Proactive Synthesis of Recursive Tree-to-String Functions from Examples

Synthesis from examples enables non-expert users to generate programs by specifying examples of their behavior. A domain-specific form of such synthesis has been recently deployed in a widely used spreadsheet software product. In this paper we contribute to foundations of such techniques and present a complete algorithm for synthesis of a class of recursive functions defined by structural recursion over a given algebraic data type definition. The functions we consider map an algebraic data type to a string; they are useful for, e.g., pretty printing and serialization of programs and data. We formalize our problem as learning deterministic sequential top-down tree-to-string transducers with a single state (1STS). The first problem we consider is learning a tree-to-string transducer from any set of input/output examples provided by the user. We show that, given a set of input/output examples, checking whether there exists a 1STS consistent with these examples is NP-complete in general. In contrast, the problem can be solved in polynomial time under a (practically useful) closure condition that each subtree of a tree in the input/output example set is also part of the input/output examples. Because coming up with relevant input/output examples may be difficult for the user while creating hard constraint problems for the synthesizer, we also study a more automated active learning scenario in which the algorithm chooses the inputs for which the user provides the outputs. Our algorithm asks a worst-case linear number of queries as a function of the size of the algebraic data type definition to determine a unique transducer. To construct our algorithms we present two new results on formal languages. First, we define a class of word equations, called sequential word equations, for which we prove that satisfiability can be solved in deterministic polynomial time. This is in contrast to the general word equations for which the best known complexity upper bound is in linear space. Second, we close a long-standing open problem about the asymptotic size of test sets for context-free languages. A test set of a language of words L is a subset T of L such that any two word homomorphisms equivalent on T are also equivalent on L. We prove that it is possible to build test sets of cubic size for context-free languages, matching for the first time the lower bound found 20 years ago

Proactive Synthesis of Recursive Tree-to-String Functions from Examples (Artifact)

This artifact, named Prosy, is an interactive command-line tool for synthesizing recursive tree-to-string functions (e.g. pretty-printers) from examples. Specifically, Prosy takes as input a Scala file containing a hierarchy of abstract and case classes, and synthesizes the printing function after interacting with the user. Prosy first pro-actively generates a finite set of trees such that their string representations uniquely determine the function to synthesize. While asking the output for each example, Prosy prunes away questions when it can infer their answers from previous answers. In the companion paper, we prove that this pruning allows Prosy not to require that the user provides answers to the entire set of questions, which is of size O(n^3) where n is the size of the input file, but only to a reasonably small subset of size O(n). Furthermore, Prosy guides the interaction by providing suggestions whenever it can

Teaching Inverse Reinforcement Learners via Features and Demonstrations

Learning near-optimal behaviour from an expert's demonstrations typically relies on the assumption that the learner knows the features that the true reward function depends on. In this paper, we study the problem of learning from demonstrations in the setting where this is not the case, i.e., where there is a mismatch between the worldviews of the learner and the expert. We introduce a natural quantity, the teaching risk, which measures the potential suboptimality of policies that look optimal to the learner in this setting. We show that bounds on the teaching risk guarantee that the learner is able to find a near-optimal policy using standard algorithms based on inverse reinforcement learning. Based on these findings, we suggest a teaching scheme in which the expert can decrease the teaching risk by updating the learner's worldview, and thus ultimately enable her to find a near-optimal policy.Comment: NeurIPS'2018 (extended version

Iterative Classroom Teaching

We consider the machine teaching problem in a classroom-like setting wherein the teacher has to deliver the same examples to a diverse group of students. Their diversity stems from differences in their initial internal states as well as their learning rates. We prove that a teacher with full knowledge about the learning dynamics of the students can teach a target concept to the entire classroom using O(min{d,N} log(1/eps)) examples, where d is the ambient dimension of the problem, N is the number of learners, and eps is the accuracy parameter. We show the robustness of our teaching strategy when the teacher has limited knowledge of the learners' internal dynamics as provided by a noisy oracle. Further, we study the trade-off between the learners' workload and the teacher's cost in teaching the target concept. Our experiments validate our theoretical results and suggest that appropriately partitioning the classroom into homogenous groups provides a balance between these two objectives.Comment: AAAI'19 (extended version

