Reasoning SS08
SUDOKU
7
1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
7
8
9
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Christoph Weidenbach Automated Reasoning SS08
LAN Router
Sent(epacket(incoming-net, router-mac, src-mac, e-ip,ippacket(ip-src, ip-dst, ip-proto, ip-data))))
RouteEntry(route(router,dst-netmask,dst-net-addr,outgoing-net))ipand(ip-dst,dst-netmask) dst-net-addr
Sent(epacket(outgoing-net, dst-mac, src-mac, e-ip,ippacket(ip-src, ip-dst, ip-proto, ip-data)))
![Page 17: Automated Reasoning SS08 Christoph Weidenbach TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A](https://reader036.vdocument.in/reader036/viewer/2022062314/56649ed05503460f94bde125/html5/thumbnails/17.jpg)
Christoph Weidenbach Automated Reasoning SS08
Summary
• first-order logic can model freely defined infinite theories
• inductive theories are out of scope
• incredible expressiveness
• full quantification
• Limits: undecidable (take serious), some important theories can not be
(finitely) represented
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Christoph Weidenbach Automated Reasoning SS08
First-Order Logic + T
All professors above 50 love squeezing all students.Chris is a professor below 50.
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Christoph Weidenbach Automated Reasoning SS08
Hybrid Automata
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Christoph Weidenbach Automated Reasoning SS08
Summary
• first-order logic + T can also model aspects involving inductive theories
• adequately represent many aspects of software, hardware
• incredible incredible expressiveness
• quantification over theory variables potentially limited
• Limits: very undecidable (take serious), in general not compact, and any
calculus not complete
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Christoph Weidenbach Automated Reasoning SS08
The End: Let’s Start
Propositional Logic DPLL 2-Watch, Learning
Propositional Logic+
TheoriesDPLL(T) Coupling
First-Order Logic SuperpositionIndexing, Sharing,
Filtering
First-Order Logic+
TheoriesSUP(T) Coupling
LinearArithmetic
Logic Calculus Algorithms