A logic you can count on

  • Authors:
  • Silvano Dal Zilio;Denis Lugiez;Charles Meyssonnier

  • Affiliations:
  • CNRS and Université de Provence;CNRS and Université de Provence;CNRS and Université de Provence

  • Venue:
  • Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • Year:
  • 2004

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Abstract

We prove the decidability of the quantifier-free, static fragment of ambient logic, with composition adjunct and iteration, which corresponds to a kind of regular expression language for semistructured data. The essence of this result is a surprising connection between formulas of the ambient logic and counting constraints on (nested) vectors of integers.Our proof method is based on a new class of tree automata for unranked, unordered trees, which may result in practical algorithms for deciding the satisfiability of a formula. A benefit of our approach is to naturally lead to an extension of the logic with recursive definitions, which is also decidable. Finally, we identify a simple syntactic restriction on formulas that improves the effectiveness of our algorithms on large examples.