# Synthesis with Explicit Dependencies

arXiv: https://arxiv.org/abs/2301.10556 · HTML: https://mlsanity.com/paper/2301.10556/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 25 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [Manthan: A Data Driven Approach for Boolean Function Synthesis](https://mlsanity.com/paper/2005.06922/) (2020)
- [DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL](https://mlsanity.com/paper/1702.08256/) (2017)
- [What's hard about Boolean Functional Synthesis](https://mlsanity.com/paper/1804.05507/) (2018)
- [Knowledge Compilation for Boolean Functional Synthesis](https://mlsanity.com/paper/1908.06275/) (2019)
- [Skolem Functions for Factored Formulas](https://mlsanity.com/paper/1508.05497/) (2015)
- [Towards Parallel Boolean Functional Synthesis](https://mlsanity.com/paper/1703.01440/) (2017)
- [Understanding and Extending Incremental Determinization for 2QBF](https://mlsanity.com/paper/1905.13411/) (2019)
- [Engineering an Efficient Boolean Functional Synthesis Engine](https://mlsanity.com/paper/2108.05717/) (2021)
- [SAT-Based Synthesis Methods for Safety Specs](https://mlsanity.com/paper/1311.3530/) (2013)
- [Certified DQBF Solving by Definition Extraction](https://mlsanity.com/paper/2106.02550/) (2021)

## Abstract (arXiv)

Quantified Boolean Formulas (QBF) extend propositional logic with quantification forall, exists. In QBF, an existentially quantified variable is allowed to depend on all universally quantified variables in its scope. Dependency Quantified Boolean Formulas (DQBF) restrict the dependencies of existentially quantified variables. In DQBF, existentially quantified variables have explicit dependencies on a subset of universally quantified variables called Henkin dependencies. Given a Boolean specification between the set of inputs and outputs, the problem of Henkin synthesis is to synthesize each output variable as a function of its Henkin dependencies such that the specification is met. Henkin synthesis has wide-ranging applications, including verification of partial circuits, controller synthesis, and circuit realizability. This work proposes a data-driven approach for Henkin synthesis called Manthan3. On an extensive evaluation of over 563 instances arising from past DQBF solving competitions, we demonstrate that Manthan3 is competitive with state-of-the-art tools. Furthermore, Manthan3 could synthesize Henkin functions for 26 benchmarks for which none of the state-of-the-art techniques could synthesize.