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Adding Nesting Structure to Words RAJEEV ALUR
 

Summary: Adding Nesting Structure to Words
RAJEEV ALUR
University of Pennsylvania
and
P. Madhusudan
University of Illinois at Urbana-Champaign
We propose the model of nested words for representation of data with both a linear ordering and
a hierarchically nested matching of items. Examples of data with such dual linear-hierarchical
structure include executions of structured programs, annotated linguistic data, and HTML/XML
documents. Nested words generalize both words and ordered trees, and allow both word and
tree operations. We define nested word automata--finite-state acceptors for nested words, and
show that the resulting class of regular languages of nested words has all the appealing the-
oretical properties that the classical regular word languages enjoys: deterministic nested word
automata are as expressive as their nondeterministic counterparts; the class is closed under union,
intersection, complementation, concatenation, Kleene-*, prefixes, and language homomorphisms;
membership, emptiness, language inclusion, and language equivalence are all decidable; and de-
finability in monadic second order logic corresponds exactly to finite-state recognizability. We
also consider regular languages of infinite nested words and show that the closure properties,
MSO-characterization, and decidability of decision problems carry over.
The linear encodings of nested words give the class of visibly pushdown languages of words, and

  

Source: Alur, Rajeev - Department of Computer and Information Science, University of Pennsylvania

 

Collections: Computer Technologies and Information Sciences