Learning universally quantified invariants of linear data structures

  • Authors:
  • Pranav Garg;Christof Löding;P. Madhusudan;Daniel Neider

  • Affiliations:
  • University of Illinois at Urbana-Champaign;RWTH Aachen University;University of Illinois at Urbana-Champaign;RWTH Aachen University

  • Venue:
  • CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
  • Year:
  • 2013

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Abstract

We propose a new automaton model, called quantified data automata over words, that can model quantified invariants over linear data structures, and build poly-time active learning algorithms for them, where the learner is allowed to query the teacher with membership and equivalence queries. In order to express invariants in decidable logics, we invent a decidable subclass of QDAs, called elastic QDAs, and prove that every QDA has a unique minimally-over-approximating elastic QDA. We then give an application of these theoretically sound and efficient active learning algorithms in a passive learning framework and show that we can efficiently learn quantified linear data structure invariants from samples obtained from dynamic runs for a large class of programs.