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35
Synthesis of loopfree programs
 In PLDI
, 2011
"... We consider the problem of synthesizing loopfree programs that implement a desired functionality using components from a given library. Specifications of the desired functionality and the library components are provided as logical relations between their respective input and output variables. The l ..."
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Cited by 24 (9 self)
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We consider the problem of synthesizing loopfree programs that implement a desired functionality using components from a given library. Specifications of the desired functionality and the library components are provided as logical relations between their respective input and output variables. The library components can be used at most once, and hence the library is required to contain a reasonable overapproximation of the multiset of the components required. We solve the above componentbased synthesis problem using a constraintbased approach that involves first generating a synthesis constraint, and then solving the constraint. The synthesis constraint is a firstorder ∃ ∀ logic formula whose size is quadratic in the number of components. We present a novel algorithm for solving such constraints. Our algorithm is based on counterexample guided iterative synthesis paradigm and uses offtheshelf SMT solvers. We present experimental results that show that our tool Brahma can efficiently synthesize highly nontrivial 1020 line loopfree bitvector programs. These programs represent a state space of approximately 20 10 programs, and are beyond the reach of the other tools based on sketching and superoptimization.
Synthesizing geometry constructions
 In PLDI
, 2011
"... In this paper, we study the problem of automatically solving ruler/compass based geometry construction problems. We first introduce a logic and a programming language for describing such constructions and then phrase the automation problem as a program synthesis problem. We then describe a new progr ..."
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Cited by 17 (11 self)
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In this paper, we study the problem of automatically solving ruler/compass based geometry construction problems. We first introduce a logic and a programming language for describing such constructions and then phrase the automation problem as a program synthesis problem. We then describe a new program synthesis technique based on three key insights: (i) reduction of symbolic reasoning to concrete reasoning (based on a deep theoretical result that reduces verification to random testing), (ii) extending the instruction set of the programming language with higher level primitives (representing basic constructions found in textbook chapters, inspired by how humans use their experience and knowledge gained from chapters to perform complicated constructions), and (iii) pruning the forward exhaustive search using a goaldirected heuristic (simulating backward reasoning performed by humans). Our tool can successfully synthesize constructions for various geometry problems picked up from highschool textbooks and examination papers in a reasonable amount of time. This opens up an amazing set of possibilities in the context of making classroom teaching interactive.
Pathbased Inductive Synthesis for Program Inversion
"... In this paper, we investigate the problem of semiautomated inversion of imperative programs, which has the potential to make it much easier and less error prone to write programs that naturally pair as inverses, such as insert/delete operations, compressors/decompressors, and so on. Viewing inversi ..."
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Cited by 15 (6 self)
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In this paper, we investigate the problem of semiautomated inversion of imperative programs, which has the potential to make it much easier and less error prone to write programs that naturally pair as inverses, such as insert/delete operations, compressors/decompressors, and so on. Viewing inversion as a subproblem of program synthesis, we propose a novel synthesis technique called Pathbased Inductive Synthesis (PINS) and apply it to inversion. PINS starts from a program P and a template T for its inverse. PINS then iteratively refines the space of template instantiations by exploring paths in the composition of P and T with symbolic execution. PINS uses an SMT solver to intelligently guide the refinement process, based on the paths explored so far. The key idea motivating this approach is the small pathbound hypothesis: that the behavior of a program can be summarized with a small, carefully chosen set of its program paths. We evaluated PINS by using it to invert 14 programs such as compressors (e.g., LempelZivWelch), encoders (e.g., UUEncode), and arithmetic operations (e.g., vector rotation). Most of these examples are difficult or impossible to invert using prior techniques, but PINS was able to invert all of them. We also found that a semiautomated technique we developed to mine a template from the program to be inverted worked well. In our experiments, PINS takes between one second to thirty minutes to synthesize inverses. We believe this proofofconcept implementation demonstrates the viability of the PINS approach to program synthesis.
Spreadsheet Table Transformations from Examples
, 2011
"... Every day, millions of computer endusers need to perform tasks over large, tabular data, yet lack the programming knowledge to do such tasks automatically. In this work, we present an automatic technique that takes from a user an example of how the user needs to transform a table of data, and provi ..."
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Cited by 14 (9 self)
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Every day, millions of computer endusers need to perform tasks over large, tabular data, yet lack the programming knowledge to do such tasks automatically. In this work, we present an automatic technique that takes from a user an example of how the user needs to transform a table of data, and provides to the user a program that implements the transformation described by the example. In particular, we present a language of programs TableProg that can describe transformations that real users require. We then present an algorithm ProgFromEx that takes an example input and output table, and infers a program in TableProg that implements the transformation described by the example. When the program is applied to the example input, it reproduces the example output. When the program is applied to another, potentially larger, table with a “similar” layout as the example input table, then the program produces
Spreadsheet data manipulation using examples
 In Communications of the ACM
, 2012
"... Millions of computer endusers need to perform tasks over large spreadsheet data, yet lack the programming knowledge to do such tasks automatically. We present a programming by example methodology that allows endusers to automate such repetitive tasks. Our methodology involves designing a domainsp ..."
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Cited by 12 (8 self)
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Millions of computer endusers need to perform tasks over large spreadsheet data, yet lack the programming knowledge to do such tasks automatically. We present a programming by example methodology that allows endusers to automate such repetitive tasks. Our methodology involves designing a domainspecific language and developing a synthesis algorithm that can learn programs in that language from userprovided examples. We present instantiations of this methodology for particular domains of tasks: (a) syntactic transformations of strings using restricted forms of regular expressions, conditionals and loops, (b) semantic transformations of strings involving lookup in relational tables, and (c) layout transformations on spreadsheet tables. We have implemented this technology as an addin for the Microsoft Excel Spreadsheet system and have evaluated it successfully over several benchmarks picked from various Excel help forums. 1.
