# Encodings of Bounded Synthesis

The reactive synthesis problem is to compute a system satisfying a given specification in temporal logic. Bounded synthesis is the approach to bound the maximum size of the system that we accept as a solution to the reactive synthesis problem. As a result, bounded synthesis is decidable whenever the corresponding verification problem is decidable, and can be applied in settings where classic synthesis fails, such as in the synthesis of distributed systems. In this paper, we study the constraint solving problem behind bounded synthesis. We consider different reductions of the bounded synthesis problem of linear-time temporal logic (LTL) to constraint systems given as boolean formulas (SAT), quantified boolean formulas (QBF), and dependency quantified boolean formulas (DQBF). The reductions represent different trade-offs between conciseness and algorithmic efficiency. In the SAT encoding, both inputs and states of the system are represented explicitly; in QBF, inputs are symbolic and states are explicit; in DQBF, both inputs and states are symbolic. We evaluate the encodings systematically using benchmarks from the reactive synthesis competition (SYNTCOMP) and state-of-the-art solvers. Our key, and perhaps surprising, empirical finding is that QBF clearly dominates both SAT and DQBF.

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08/12/2020

### Reactive Synthesis from Extended Bounded Response LTL Specifications

Reactive synthesis is a key technique for the design of correct-by-const...
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### BoSy: An Experimentation Framework for Bounded Synthesis

We present BoSy, a reactive synthesis tool based on the bounded synthesi...
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### Bounded Synthesis of Reactive Programs

Most algorithms for the synthesis of reactive systems focus on the const...
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### A Symbolic Approach to Safety LTL Synthesis

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### Synthesis of Boolean Functions with Clausal Abstraction

Dependency quantified Boolean formulas (DQBF) is a logic admitting exist...
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### Program Synthesis as Dependency Quantified Formula Modulo Theory

Given a specification φ(X,Y) over inputs X and output Y, defined over a ...
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### Symbolic vs. Bounded Synthesis for Petri Games

Petri games are a multiplayer game model for the automatic synthesis of ...