1. DLL Algorithm

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

3. 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 , 1962
Basic framework for many modern SAT solvers
Also known as DPLL for historical reasons
DFS – depth first search

4. Possible representationc d
Marker, etc 10 01 11
1=used
0=unused
etc
Used = converted to 1, satisfied
Non-used = not satisfied yet

11. Think how to check conflict in hardware using our implementation on stack??!

27. 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.