Bottom-up synthesis of recursive functional programs using angelic execution

We present a novel bottom-up method for the synthesis of functional recursive programs. While bottom-up synthesis techniques can work better than top-down methods in certain settings, there is no prior technique for synthesizing recursive programs from logical specifications in a purely bottom-up fashion. The main challenge is that effective bottom-up methods need to execute sub-expressions of the code being synthesized, but it is impossible to execute a recursive subexpression of a program that has not been fully constructed yet. In this paper, we address this challenge using the concept of angelic semantics. Specifically, our method finds a program that satisfies the specification under angelic semantics (we refer to this as angelic synthesis), analyzes the assumptions made during its angelic execution, uses this analysis to strengthen the specification, and finally reattempts synthesis with the strengthened specification. Our proposed angelic synthesis algorithm is based on version space learning and therefore deals effectively with many incremental synthesis calls made during the overall algorithm. We have implemented this approach in a prototype called Burst and evaluate it on synthesis problems from prior work. Our experiments show that Burst is able to synthesize a solution to 94% of the benchmarks in our benchmark suite, outperforming prior work.

Inductive logic programming at 30

Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples and background knowledge. As ILP turns 30, we review the last decade of research. We focus on (i) new meta-level search methods, (ii) techniques for learning recursive programs, (iii) new approaches for predicate invention, and (iv) the use of different technologies. We conclude by discussing current limitations of ILP and directions for future research.

Dynaplex: analyzing program complexity using dynamically inferred recurrence relations

Being able to detect program runtime complexity is useful in many tasks (e.g., checking expected performance and identifying potential security vulnerabilities). In this work, we introduce a new dynamic approach for inferring the asymptotic complexity bounds of recursive programs. From program execution traces, we learn recurrence relations and solve them using pattern matching to obtain closed-form solutions representing the complexity bounds of the program. This approach allows us to efficiently infer simple recurrence relations that represent nontrivial, potentially nonlinear polynomial and non-polynomial, complexity bounds. We present Dynaplex, a tool that implements these ideas to automatically generate recurrence relations from execution traces. Our preliminary results on popular and challenging recursive programs show that Dynaplex can learn precise relations capturing worst-case complexity bounds (e.g., O ( n log n ) for mergesort, O (2 n ) for Tower of Hanoi and O ( n 1.58 ) for Karatsuba’s multiplication algorithm).

Compositional learning of mutually recursive procedural systems

This paper presents a compositional approach to active automata learning of Systems of Procedural Automata (SPAs), an extension of Deterministic Finite Automata (DFAs) to systems of DFAs that can mutually call each other. SPAs are of high practical relevance, as they allow one to efficiently learn intuitive recursive models of recursive programs after an easy instrumentation that makes calls and returns observable. Key to our approach is the simultaneous inference of individual DFAs for each of the involved procedures via expansion and projection: membership queries for the individual DFAs are expanded to membership queries of the entire SPA, and global counterexample traces are transformed into counterexamples for the DFAs of concerned procedures. This reduces the inference of SPAs to a simultaneous inference of the DFAs for the involved procedures for which we can utilize various existing regular learning algorithms. The inferred models are easy to understand and allow for an intuitive display of the procedural system under learning that reveals its recursive structure. We implemented the algorithm within the LearnLib framework in order to provide a ready-to-use tool for practical application which is publicly available on GitHub for experimentation.

Formal semantics and high performance in declarative machine learning using Datalog

With an escalating arms race to adopt machine learning (ML) in diverse application domains, there is an urgent need to support declarative machine learning over distributed data platforms. Toward this goal, a new framework is needed where users can specify ML tasks in a manner where programming is decoupled from the underlying algorithmic and system concerns. In this paper, we argue that declarative abstractions based on Datalog are natural fits for machine learning and propose a purely declarative ML framework with a Datalog query interface. We show that using aggregates in recursive Datalog programs entails a concise expression of ML applications, while providing a strictly declarative formal semantics. This is achieved by introducing simple conditions under which the semantics of recursive programs is guaranteed to be equivalent to that of aggregate-stratified ones. We further provide specialized compilation and planning techniques for semi-naive fixpoint computation in the presence of aggregates and optimization strategies that are effective on diverse recursive programs and distributed data platforms. To test and demonstrate these research advances, we have developed a powerful and user-friendly system on top of Apache Spark. Extensive evaluations on large-scale datasets illustrate that this approach will achieve promising performance gains while improving both programming flexibility and ease of development and deployment for ML applications.

Learning programs by learning from failures

We describe an inductive logic programming (ILP) approach calledlearning from failures. In this approach, an ILP system (the learner) decomposes the learning problem into three separate stages:generate,test, andconstrain. In the generate stage, the learner generates a hypothesis (a logic program) that satisfies a set ofhypothesis constraints(constraints on the syntactic form of hypotheses). In the test stage, the learner tests the hypothesis against training examples. A hypothesisfailswhen it does not entail all the positive examples or entails a negative example. If a hypothesis fails, then, in the constrain stage, the learner learns constraints from the failed hypothesis to prune the hypothesis space, i.e. to constrain subsequent hypothesis generation. For instance, if a hypothesis is too general (entails a negative example), the constraints prune generalisations of the hypothesis. If a hypothesis is too specific (does not entail all the positive examples), the constraints prune specialisations of the hypothesis. This loop repeats until either (i) the learner finds a hypothesis that entails all the positive and none of the negative examples, or (ii) there are no more hypotheses to test. We introduce Popper, an ILP system that implements this approach by combining answer set programming and Prolog. Popper supports infinite problem domains, reasoning about lists and numbers, learning textually minimal programs, and learning recursive programs. Our experimental results on three domains (toy game problems, robot strategies, and list transformations) show that (i) constraints drastically improve learning performance, and (ii) Popper can outperform existing ILP systems, both in terms of predictive accuracies and learning times.

Turning 30: New Ideas in Inductive Logic Programming

Common criticisms of state-of-the-art machine learning include poor generalisation, a lack of interpretability, and a need for large amounts of training data. We survey recent work in inductive logic programming (ILP), a form of machine learning that induces logic programs from data, which has shown promise at addressing these limitations. We focus on new methods for learning recursive programs that generalise from few examples, a shift from using hand-crafted background knowledge to learning background knowledge, and the use of different technologies, notably answer set programming and neural networks. As ILP approaches 30, we also discuss directions for future research.