On the Equivalence Problem for Attribute Systems

The authors have shown in Courcelle et al. (1982) that certain attribute systems called strongly noneireular can be translated into recursive program schemes taking derivation trees as arguments and called primitive reeursive schemes with parameters. In particular, the equivalence problem for strongly noncircular attribute systems reduces to the equivalence problem for the latter class of program schemes. This latter problem seems deeply related with the DPDA equivalence problem. We solve it in the special case of separated and non-nested primitive recursive schemes hence we obtain the decidability of the equivalence problem for separated and non-nested attribute systems (they are necessarly strongly noncircular). Our proof generalizes the decidability of the equivalence problem for purely synthesized attribute systems solved in Courcelle et al. (1982). As a corollary we obtain the decidability of the equivalence problem for nonnested recursive schemes shown to be decidable in Courcelle (1978) with help of a chain of reductions to the equivalence problem for finite-turn DPDAs shown to be decidable by Valiant (1974). The present proof does not use any reduction to finite-turn DPDAs. But it uses the formalism of decision systems introduced in Courcelle (1983).