An Algebraic Approach to Regular Sets
In recent years an increasing interest in regular sets for different kinds of elements could be observed. The introduction of XML has led to investigations of regular sets of both ranked and unranked trees and also of attributed unranked trees.
The aim of this short note is to introduce a uniform notion of regularity. If instantiated for strings, ranked trees and unranked trees it will coincide with the existing concepts and it can easily be extended to arbitrary data types. This leads to a natural notion of regularity for different kinds of attributed unranked trees and also to regular sets of structured elements which have not yet been investigated. The approach takes advantage from freeness constraints and parametric abstract data types as offered by the algebraic specification language Casl
KeywordsRegular Expression Extended Signature Ground Term Tree Automaton Partial Algebra
Unable to display preview. Download preview PDF.
- 1.Murata, M., Brüggemann-Klein, A., Wood, D.: Regular tree and regular hedge languages over unranked alphabets: Version 1. Technical Report HKUST-TCSC- 2001-0, The Hongkong University of Science and Technology (April 2001)Google Scholar
- 3.Barr, M., Wells, C.: Category Theory for Computing Science, 2nd edn. International Series in Computer Science, Prentice–Hall, Englewood Cliffs (1995)Google Scholar
- 5.Burstall, R., Goguen, J.: The semantics of CLEAR, a specification language, vol. 86, pp. 292–332. Springer, Heidelberg (1979)Google Scholar
- 6.Ehrig, H., Mahr, B.: Fundamentals of Algebraic Specification 1: Equations and Initial Semantics. In: eatcs monographs on theoretical computer science edition, vol. 6, Springer, Heidelberg (1985)Google Scholar
- 7.Ehrig, H., Mahr, B.: Fundamentals of Algebraic Specification 2: Module Specifications and Constraints. In: eatcs monographs on theoretical computer science edition, vol. 21, Springer, Heidelberg (1990)Google Scholar
- 12.Neven, F.: Automata theory for XML researchers. SIGMOD Record 31(3) (2002)Google Scholar