Scarab: SAT-based Constraint Programming System in Scala / Scala上で実...

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Scarab
SAT-based Constraint Programming System in Scala
Takehide Soh1
worked in cooperation with
Daniel Le Berre2 Step...

Contents of Talk
1 What is SAT?
2 Scarab: SAT-based CP System in Scala
3 Designing Constraint Models in Scarab
4 Advan...

SAT (Boolean satis

ability testing) Problems
SAT is a problem of deciding whether a given Boolean formula is
satis

able or not.
SAT was the

rst NP-complete problem [Cook, 1971] and is the most
fundamental problem in Computer Science both theoretically and
prac...

SAT (Boolean satis

ability testing) Problems
SAT is a problem of deciding whether a given Boolean formula is
satis

able or not.
SAT was the

rst NP-complete problem [Cook, 1971] and is the most
fundamental problem in Computer Science both theoretically and
prac...

able or not?
(a _ b _ c) ^
(:a _ :b) ^
(:a _ :c) ^
(:b _ :c)
Answer: Yes.
There is an assignment (a; b; c) = (True; ...

SAT Solvers
There are 2n combinations for assignments.
We cannot solve any SAT instances even for small n (e.g. n = 100)...

able (SAT) or unsatis

able (UNSAT).
Most of all SAT solvers return a satis

able assignment when the
instance is SAT.
Complete SAT solvers originated in DPLL [Davis et al., 1962].
In particular, ...

Progress of SAT Solvers (shown by [Simon 2011])
1200
1000
800
Results of the SAT competition/race winners on the SAT 2...

Applications of SAT Technology
Thanks to the remarkable progress of SAT solvers, SAT-based Systems
have been actively st...

Other News around SAT
A SAT solver Sat4j implemented on Java has been integrated into
Eclipse for managing plugins depen...

ability and The Art of
Computer Programming at the International Conference on Theory
and Applications of Satis

ability Testing 2012.
In addition, SAT will be appeared in Volume 4b of The Art Of
Computer Programming.
Reference to S...

ability, volume 185 of Frontiers in Arti

cial
Intelligence and Applications (FAIA). IOS Press.
(in Japanese) Recent Advances in SAT Techniques, Journal of the
J...

cial Intelligence, Special Issue, 25(1), 2010.
8 / 60

Contents of Talk
1 What is SAT?
2 Scarab: SAT-based CP System in Scala
3 Designing Constraint Models in Scarab
4 Advan...

Motivation
Modern fast SAT solvers have promoted the development of
SAT-based systems for various problems.
For an inte...

Scarab
Scarab is a prototyping tool for developing SAT-based Constraint
Programming (CP) systems.
Its major design prin...

Scarab
Scarab is a prototyping tool for developing SAT-based Constraint
Programming (CP) systems.
Its major design prin...

c Language for Constraint Programming
2 API of CSP Solver
3 SAT encoding module
4 API of SAT solvers
Scarab
DSL
SAT ...

Scarab
Scarab is a prototyping tool for developing SAT-based Constraint
Programming (CP) systems.
Its major design prin...

c Language for Constraint Programming
2 API of CSP Solver
3 SAT encoding module
4 API of SAT solvers
Scarab
DSL
SAT ...

Scarab
Scarab is a prototyping tool for developing SAT-based Constraint
Programming (CP) systems.
Its major design prin...

c Language for Constraint Programming
2 API of CSP Solver
3 SAT encoding module
4 API of SAT solvers
Scarab
Program
...

Scarab
Scarab is a prototyping tool for developing SAT-based Constraint
Programming (CP) systems.
Its major design prin...

c Language for Constraint Programming
2 API of CSP Solver
3 SAT encoding module
4 API of SAT solvers
CSP Encoder
Scar...

Scarab
Scarab is a prototyping tool for developing SAT-based Constraint
Programming (CP) systems.
Its major design prin...

c Language for Constraint Programming
2 API of CSP Solver
3 SAT encoding module
4 API of SAT solvers
Sat4j
CSP Encode...

Scarab
Scarab is a prototyping tool for developing SAT-based Constraint
Programming (CP) systems.
Its major design prin...

c Language for Constraint Programming
2 API of CSP Solver
3 SAT encoding module
4 API of SAT solvers
Scarab
Program
...

Other Features
Eciency Scarab is ecient in the sense that it uses an optimized
version of the order encoding for encodin...

Example of Scarab Program: GCP.scala
Graph coloring problem (GCP) is a
problem of

nding a coloring of the
nodes such that colors of adjacent
nodes are dierent.
1
5 2
4
3
1
Input Solution
2
4 3
...

Imports
import jp.kobe_u.scarab.csp._
import jp.kobe_u.scarab.solver._
import jp.kobe_u.scarab.sapp._
First 2 lines im...

nes an integer variable.
add(c) method de

nes a constraint.
find method searches a solution.
solution method returns the solution.
etc.
20 / 60

Instance Structure
val nodes = Seq(1,2,3,4,5)
val edges = Seq((1,2),(1,5),(2,3),(2,4),(3,4),(4,5))
val colors = 3
It de

nes the given set of nodes and edges as the sequence object in
Scala.
Available number of colors are de

ned as 3.
21 / 60

ning CSP
for (i - nodes) int('n(i),1,3)
It adds an integer variable to the default CSP object by the int
method.
'n is...

ned in Scarab.
for ((i,j) - edges) add('n(i) !== 'n(j))
It adds constraints to the default CSP object.
The following op...

Solving CSP
if (find) println(solution)
The find method encodes the CSP to SAT by order encoding, and
call Sat4j to com...

able assignment of the CSP.
23 / 60

Contents of Talk
1 What is SAT?
2 Scarab: SAT-based CP System in Scala
3 Designing Constraint Models in Scarab
4 Advan...

Designing Constraint Models in Scarab
Pandiagonal Latin Square PLS(n) is a problem of placing dierent n
numbers into n ...

alldi Model
Pandiagonal Latin Square PLS(5)
x11 x12 x13 x14 x15
x21 x22 x23 x24 x25
x31 x32 x33 x34 x35
x41 x42 x43 x...

alldi Model
Pandiagonal Latin Square PLS(5)
x11 x12 x13 x14 x15
x21 x22 x23 x24 x25
x31 x32 x33 x34 x35
x41 x42 x43 x...

alldi Model
Pandiagonal Latin Square PLS(5)
x11 x12 x13 x14 x15
x21 x22 x23 x24 x25
x31 x32 x33 x34 x35
x41 x42 x43 x...

alldi Model
Pandiagonal Latin Square PLS(5)
x11 x12 x13 x14 x15
x21 x22 x23 x24 x25
x31 x32 x33 x34 x35
x41 x42 x43 x...

alldi Model
Pandiagonal Latin Square PLS(5)
x11 x12 x13 x14 x15
x21 x22 x23 x24 x25
x31 x32 x33 x34 x35
x41 x42 x43 x...

alldi Model
Pandiagonal Latin Square PLS(5)
x11 x12 x13 x14 x15
x21 x22 x23 x24 x25
x31 x32 x33 x34 x35
x41 x42 x43 x...

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