SAT-Based Generation of Optimum Circuits with Polymorphic Behavior Support

Abstract

This paper presents a method for generating optimum multi-level implementations of Boolean functions based on Satisfiability (SAT) and Pseudo-Boolean Optimization (PBO) problems solving. The method is able to generate one or enumerate all optimum implementations, while the allowed target gate types and gates costs can be arbitrarily specified. Polymorphic circuits represent a newly emerging computation paradigm, where one hardware structure is capable of performing two or more different intended functions, depending on instantaneous conditions in the target operating environment. In this paper we propose the first method ever, generating provably size-optimal polymorphic circuits. Scalability and feasibility of the method are documented by providing experimental results for all NPN-equivalence classes of four-input functions implemented in AND–Inverter and AND–XOR–Inverter logics without polymorphic behavior support being used and for all pairs of NPN–equivalence classes of three-input functions for polymorphic circuits. Finally, several smaller benchmark circuits were synthesized optimally, both in standard and polymorphic logics.

Towards Area Efficient Logic Circuit: Exploring Potential of Reconfigurable Gate by Generic Exact Synthesis

“…Based on And-Inverter-Graph (AIG), its circuits only involve And and Inverter during the synthesis. This scheme improves the representation ability of the circuits by allowing polymorphic (reconfigurable) edges, i.e., reconfigurable buffers/inverters that are controlled by one of the function inputs [33][34][35]. Such a method was then combined with rewriting techniques and applied to large circuits [36,37].…”

“…Although logic synthesis and technology mapping are usually separated in modern synthesis flow, the synthesis for reconfigurable circuits should take the technology into account. Nevertheless, SAT-based exact synthesis is still one of the most promising logic synthesis approaches because of its ability to find the area-optimal circuit with a customizable synthesis target [33][34][35][36][37][38][39][40]. Another great advantage of SAT-based exact synthesis is that users can flexibly describe the desired logic circuit by adding customized constraints.…”