SAT vs. BDDs

1
SAT vs. BDDs

• IWLS 2002 Focus Group 5
• Mukul Prasad

2
Group Members

• Karem Sakallah
• Christoph Meinel
• Christian Stangier
• Fadi Aloul
• Mukul Prasad
• Amit Prakash
• Harald Sack
• Volker Schillings

• Whitney Townsend
• Vinicius Comeia
• Felipe Marques
• Jorgiano Vidal
• Farzan Fallah

3
SAT vs BDDs

• SAT
• Time intensive
• Large problems (where BDDs could blow up)
• Witness/one soln.
• Canonicity not reqd.
• Local reasoning
• QBFs still a problem
• Can work with equiv. classes only if small

• BDDs
• Space intensive
• Small problems
• All Solutions
• Canonicity required
• Global reasoning
• QBFs Better perf.
• Equiv. class manipulation

SAT BEDs Free BDDs ROBDDs
4
Challenges for SAT/BDDs

• Challenge 1 How to effectively combine SAT and
  BDDs
• Challenge 2 How to make BDD and SAT technology
  best work for word-level apps. and/or higher
  levels of abstraction

5
SATBDDs Previous Work

• SATBDDs for equiv. Checking
• Mukherjee, Jain et al (Fujitsu)
• Burch Singhal (Cadence)
• Kuelmann, Krohm et al (IBM)
• Using SATBDDs in model checking
• Gupta et al (NEC Labs.)
• Combining SAT with ZBDDs
• Aloul et al (U of M)

6
SAT BDDs Thoughts Suggestions

• If SAT or BDD can single-handedly work in an
  application try that first
• First set of solutions to combination will be
  application dependent
• Final goal An app. Independent general-purpose
  SATBDD solver

7
SAT/BDDs for Higher Abstractions
Boolean
SAT
BDDs
Constraint-based
Symbolic, Canonical
Finite Domains
MV-SAT, CSPs, ILP
MDDs, ADDs, MTDDs
?
Issue Move to more expressive systems/logics or
find better translation to prop. Logic ?
Issue Intrinsically Boolean methods with some
encoding
8
More Issues/Suggestions

• Look for use of SAT in apps. Where BDDs are the
  traditional choice e.g. synthesis
• Maybe need to revisit other variants of DDs that
  have better space-time tradeoff than ROBDDs
• Extensions to Boolean SAT CSPs and
  pseudo-Boolean SAT