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Path Querying with Conjunctive Grammars by Matrix Multiplication

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Abstract

Problems in many areas can be reduced to one of the formal-languages-constrained path problems. Conjunctive grammars are more expressive than context-free grammars and are used, for example, in static analysis to describe an interleaved matched-parentheses language, which is not context-free. Path querying with conjunctive grammars is known to be undecidable. There is an algorithm for path querying with linear conjunctive grammars which provides an over-approximation of the result, but there is no algorithm for arbitrary conjunctive grammars. We propose the first algorithm for path querying with arbitrary conjunctive grammars. The proposed algorithm is matrix-based and allows us to efficiently apply GPGPU (General-Purpose computing on Graphics Processing Units) computing techniques and other optimizations for matrix operations.

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Notes

  1. 1.

    GitHub repository of the YaccConstructor project: https:// github.com/YaccConstructor/YaccConstructor.

  2. 2.

    The Math.Net Numerics WebSite: https://numerics.mathdotnet.com/.

  3. 3.

    GitHub repository of the managedCuda library: https://kunzmi.github.io/managedCuda/.

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Correspondence to R. Azimov or S. Grigorev.

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Azimov, R., Grigorev, S. Path Querying with Conjunctive Grammars by Matrix Multiplication. Program Comput Soft 45, 357–364 (2019) doi:10.1134/S0361768819070041

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Keywords:

  • conjunctive grammars
  • path querying
  • graphs
  • transitive closure
  • GPGPU
  • static analysis
  • matrix multiplication