Synthesis of wiring signature-invariant equivalence class circuit mutants and applications to benchmarking

This paper formalizes the synthesis process of wiring signature-invariant (WSI) combinational circuit mutants. The signature \sigma_0 is defined by a reference circuit \eta_0, which itself is modeled as a canonical form of a directed bipartite graph. A wiring perturbation \gamma induces a perturbed reference circuit \eta_{\gamma}. A number of mutant circuits \eta_{\gamma_i} can be resynthesized from the perturbed circuit \eta_\gamma. The mutants of interest are the ones that belong to the wiring-signature-invariant equivalence class {\cal N}_\sigma{}_0, i.e. the mutants \eta_{\gamma{}_i} \in {\cal N}_\sigma{}_0. Circuit mutants \eta_{\gamma{}_i} \in {\cal N}_\sigma{}_0 have a number of useful properties. For any wiring perturbation \gamma, the size of the wiring-signature-invariant equivalence class is huge. Notably, circuits in this class are not random, although for unbiased testing and benchmarking purposes, mutant selections from this class are typically random. For each reference circuit, we synthesized eight equivalence subclasses of circuit mutants, based on 0 to 100\% perturbation. Each subclass contains 100 randomly chosen mutant circuits, each listed in a different random order. The 14,400 benchmarking experiments with 3200 mutants in 4 equivalence classes, covering 13 typical EDA algorithms, demonstrate that an unbiased random selection of such circuits can lead to statistically meaningful differentiation and improvements of existing and new algorithms.