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Given a Boolean formula $\varphi$ over the set of variables $X$ and aprojection set $\mathcal{P} \subseteq X$, a subset of variables $\mathcal{I}$is independent support of $\mathcal{P}$ if two solutions agree on$\mathcal{I}$, then they also agree on $\mathcal{P}$. The notion of independentsupport is related to the classical notion of definability dating back to 1901,and have been studied over the decades. Recently, the computational problem ofdetermining independent support for a given formula has attained importanceowing to the crucial importance of independent support for hashing-basedcounting and sampling techniques.  In this paper, we design an efficient and scalable independent supportcomputation technique that can handle formulas arising from real-worldbenchmarks. Our algorithmic framework, called Arjun, employs implicit andexplicit definability notions, and is based on a tight integration ofgate-identification techniques and assumption-based framework. We demonstratethat augmenting the state of the art model counter ApproxMC4 and samplerUniGen3 with Arjun leads to significant performance improvements. Inparticular, ApproxMC4 augmented with Arjun counts 387 more benchmarks out of1896 while UniGen3 augmented with Arjun samples 319 more benchmarks within thesame time limit.

Arjun: An Efficient Independent Support Computation Technique and its Applications to Counting and Sampling