Minimal Synthesis of String To String Functions From Examples

We study the problem of synthesizing string to string transformations from a set of input/output examples. The transformations we consider are expressed using deterministic finite automata (DFA) that read pairs of letters, one letter from the input and one from the output. The DFA corresponding to these transformations have additional constraints, ensuring that each input string is mapped to exactly one output string. We suggest that, given a set of input/output examples, the smallest DFA consistent with the examples is a good candidate for the transformation the user was expecting. We therefore study the problem of, given a set of examples, finding a minimal DFA consistent with the examples and satisfying the functionality and totality constraints mentioned above. We prove that, in general, this problem (the corresponding decision problem) is NP-complete. This is unlike the standard DFA minimization problem which can be solved in polynomial time. We provide several NP-hardness proofs that show the hardness of multiple (independent) variants of the problem. Finally, we propose an algorithm for finding the minimal DFA consistent with input/output examples, that uses a reduction to SMT solvers. We implemented the algorithm, and used it to evaluate the likelihood that the minimal DFA indeed corresponds to the DFA expected by the user.Comment: SYNT 201

Iterative Classroom Teaching

We consider the machine teaching problem in a classroom-like setting wherein the teacher has to deliver the same examples to a diverse group of students. Their diversity stems from differences in their initial internal states as well as their learning rates. We prove that a teacher with full knowledge about the learning dynamics of the students can teach a target concept to the entire classroom using O (min{d,N} log 1/eps) examples, where d is the ambient dimension of the problem, N is the number of learners, and eps is the accuracy parameter. We show the robustness of our teaching strategy when the teacher has limited knowledge of the learners' internal dynamics as provided by a noisy oracle. Further, we study the trade-off between the learners' workload and the teacher's cost in teaching the target concept. Our experiments validate our theoretical results and suggest that appropriately partitioning the classroom into homogenous groups provides a balance between these two objectives

Interactive Programming by Example

As of today, programming has never been so accessible. Yet, it remains a challenge for end-users: students, non-technical employees, experts in their domains outside of computer science, and so on. With its forecast potential for solving problems by only observing inputs and outputs, programming-by-example was supposed to alleviate complex tasks requiring programming for end-users. The initial ideas of macro-based editors paved the way to subsequent practical solutions, such as spreadsheet transformations from examples. Finding the right program is the core of the programming-by-example systems. However, users find it difficult to trust such generated programs. In this thesis, we contribute to proving that some forms of interaction alleviate, by having users provide examples, the problem of finding correct and reliable programs. We first report on two experiments that enable us to conjecture what kind of interaction brings benefits to programming-by-example. First, we present a new kind of game engine, Pong Designer. In this game engine, by using their finger, users program rules on the fly, by modifying the game state. We analyze its potential, and its eventual downsides that have probably prevented its wide adoption. Second, we present StriSynth, an interactive command-line tool that uses programming-by-example to transform string and collections. The resulting programs can also rename or otherwise manage files. We obtained the result that confirms that many users preferred StriSynth over usual programming languages, but would appreciate to have both. We then report on two new exciting experiments with verified results, using two forms of interaction truly benefiting programming-by-example. Third, on top of a programmingby- example-based engine for extracting structured data out of text files, in this thesis we study two interaction models implemented in a tool named FlashProg: a view of the program with notification about ambiguities, and the asking of clarification questions. In this thesis, we prove that these two interaction models enable users to perform tasks with less errors and to be more confident with the results. Last, for learning recursive tree-to-string functions (e.g., pretty-printers), in this thesis we prove that questioning breaks down the learning complexity from a cubic to a linear number of questions, in practice making programming-by-example even more accessible than regular programming. The implementation, named Prosy, could be easily added to integrated development environments