Boolean Synthesis via Decomposition Lucas M. Tabajara Joint work - PowerPoint PPT Presentation

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Boolean Synthesis via Decomposition Lucas M. Tabajara Joint work with Supratik Chakraborty, Dror Fried and Moshe Y. Vardi lucasmt@rice.edu Rice University Lucas M. Tabajara (Rice University) Boolean Synthesis via Decomposition October 5, 2017

Boolean Synthesis via Decomposition Lucas M. Tabajara Joint work with Supratik Chakraborty, Dror Fried and Moshe Y. Vardi lucasmt@rice.edu Rice University Lucas M. Tabajara (Rice University) Boolean Synthesis via Decomposition October 5, 2017 1 / 5
Boolean Synthesis g f ( x 0 ⊕ y 0 = 0) y 0 := x 0 ∧ y 1 := x 1 ⊕ x 0 ( x 1 ⊕ y 1 ⊕ ( x 0 ∧ y 0 ) = 0) Boolean function Specification of a system implementing system behavior encoded as a Boolean formula Our goal: To decompose the specification into formulas that are easier to synthesize. Lucas M. Tabajara (Rice University) Boolean Synthesis via Decomposition October 5, 2017 2 / 5
Decomposition using Factored Formulas F ( � x , y 1 , y 2 , y 3 , y 4 ) = F 1 ( � x , y 2 , y 4 ) ∧ F 2 ( � x , y 1 , y 2 , y 3 ) ∧ F 3 ( � x , y 3 ) ◮ Easy to perform decomposition. ◮ Has been shown to significantly improve synthesis algorithms. However: Dependences between factors prevent us from taking full advantage of the decomposition. Lucas M. Tabajara (Rice University) Boolean Synthesis via Decomposition October 5, 2017 3 / 5
Towards Sequential Decomposition Sequential Decomposition Given: A Boolean formula F ( � x , � y ) between input variables � x and output variables � y . Return: Two Boolean formulas F 1 ( � z ) and F 2 ( � y ) that can be x , � z , � composed back into F . Lucas M. Tabajara (Rice University) Boolean Synthesis via Decomposition October 5, 2017 4 / 5
Sequential Decomposition F F 1 F 2 g 1 g 2 Lucas M. Tabajara (Rice University) Boolean Synthesis via Decomposition October 5, 2017 5 / 5
Sequential Decomposition g � z g 1 g 2 � y � x Lucas M. Tabajara (Rice University) Boolean Synthesis via Decomposition October 5, 2017 5 / 5

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