Formal verification of hybrid systems
, 2011
"... In formal verification, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements. The appropriate mathematical model for embedded control systems is hybrid systems that combines th ..."
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Cited by 11 (0 self)
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In formal verification, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements. The appropriate mathematical model for embedded control systems is hybrid systems that combines the traditional statemachine based models for discrete control with classical differentialequations based models for continuously evolving physical activities. In this article, we briefly review selected existing approaches to formal verification of hybrid systems, along with directions for future research.
Automatically Generating Algebra Problems
"... We propose computerassisted techniques for helping with pedagogy in Algebra. In particular, given a proof problem p (of the form Lefthandsideterm = Righthandsideterm), we show how to automatically generate problems that are similar to p. We believe that such a tool can be used by teachers in m ..."
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Cited by 9 (5 self)
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We propose computerassisted techniques for helping with pedagogy in Algebra. In particular, given a proof problem p (of the form Lefthandsideterm = Righthandsideterm), we show how to automatically generate problems that are similar to p. We believe that such a tool can be used by teachers in making examinations where they need to test students on problems similar to what they taught in class, and students in generating practice problems tailored to their specific needs. Our first insight is that we can generalize p syntactically to a query Q that implicitly represents a set of problems [[Q]] (which includes p). Our second insight is that we can explore the space of problems [[Q]] automatically, use classical results from polynomial identity testing to generate only those problems in [[Q]] that are correct, and then use pruning techniques to generate only unique and interesting problems. Our third insight is that with a small amount of manual tuning on the query Q, the user can interactively guide the computer to generate problems of interest to her. We present the technical details of the above mentioned steps, and also describe a tool where these steps have been implemented. We also present an empirical evaluation on a wide variety of problems from various subfields of algebra including polynomials, trigonometry, calculus, determinants etc. Our tool is able to generate a rich corpus of similar problems from each given problem; while some of these similar problems were already present in the textbook, several were new! 1
Synthesis from examples: Interaction models and algorithms
 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
, 2012
"... Abstract—Examples are often a natural way to specify various computational artifacts such as programs, queries, and sequences. Synthesizing such artifacts from example based specifications has various applications in the domains of enduser programming and intelligent tutoring systems. Synthesis from ..."
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Cited by 7 (5 self)
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Abstract—Examples are often a natural way to specify various computational artifacts such as programs, queries, and sequences. Synthesizing such artifacts from example based specifications has various applications in the domains of enduser programming and intelligent tutoring systems. Synthesis from examples involves addressing two key technical challenges: (i) design of a user interaction model to deal with the inherent ambiguity in the example based specification. (ii) design of an efficient search algorithm these algorithms have been based on paradigms from various communities including use of SAT/SMT solvers (formal methods community), version space algebras (machine learning community), and A*style goaldirected heuristics (AI community). This paper describes some effective user interaction models and algorithmic methodologies for synthesis from examples while discussing synthesizers for a variety of artifacts ranging from tricky bitvector algorithms, spreadsheet macros for automating repetitive data manipulation tasks, ruler/compass based geometry constructions, algebraic identities, and predictive intellisense for repetitive drawings and mathematical terms.
Learning Semantic String Transformations from Examples
"... We address the problem of performing semantic transformations on strings, which may represent a variety of data types (or their combination) such as a column in a relational table, time, date, currency, etc. Unlike syntactic transformations, which are based on regular expressions and which interpret ..."
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Cited by 6 (6 self)
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We address the problem of performing semantic transformations on strings, which may represent a variety of data types (or their combination) such as a column in a relational table, time, date, currency, etc. Unlike syntactic transformations, which are based on regular expressions and which interpret a string as a sequence of characters, semantic transformations additionally require exploiting the semantics of the data type represented by the string, which may be encoded as a database of relational tables. Manually performing such transformations on a large collection of strings is error prone and cumbersome, while programmatic solutions are beyond the skillset of endusers. We present a programming by example technology that allows endusers to automate such repetitive tasks. We describe an expressive transformation language for semantic manipulation that combines table lookup operations and syntactic manipulations. We then present a synthesis algorithm that can learn all transformations in the language that are consistent with the userprovided set of inputoutput examples. We have implemented this technology as an addin for the Microsoft Excel Spreadsheet system and have evaluated it successfully over several benchmarks picked from various Excel helpforums. 1.
Synthesis from Examples
"... Examples are often a natural way to specify computational structures such as programs, queries, and sequences. Synthesizing such structures from example based specification has applications in automating enduser programming and in building intelligent tutoring systems. Synthesis from examples invol ..."
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Cited by 5 (4 self)
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Examples are often a natural way to specify computational structures such as programs, queries, and sequences. Synthesizing such structures from example based specification has applications in automating enduser programming and in building intelligent tutoring systems. Synthesis from examples involves addressing two key technical challenges: (i) design of an efficient search algorithm – these algorithms have been based on various paradigms including versionspace algebras, SAT/SMT solvers, numerical methods, and even exhaustive search, (ii) design of a user interaction model to deal with the inherent ambiguity in the example based specification. This paper illustrates various algorithmic techniques and user interaction models by describing inductive synthesizers for varied applications including synthesis of tricky bitvector algorithms, spreadsheet macros for automating repetitive data manipulation tasks, ruler/compass based geometry constructions, new algebra problems, sequences for mathematical intellisense, and grading of programming problems. 1.