A Decision Procedure for Regular Membership and Length Constraints over Unbounded Strings

by Tianyi Liang, Nestan Tsiskaridze, Andrew Reynolds, Cesare Tinelli, Clark Barrett
Abstract:
We prove that the quantifier-free fragment of the theory of character strings with regular language membership constraints and linear integer constraints over string lengths is decidable. We do that by describing a sound, complete and terminating tableaux calculus for that fragment which uses as oracles a decision procedure for linear integer arithmetic and a number of computable functions over regular expressions. A distinguishing feature of this calculus is that it provides a completely algebraic method for solving membership constraints which can be easily integrated into multi-theory SMT solvers. Another is that it can be used to generate symbolic solutions for such constraints, that is, solved forms that provide simple and compact representations of entire sets of complete solutions. The calculus is part of a larger one providing the theoretical foundations of a high performance theory solver for string constraints implemented in the SMT solver CVC4.
Reference:
A Decision Procedure for Regular Membership and Length Constraints over Unbounded Strings (Tianyi Liang, Nestan Tsiskaridze, Andrew Reynolds, Cesare Tinelli, Clark Barrett), In Proceedings of the 10th International Symposium on Frontiers of Combining Systems (FroCoS ’15) (Carsten Lutz, Silvio Ranise, eds.), Springer, volume 9322, 2015. (Wroclaw, Poland)
Bibtex Entry:
@inproceedings{LTR+15,
  url       = "http://www.cs.stanford.edu/~barrett/pubs/LTR+15.pdf",
  author    = "Tianyi Liang and Nestan Tsiskaridze and Andrew Reynolds and Cesare Tinelli and Clark Barrett",
  title     = "A Decision Procedure for Regular Membership and Length Constraints over Unbounded Strings",
  booktitle = "Proceedings of the 10th International Symposium on Frontiers of Combining Systems (FroCoS '15)",
  volume    = 9322,
  editor    = "Lutz, Carsten and Ranise, Silvio",
  pages     = "135--150",
  doi       = "10.1007/978-3-319-24246-0_9",
  series    = "Lecture Notes in Artificial Intelligence",
  publisher = "Springer",
  month     = sep,
  year      = 2015,
  note      = "Wroclaw, Poland",
  category  = "Conference Publications",
  abstract  = "We prove that the quantifier-free fragment of the theory of
character strings with regular language membership constraints and linear
integer constraints over string lengths is decidable. We do that by
describing a sound, complete and terminating tableaux calculus for that
fragment which uses as oracles a decision procedure for linear integer
arithmetic and a number of computable functions over regular expressions.
A distinguishing feature of this calculus is that it provides a completely
algebraic method for solving membership constraints which can
be easily integrated into multi-theory SMT solvers. Another is that it
can be used to generate symbolic solutions for such constraints, that is,
solved forms that provide simple and compact representations of entire
sets of complete solutions. The calculus is part of a larger one providing
the theoretical foundations of a high performance theory solver for string
constraints implemented in the SMT solver CVC4."
}

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