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

Safety-Aware Apprenticeship Learning

Apprenticeship learning (AL) is a kind of Learning from Demonstration techniques where the reward function of a Markov Decision Process (MDP) is unknown to the learning agent and the agent has to derive a good policy by observing an expert's demonstrations. In this paper, we study the problem of how to make AL algorithms inherently safe while still meeting its learning objective. We consider a setting where the unknown reward function is assumed to be a linear combination of a set of state features, and the safety property is specified in Probabilistic Computation Tree Logic (PCTL). By embedding probabilistic model checking inside AL, we propose a novel counterexample-guided approach that can ensure safety while retaining performance of the learnt policy. We demonstrate the effectiveness of our approach on several challenging AL scenarios where safety is essential.Comment: Accepted by International Conference on Computer Aided Verification (CAV) 201

Program synthesis from polymorphic refinement types

We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two reasons. First, they offer a unique combination of expressive power and decidability, which enables automatic verification—and hence synthesis—of nontrivial programs. Second, a type-based specification for a program can often be effectively decomposed into independent specifications for its components, causing the synthesizer to consider fewer component combinations and leading to a combinatorial reduction in the size of the search space. At the core of our synthesis procedure is a newalgorithm for refinement type checking, which supports specification decomposition. We have evaluated our prototype implementation on a large set of synthesis problems and found that it exceeds the state of the art in terms of both scalability and usability. The tool was able to synthesize more complex programs than those reported in prior work (several sorting algorithms and operations on balanced search trees), as well as most of the benchmarks tackled by existing synthesizers, often starting from a more concise and intuitive user input.National Science Foundation (U.S.) (Grant CCF-1438969)National Science Foundation (U.S.) (Grant CCF-1139056)United States. Defense Advanced Research Projects Agency (Grant FA8750-14-2-0242

Bounded Synthesis of Reactive Programs

Most algorithms for the synthesis of reactive systems focus on the construction of finite-state machines rather than actual programs. This often leads to badly structured, unreadable code. In this paper, we present a bounded synthesis approach that automatically constructs, from a given specification in linear-time temporal logic (LTL), a program in Madhusudan's simple imperative language for reactive programs. We develop and compare two principal approaches for the reduction of the synthesis problem to a Boolean constraint satisfaction problem. The first reduction is based on a generalization of bounded synthesis to two-way alternating automata, the second reduction is based on a direct encoding of the program syntax in the constraint system. We report on preliminary experience with a prototype implementation, which indicates that the direct encoding outperforms the automata approach

Verified lifting of stencil computations

This paper demonstrates a novel combination of program synthesis and verification to lift stencil computations from low-level Fortran code to a high-level summary expressed using a predicate language. The technique is sound and mostly automated, and leverages counter-example guided inductive synthesis (CEGIS) to find provably correct translations. Lifting existing code to a high-performance description language has a number of benefits, including maintainability and performance portability. For example, our experiments show that the lifted summaries can enable domain specific compilers to do a better job of parallelization as compared to an off-the-shelf compiler working on the original code, and can even support fully automatic migration to hardware accelerators such as GPUs. We have implemented verified lifting in a system called STNG and have evaluated it using microbenchmarks, mini-apps, and real-world applications. We demonstrate the benefits of verified lifting by first automatically summarizing Fortran source code into a high-level predicate language, and subsequently translating the lifted summaries into Halide, with the translated code achieving median performance speedups of 4.1X and up to 24X for non-trivial stencils as compared to the original implementation.United States. Department of Energy. Office of Science (Award DE-SC0008923)United States. Department of Energy. Office of Science (Award DE-SC0005288

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

Abstract Learning Frameworks for Synthesis

We develop abstract learning frameworks (ALFs) for synthesis that embody the principles of CEGIS (counter-example based inductive synthesis) strategies that have become widely applicable in recent years. Our framework defines a general abstract framework of iterative learning, based on a hypothesis space that captures the synthesized objects, a sample space that forms the space on which induction is performed, and a concept space that abstractly defines the semantics of the learning process. We show that a variety of synthesis algorithms in current literature can be embedded in this general framework. While studying these embeddings, we also generalize some of the synthesis problems these instances are of, resulting in new ways of looking at synthesis problems using learning. We also investigate convergence issues for the general framework, and exhibit three recipes for convergence in finite time. The first two recipes generalize current techniques for convergence used by existing synthesis engines. The third technique is a more involved technique of which we know of no existing instantiation, and we instantiate it to concrete synthesis problems