SAT-Based Synthesis Methods for Safety Specs

Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their scalability limitations. Instead of BDDs, we propose several new methods to synthesize finite-state systems from safety specifications using decision procedures for the satisfiability of quantified and unquantified Boolean formulas (SAT-, QBF- and EPR-solvers). The presented approaches are based on computational learning, templates, or reduction to first-order logic. We also present an efficient parallelization, and optimizations to utilize reachability information and incremental solving. Finally, we compare all methods in an extensive case study. Our new methods outperform BDDs and other existing work on some classes of benchmarks, and our parallelization achieves a super-linear speedup. This is an extended version of [5], featuring an additional appendix.Comment: Extended version of a paper at VMCAI'1

CUBES: A Parallel Synthesizer for SQL Using Examples

In recent years, more people have seen their work depend on data manipulation tasks. However, many of these users do not have the background in programming required to write complex programs, particularly SQL queries. One way of helping these users is automatically synthesizing the SQL query given a small set of examples. Several program synthesizers for SQL have been recently proposed, but they do not leverage multicore architectures. This paper proposes CUBES, a parallel program synthesizer for the domain of SQL queries using input-output examples. Since input-output examples are an under-specification of the desired SQL query, sometimes, the synthesized query does not match the user's intent. CUBES incorporates a new disambiguation procedure based on fuzzing techniques that interacts with the user and increases the confidence that the returned query matches the user intent. We perform an extensive evaluation on around 4000 SQL queries from different domains. Experimental results show that our sequential version can solve more instances than other state-of-the-art SQL synthesizers. Moreover, the parallel approach can scale up to 16 processes with super-linear speedups for many hard instances. Our disambiguation approach is critical to achieving an accuracy of around 60%, significantly larger than other SQL synthesizers

On the Effect of Quantum Interaction Distance on Quantum Addition Circuits

We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of qubits and gates of any $\Omega(\log n)$-depth quantum adder circuit for two $n$-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates. Unfortunately, on the chosen $k$-dimensional practical architecture, we prove that the depth lower bound of any exact quantum addition circuits is no longer $\Omega(\log {n})$, but $\Omega(\sqrt[k]{n})$. This result, the first application of graph embedding to quantum circuits and devices, provides a new tool for compiler development, emphasizes the impact of quantum computer architecture on performance, and acts as a cautionary note when evaluating the time performance of quantum algorithms.Comment: accepted for ACM Journal on Emerging Technologies in Computing System