Bridging boolean and quantitative synthesis using smoothed proof search

Abstract

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.

Continualization of Probabilistic Programs With Correction

“…Because the GPA impacts the number of interviews a student receives, our model incorporates control flow where each branch captures the distribution of interviews received, conditioned on the GPA being in a certain range (lines [11][12][13][14][15][16][17]. Each student's resume is available to all recruiters and each recruiter can request an interview or not, hence all three of the Interviews distributions follow a Binomial distribution (here denoted as bin) with the same n (number of recruiters) but with different probabilities (higher probabilities for higher GPAs).…”

Optimizing synthesis with metasketches

“…Recent work has considered optimality in synthesis, with various forms of ranking and weighting formulations [13,22,28], and in SMT problems in general. Chaudhuri et al [6], for example, propose a smoothed proof search technique for synthesizing parameter holes in a program while optimizing a quantitative objective. Smoothed proof search reduces optimal synthesis to a sequence of optimization problems that can be solved numerically to satisfy the specification in the limit.…”

Optimal Guard Synthesis for Memory Safety

“…Hence, we add all constraints with no descendants in Δ to Resolved and update S with the corresponding solutions given by S 0 (lines [21][22][23].…”

“…There are a few approaches to synthesis that consider optimality as an objective [20][21][22][23]. However, in these papers, optimality is defined with respect to an explicit quantitative aspect of program executions, for example execution time.…”