Logic Synthesis for AND-XOR- OR type Sense-Amplifying PLA Yoshida, H. Yamaoka, H. Ikeda, M. Asada, K. ASP-DAC 2002.and the 15th International Conference on VLSID Speaker 洪仲昀

Proposed synthesis flow Initial circuit Generate a candidate for a cube c Extract an XOR term Synthesis with extracted XOR terms Any other candidates? Optimized circuit yes no

Extraction of XOR Terms Let c = l 1 l 2 ・ ・ ・ l n Then f c ⊆ d ⊆ f l 1 f l 2 … f l n f ⊇ c ♁ d Ex: f = x 1 x 2 x 4 + x 1 x 3 x 4 + x 2 x 3 x 4 + x 2 x 3 x 4 let c = x 1 x 2 then f c = x 3 x 4 and f x 1 f x 2 = x 3 x 4 so d = x 3 x 4 thus f contains x 1 x 2 ♁ x 3 x 4

Proof f c ⊆ d ⊆ f l 1 f l 2 … f l n f ⊇ c ♁ d f c ⊆ d ⊆ f l 1 f l 2 … f l n f ⊇ c ♁ d f ⊇ c ♁ d f ⊇ cd and f ⊇ cd

Proof f c ⊆ d ⊆ f l 1 f l 2 … f l n f ⊇ c ♁ d Lemma A.1 f c ⊇ d f ⊇ cd proof f ⊇ c f c ⊇ cd ( f = c f c + c f c ) so f c ⊇ d f ⊇ cd f c ⊇ d cofactor

Proof f c ⊆ d ⊆ f l 1 f l 2 … f l n f ⊇ c ♁ d Lemma A.2 c = l 1 l 2 ・ ・ ・ l n f ⊇ l k f l k ⊇ l k f l 1 f l 2 … f l n (for any k) proof f ⊇ ( l 1 + l 2 + ・ ・ ・ l n ) f l 1 f l 2 … f l n = c f l 1 f l 2 … f l n ⊇ cd since c = l 1 l 2 ・ ・ ・ l n we have f ⊇ cd = l 1 d + l 2 d + ・ ・ ・ l n d f l k ⊇ d thus f l 1 f l 2 … f l n ⊇ d cofactor

Exact Method  Exact method uses all possible cubes as candidates for cube c. form don’t care set

Prime implicants f = a`b`c` + a`b`c + ab`c + ab`c` + abc implicants: * * 1 * * 1 1*1 1 prime implicants: *0* 1 * 1*1 1

Covering problem