Regular sets over extended tree structures
Résumé
We investigate notions of decidability and definability for the Monadic Second-Order Logic of labeled tree structures, and links with finite automata using oracles to test input prefixes. A general framework is defined allowing to transfer some MSO-properties from a graph-structure to a labeled tree structure. Transferred properties are decidability of sentences and existence of a definable model for every satisfiable formula. A class of finite automata with prefix-oracles is also defined, recognizing exactly languages defined by MSO-formulas in any labeled tree-structure. Applying these results, the well-known equality between languages recognized by finite automata,sets of vertices MSO definable in a tree-structure and sets of pushdown contexts generated by pushdown-automata is extended to iterated pushdown automata.
Domaines
Informatique et langage [cs.CL]
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