The notion of a generalized sum and the composition theorem to reduce the monadiac second-order thery of the generalized sum to the monadic second-order theories of the summands and of its index structure are presented. The theorems reduce reasoning about compound data structures to reasoning about their parts. The composition theorem for linear orders is used to obtain decidability results for the monadiac theory of linear orders. It is concluded that the compositional method is useful for the proofs of the limitation of the expressive power and also for the proofs of positive results on the expressive power.
|Number of pages||3|
|Journal||Electronic Notes in Theoretical Computer Science|
|State||Published - 1 Mar 2005|
|Event||Proceedings of the 11th Workshop on Logic, Language, Information and Computation (WoLLIC 2004) - |
Duration: 19 Jul 2004 → 22 Jul 2004