Linear delay enumeration and monadic second-order logic

  • Authors:
  • Bruno Courcelle

  • Affiliations:
  • Bordeaux University and CNRS, LaBRI, Institut Universitaire de France, France

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

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Abstract

The results of a query expressed by a monadic second-order formula on a tree, on a graph or on a relational structure of tree-width at most k, can be enumerated with a delay between two outputs proportional to the size of the next output. This is possible by using a preprocessing that takes time O(n@?log(n)), where n is the number of vertices or elements. One can also output directly the i-th element with respect to a fixed ordering, however, in more than linear time in its size. These results extend to graphs of bounded clique-width. We also consider the enumeration of finite parts of recognizable sets of terms specified by parameters such as size, height or Strahler number.