Bridging boolean and quantitative synthesis using smoothed proof search

We present a new technique for parameter synthesis under boolean and quantitative objectives. The input to the technique is a "sketch" --- a program with missing numerical parameters --- and a probabilistic assumption about the program's inputs. The goal is to automatically synthesize values for the parameters such that the resulting program satisfies: (1) a {boolean specification}, which states that the program must meet certain assertions, and (2) a {quantitative specification}, which assigns a real valued rating to every program and which the synthesizer is expected to optimize. Our method --- called smoothed proof search --- reduces this task to a sequence of unconstrained smooth optimization problems that are then solved numerically. By iteratively solving these problems, we obtain parameter values that get closer and closer to meeting the boolean specification; at the limit, we obtain values that provably meet the specification. The approximations are computed using a new notion of smoothing for program abstractions, where an abstract transformer is approximated by a function that is continuous according to a metric over abstract states. We present a prototype implementation of our synthesis procedure, and experimental results on two benchmarks from the embedded control domain. The experiments demonstrate the benefits of smoothed proof search over an approach that does not meet the boolean and quantitative synthesis goals simultaneously.National Science Foundation (U.S.) (NSF Award #1162076

Program Synthesis and Linear Operator Semantics

For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the representation of the semantics of programs and program fragments in terms of linear operators, i.e. as matrices. We exploit in particular the fact that we can automatically generate the representation of the semantics of elementary blocks. These can then can be used in order to compositionally assemble the semantics of a whole program, i.e. the generator of the corresponding Discrete Time Markov Chain (DTMC). We also utilise a generalised version of Abstract Interpretation suitable for this linear algebraic or functional analytical framework in order to formulate semantical constraints (invariants) and optimisation objectives (for example performance requirements).Comment: In Proceedings SYNT 2014, arXiv:1407.493

On the Link between Gaussian Homotopy Continuation and Convex Envelopes

Abstract. The continuation method is a popular heuristic in computer vision for nonconvex optimization. The idea is to start from a simpli-fied problem and gradually deform it to the actual task while tracking the solution. It was first used in computer vision under the name of graduated nonconvexity. Since then, it has been utilized explicitly or im-plicitly in various applications. In fact, state-of-the-art optical flow and shape estimation rely on a form of continuation. Despite its empirical success, there is little theoretical understanding of this method. This work provides some novel insights into this technique. Specifically, there are many ways to choose the initial problem and many ways to progres-sively deform it to the original task. However, here we show that when this process is constructed by Gaussian smoothing, it is optimal in a specific sense. In fact, we prove that Gaussian smoothing emerges from the best affine approximation to Vese’s nonlinear PDE. The latter PDE evolves any function to its convex envelope, hence providing the optimal convexification

Comparative Synthesis: Learning Near-Optimal Network Designs by Query

When managing wide-area networks, network architects must decide how to balance multiple conflicting metrics, and ensure fair allocations to competing traffic while prioritizing critical traffic. The state of practice poses challenges since architects must precisely encode their intent into formal optimization models using abstract notions such as utility functions, and ad-hoc manually tuned knobs. In this paper, we present the first effort to synthesize optimal network designs with indeterminate objectives using an interactive program-synthesis-based approach. We make three contributions. First, we present comparative synthesis, an interactive synthesis framework which produces near-optimal programs (network designs) through two kinds of queries (Propose and Compare), without an objective explicitly given. Second, we develop the first learning algorithm for comparative synthesis in which a voting-guided learner picks the most informative query in each iteration. We present theoretical analysis of the convergence rate of the algorithm. Third, we implemented Net10Q, a system based on our approach, and demonstrate its effectiveness on four real-world network case studies using black-box oracles and simulation experiments, as well as a pilot user study comprising network researchers and practitioners. Both theoretical and experimental results show the promise of our approach

Automated formal synthesis of provably safe digital controllers for continuous plants

Abstract: We present a sound and automated approach to synthesizing safe, digital controllers for physical plants represented as time-invariant models. Models are linear differential equations with inputs, evolving over a continuous state space. The synthesis precisely accounts for the effects of finite-precision arithmetic introduced by the controller. The approach uses counterexample-guided inductive synthesis: an inductive generalization phase produces a controller that is known to stabilize the model but that may not be safe for all initial conditions of the model. Safety is then verified via bounded model checking: if the verification step fails, a counterexample is provided to the inductive generalization, and the process further iterates until a safe controller is obtained. We demonstrate the practical value of this approach by automatically synthesizing safe controllers for physical plant models from the digital control literature