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DPLL example

a. DPLL example. Legend. false. C1:(a  b) C2:(  a   b) C3:(a   c) C4:(c  d  e) C5:(d   e) C6:(  d   f) C7:(f  e) C8:(  f   e). true. a =false by branching. a =false by pure symbol. a. a. a =true by an unit clause. a. e. d. b. c.

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DPLL example

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  1. a DPLL example Legend false C1:(a  b) C2:(a b) C3:(a c) C4:(c  d  e) C5:(d e) C6:(d f) C7:(f  e) C8:(f e) true a=false by branching a=false by pure symbol a a a=true by an unit clause

  2. a e d b c branching pure symbol unit clause false true DPLL example Unit Clause? Pure Symbol ? C1:(a  b) C2:(a b) C3:(a c) C4:(c  d  e) C5:(d e) C6:(d f) C7:(f  e) C8:(f e) C4 is a unit clause No unit clause Yes C3 is an unit clause Yes, b in C1 is pure No pure symbol C5 is unsatisfied, Early termination Backtrack upto the last branching: d = false

  3. a b c d f e branching pure symbol unit clause false true DPLL example C1:(a  b) C2:(a b) C3:(a c) C4:(c  d  e) C5:(d e) C6:(d f) C7:(f  e) C8:(f e) Formula Satisfied! C6 is an unit clause e is pure

  4. Exercise • Find a satisfying assignment using DPLL (a  b) (a b  c) (c  d  e) (a  c) (d  f) (a  c) (e f)

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