BDD-Based Boolean Functional Synthesis

Knowledge Compilation for Boolean Functional Synthesis

“…. It has been argued in [14], [11], [2], [12] that the BFnS problem for F (X, Y) can be solved by first ordering the outputs, say as x 1 ≺ x 2 · · · ≺ x n , and then synthesizing a function…”

“…While variants of the problem have been studied since long [17], [3], there has been significant recent interest in designing practically efficient algorithms for Boolean functional synthesis. The resulting breed of algorithms [14], [23], [22], [11], [25], [18], [13], [2], [1], [15], [7], [24] have been empirically shown to work well on large collections of benchmarks. Nevertheless, there are not-so-large examples that are currently not solvable within reasonable resources by any known algorithm.…”

“…However, if we are interested in only the result of existentially quantifying a given set of variables, these forms can be unnecessarily restrictive and exponentially larger. Recent work on Boolean functional synthesis [13], [14], [18], [24], [11], [2], [1], [8] has focused more on algorithms to directly synthesize outputs as functions of inputs. Some of these algorithms (viz.…”

“…Some of these algorithms (viz. [11], [1], [8]) exploit properties of specific input representations for optimizing the synthesis process. This has led to the articulation of sufficient conditions on representation of specifications for efficient synthesis.…”

“…This has led to the articulation of sufficient conditions on representation of specifications for efficient synthesis. For example, [15] suggested using input-first ROBDDs for efficient synthesis, and a quadratic-time algorithm for synthesis from input-first ROBDDs was presented in [11]. This result was subsequently generalized in [1], where it was shown that specifications in wDNNF (which strictly subsumes ROBDDs) suffice to give a quadratic-time algorithm for synthesis.…”