Understanding and Extending Incremental Determinization for 2QBF

Abstract

Incremental determinization is a recently proposed algorithm for solving quantified Boolean formulas with one quantifier alternation. In this paper, we formalize incremental determinization as a set of inference rules to help understand the design space of similar algorithms. We then present additional inference rules that extend incremental determinization in two ways. The first extension integrates the popular CEGAR principle and the second extension allows us to analyze different cases in isolation. The experimental evaluation demonstrates that the extensions significantly improve the performance.

Knowledge Compilation for Boolean Functional Synthesis

“…Therefore, any algorithm that compiles a CNF specification to an ROBDD can be viewed as an alternative to C2Syn for compiling a CNF specification to SynNNF (albeit without refinement). We compare the performance of C2Syn with that of a BDD compiler and two state-of-the-art boolean function synthesis tools, namely, (i) the AIG-NNF pipeline of BFSS [1] with ABC's MiniSat as the SAT solver and (ii) CADET [22], [24]. For the BDD Compiler, the .qdimacs input was converted to an AIG using simple Tseitin variable detection; this AIG was then simplified and ROBDDs built using dynamic variable ordering (of all input and output variables) -this is part of the BDD pipeline of BFSS [1], henceforth called BDD BFSS .…”

“…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.…”

Incremental Determinization for Quantifier Elimination and Functional Synthesis

“…As soon as ID found a clause that prevents the model construction from trying the same partial model again, it switches back to the model search. Since there are only finitely many clauses and models, either the model construction or the refutation proof must eventually finish [22,23]. Example 1.…”

“…It follows a proof-theoretic approach, very similar to a SAT solver, alternating between building a model (i.e. Skolem functions for the existential variables Y ) and a refutation proof [23]. This allows ID to provide a model (i.e.…”