Recursive Program Schemes Research Articles

A representation of trees by languages I

A tree can be represented by a language consisting of a suitable coding of its finite branches. We investigate this representation and derive a number of reductions between certain equivalence problems for context-free tree grammars and recursive program schemes and the (open) equivalence problem for DPDA's. This is the first part of this work: it is devoted to technical results on prefix-free languages and strict deterministic grammars. Application to context-free tree grammars will be published in the second part.

A representation of trees by languages II

We apply certain technical results, published in the first part of the present work to obtain reductions between equivalence problems for simple deterministic tree grammars recursive program schemes and the (open) equivalence problem for DPDA's.

IO and OI. I

A fixed-point characterization of the inside-out (IO) and outside-in (OI) context-free tree languages is given. This characterization is used to obtain a theory of nondeterministic systems of context-free equations with parameters. Several “Mezei-and-Wright-like” results are obtained which relate the context-free tree languages to recognizable tree languages and to nondeterministic recursive program(scheme)s (called by value and called by name). Closure properties of the context-free tree languages are discussed. Hierarchies of higher level equational subsets of an algebra are considered.

Syntactic properties of recursive program schemes

Syntactic properties of recursive program schemes

IO and OI

A fixed point characterization of the inside-out (IO) and the outside- in (OI) context-free tree languages is given. This characterization is used to obtain a theory of nondeterministic systems of context-free equations with parameters. Several ''Mezei and Wright like'' results are obtained which relate to context-free tree languages, to recognizable tree languages and to nondeterministic recursive program(scheme)s (called by value and called by name). The emptiness problem and closure properties of the context-free tree languages are discussed. Hierarchies of higher level equational subsets of an algebra are considered.