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International Conference on Verification, Model Checking, and Abstract Interpretation

VMCAI 2019: Verification, Model Checking, and Abstract Interpretation pp 92–113Cite as

Lazy but Effective Functional Synthesis

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11388))

Abstract

We present a new technique for generating a function implementation from a declarative specification formulated as a \(\forall \exists \)-formula in first-order logic. We follow a classic approach of eliminating existential quantifiers and extracting Skolem functions for the theory of linear arithmetic. Our method eliminates quantifiers lazily and produces a synthesis solution in the form of a decision tree. Compared to prior approaches, our decision trees have fewer nodes due to deriving theory terms that can be shared both within a single output as well as across multiple outputs. Our approach is implemented in a tool called AE-VAL, and its evaluation on a set of reactive synthesis benchmarks shows promise.

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Notes

  1. 1.

    Here and later, we use the vector notation to denote multiple variables.

  2. 2.

    http://sygus.seas.upenn.edu/SyGuS-COMP2018.html.

  3. 3.

    We do not consider the modulo operation in this work, but our approach can be extended to support it.

  4. 4.

    Not to be confused with the evaluation of [13] which applied AE-VAL iteratively, and most of the formulas were invalid. Here, we considered only valid formulas and focused only on the Skolem extraction.

  5. 5.

    These benchmarks are available at: http://www.cs.princeton.edu/~grigoryf/aeval-benchs.zip.

  6. 6.

    Without taking into account the individual ite-s due to computing greatest and lowest bounds and handling disequalities, as described in Sect. 4.

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Acknowledgments

We thank Andreas Katis for providing encodings of benchmarks for reactive synthesis from Assume-Guarantee contracts into an SMT-LIB2 format acceptable by AE-VAL.

This work was supported in part by NSF Grant 1525936. Any opinions, findings, and conclusions expressed herein are those of the authors and do not necessarily reflect those of the NSF.

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Authors and Affiliations

  1. Princeton University, Princeton, USA

    Grigory Fedyukovich & Aarti Gupta

  2. University of Waterloo, Waterloo, Canada

    Arie Gurfinkel

Authors
  1. Grigory Fedyukovich
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  2. Arie Gurfinkel
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  3. Aarti Gupta
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Correspondence to Grigory Fedyukovich .

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Editors and Affiliations

  1. IRIF, University Paris Diderot and CNRS, Paris, France

    Constantin Enea

  2. Yale University, New Haven, CT, USA

    Ruzica Piskac

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Fedyukovich, G., Gurfinkel, A., Gupta, A. (2019). Lazy but Effective Functional Synthesis. In: Enea, C., Piskac, R. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2019. Lecture Notes in Computer Science(), vol 11388. Springer, Cham. https://doi.org/10.1007/978-3-030-11245-5_5

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  • DOI: https://doi.org/10.1007/978-3-030-11245-5_5

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  • Online ISBN: 978-3-030-11245-5

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