4 BOTTOM RIGHT LEFT TOP Logic synthesis problem Example fT x 1 x 2 x 3 x 1 x 4

4 bottom right left top logic synthesis problem

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4 BOTTOM RIGHT LEFT TOP
Logic synthesis problem Example: fT = x 1 x 2 x 3+ x 1 x 4 +x 1 x 5 9 TOP-TO-BOTTOM PATHS! x 1 x 1 x 1 x 2 x 5 x 5 x 3 x 4 LEFT TOP RIGHT BOTTOM
Boolean Function Duality Given: Obtain: ) , ..... , ( 11 rc X X f ) , ..... , ( 11 rc D X X f f
Our synthesis method Example: fT = x 1 x 2 x 3+ x 1 x 4 +x 1 x 5 fTD = ( x 1+ x 2+ x 3)( x 1+ x 4) ( x 1+ x 5) fTD = x 1 + x 2 x 4 x 5 + x3 x 4 x 5 § Obtain the dual of fT . § Assign each product of fT to a column. § Assign each product of fT D to a row. § Compute an intersection set for each site. § Arbitrarily select a literal from an intersection set and assign it to the corresponding site. x 5 x 1 x 1 x 2 x 1 x 5 x 3 x 4 x 1 x 2 x 3 x 1 x 4 x 1 x 5 x 1 x 2 x 4 x 5 x 3 x 4 x 5
Our synthesis method x 1 x 1 x 1 x 1 x 2 x 3 x 3 x 4 x 1 x 2 x 3 x 2 x 4 x 5 x 3 x 2 x 3 x 2 x 4 x 4 x 5 x 5 x 1 x 4 x 2 x 3 x 4 x 2 x 4 x 5 x 3 x 5 x 1 x 2 x 5 x 1 x 3 x 4 x 2 x 3 x 4 x 2 x 4 x 5 { x 2 , x 3 , x 4 } Example: f T = x 1 x 2 x 3 + x 1 x 4 + x 2 x 3 x 4 + x 2 x 4 x 5 + x 3 x 5 f T D = x 1 x 2 x 5 + x 1 x 3 x 4 + x 2 x 3 x 4 + x 2 x 4 x 5
Our method’s performance Area of the lattice: m×n The time complexity: O ( m 2 n 2) n and m are the number of products of the target function fT and its dual fTD , respectively.

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• Spring '14
• Riedel,Marc
• Logic, BMW Sports Activity Series, X1

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