Program synthesis is the generation of a program from a specification. Correct synthesis is difficult, and methods that provide formal guarantees suffer from scalability issues. On the other hand, neural networks are able to generate programs from examples quickly but are unable to guarantee that the program they output actually meets the logical specification. In this work we combine neural networks with formal reasoning: using the latter to convert a logical specification into a sequence of examples that guides the neural network towards a correct solution, and to guarantee that any solution returned satisfies the formal specification. We apply our technique to synthesising loop invariants and compare the performance to existing solvers that use SMT and existing techniques that use neural networks. Our results show that the formal reasoning based guidance improves the performance of the neural network substantially, nearly doubling the number of benchmarks it can solve.
Recent advances in learning-based perception systems have led to drastic improvements in the performance of robotic systems like autonomous vehicles and surgical robots. These perception systems, however, are hard to analyze and errors in them can propagate to cause catastrophic failures. In this paper, we consider the problem of synthesizing safe and robust controllers for robotic systems which rely on complex perception modules for feedback. We propose a counterexample-guided synthesis framework that iteratively builds simple surrogate models of the complex perception module and enables us t…
Program synthesis is the task of automatically generating expressions that satisfy a given specification. Program synthesis techniques have been used to automate the generation of loop invariants in code, synthesize function summaries, and to assist programmers via program sketching. Syntax-guided synthesis has been a successful paradigm in this area, however, one area where the state-of-the-art solvers fall-down is reasoning about potentially unbounded data structures such as arrays where both specifications and solutions may require quantifiers and quantifier alternations. We present SynRG, …
In reactive controller synthesis, a number of implementations (controllers) are possible for a given specification because of the incomplete nature of specification. To choose the most desirable one from the various options, we need to specify additional properties which can guide the synthesis. In this paper, We propose a technique for guided controller synthesis from regular requirements which are specified using an interval temporal logic QDDC. We find that QDDC is well suited for guided synthesis due to its superiority in dealing with both qualitative and quantitative specifications. Our f…
This article presents resource-guided synthesis, a technique for synthesizing recursive programs that satisfy both a functional specification and a symbolic resource bound. The technique is type-directed and rests upon a novel type system that combines polymorphic refinement types with potential annotations of automatic amortized resource analysis. The type system enables efficient constraint-based type checking and can express precise refinement-based resource bounds. The proof of type soundness shows that synthesized programs are correct by construction. By tightly integrating program explor…
We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but lack of formal soundness. Symbolic computational methods for Lyapunov functions, which are in between, give formal guarantees but are typically semi-automatic because they rely on the user to provide appropriate function templates. We propose a method that finds Lyapunov functions fully automatically$-$using machine learning$-$while also providing formal guara…
Reactive synthesis transforms a specification of a reactive system, given in a temporal logic, into an implementation. The main advantage of synthesis is that it is automatic. The main disadvantage is that the implementation is usually very difficult to understand. In this paper, we present a new synthesis process that explains the synthesized implementation to the user. The process starts with a simple version of the specification and a corresponding simple implementation. Then, desired properties are added one by one, and the corresponding transformations, repairing the implementation, are e…
Compositional synthesis relies on the discovery of assumptions, i.e., restrictions on the behavior of the remainder of the system that allow a component to realize its specification. In order to avoid losing valid solutions, these assumptions should be necessary conditions for realizability. However, because there are typically many different behaviors that realize the same specification, necessary behavioral restrictions often do not exist. In this paper, we introduce a new class of assumptions for compositional synthesis, which we call information flow assumptions. Such assumptions capture a…
Neuro Symbolic Reasoning for Planning: Counterexample Guided Inductive Synthesis using Large Language Models and Satisfiability Solving
Florida International University（佛罗里达国际大学）；SRI International（SRI国际（斯坦福国际研究院））；United States Military Academy（美国军事学院（西点军校））；University of Colorado Boulder（科罗拉多大学博尔德分校）；University of Central Florida（中佛罗里达大学）；Vanderbilt University（范德堡大学）
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Synthesizing a program that realizes a logical specification is a classical problem in computer science. We examine a particular type of program synthesis, where the objective is to synthesize a strategy that reacts to a potentially adversarial environment while ensuring that all executions satisfy a Linear Temporal Logic (LTL) specification. Unfortunately, exact methods to solve so-called LTL synthesis via logical inference do not scale. In this work, we cast LTL synthesis as an optimization problem. We employ a neural network to learn a Q-function that is then used to guide search, and to co…
Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background theories. Such logics, unlike pure first-order logic, do not admit even complete procedures. In this paper, we undertake a novel approach for synthesizing inductive hypotheses to prove validity in this logic. The idea is to utilize several kinds of finite first-order models as counterexamples that capture the non-provability and invalidity of formulas to guide the search for inductive hypothes…
