Dynamic tree isomorphism via first-order updates to a relational database
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Inherent complexity of recursive queries
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Proceedings of the 15th International Conference on Database Theory
Pure pointer programs and tree isomorphism
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
| Hi-index | 0.00 |
We prove that tree isomorphism is not expressible in the language (FO + TC + COUNT). This is surprising since in the presence of ordering the language captures NL, whereas tree isomorphism and canonization are in L ([L90]). To prove this result we introduce a new Ehrenfeucht- Fraisse game for transitive closure logics. As a corresponding upper bound, we show that tree canonization is expressible in (FO + COUNT)[log n]. The best previous upper bound had been (FO + COUNT)[n^O(1)]. ([DM90]). The lower bound remains true for bounded-degree trees, and we show that for bounded-degree trees counting is not needed in the upper bound. These results are the first separations of the unordered versions of the logical languages for NL, AC^1, and ThC^1. Our results were motivated by a conjecture in [EI94a] that (FO + TC + COUNT + 1LO) = NL, i.e., that a one-way local ordering sufficed to capture NL. We disprove this conjecture, but we prove that a TWO-WAY local ordering does suffice, i.e., (FO + TC + COUNT + 2LO)=NL.