DLL Algorithm

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DLL Algorithm
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How to realize search in hardware

1. We need to realize hardware stack
2. Tree search is organized with hardware stack.
3. The node of the tree is variable.
4. The item on the stack is a sum of three literals
   (in 3SAT, can be more in general POS SAT).
5. Encoding 10 negated variable, 01 positive
   variable, 11 no variable, 00 mark or not
   used.
6. Example 1010011101 with order of variables abcd
   from left means a b c e (d variable
   missing)
7. This encoding is standard to logic, is used in
   Cube Calculus.

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DLL Algorithm

• Davis, Logemann and Loveland
• M. Davis, G. Logemann and D. Loveland, A Machine
  Program for Theorem-Proving, Communications of
  ACM, Vol. 5, No. 7, pp. 394-397, 1962
• Basic framework for many modern SAT solvers
• Also known as DPLL for historical reasons
• DFS depth first search

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Possible representation
a b c d Marker, etc
10 01 01 11 1used
01 11 01 01 0unused
01 11 01 10
01 11 10 01
etc

• Used converted to 1, satisfied
• Non-used not satisfied yet

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Think how to check conflict in hardware using our
implementation on stack??!
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Problems to think about

• How can I improve my SAT oracle to allow for
  implementing DLL in hardware?
• How can I represent this problem with Pipelining?
• Can I invent other ideas for backtracking?
• How to use stack for backtracking?
• How to represent set of clauses on the stack?
• You can assume that you solve 3SAT.
• This will simplify the problem.