The tree isomorphism problem is the problem of determining whether two trees are isomorphic. The tree canonization problem is the problem of producing a canonical tree isomorphic to a given tree. The tree comparison problem is the problem of determining whether one tree is less than a second tree in a natural ordering on trees. We present alternating logarithmic time algorithms for the tree iso...

XQuery is a powerful language defined by the W3C to query XML documents. Its query functionalities and its expressiveness satisfy the major needs of both the database community and the text and documents community. As an inconvenient, the grammar used to define XQuery is thus very complex and leads to several equivalent query expressions for one same query. This complexity often discourages XQu...

We study the time complexity of McKay's algorithm to compute canonical forms and automorphism groups of graphs. The algorithm is based on a type of backtrack search, and it performs pruning by discovered auto-morphisms and by hashing partial information of vertex labelings. In practice, the algorithm is implemented in the nauty package. We obtain colorings of F urer's graphs that allow the algo...

We present a logspace algorithm for computing a canonical labeling, in fact a canonical interval representation, for interval graphs. To achieve this, we compute canonical interval representations of interval hypergraphs. This approach also yields a canonical labeling of convex graphs. As a consequence, the isomorphism and automorphism problems for these graph classes are solvable in logspace. ...

Straight-line (linear) context-free tree (SLT) grammars have been used to compactly represent ordered trees. Equivalence of SLT grammars is decidable in polynomial time. Here we extend this result and show that isomorphism of unordered trees given as SLT grammars is decidable in polynomial time. The result generalizes to isomorphism of unrooted trees and bisimulation equivalence. For non-linear...

Motivated by a Tukey classification problem we develop here a new topological Ramsey space R1 that in its complexity comes immediately after the classical Ellentuck space [8]. Associated with R1 is an ultrafilter U1 which is weakly Ramsey but not Ramsey. We prove a canonization theorem for equivalence relations on fronts on R1. This extends the Pudlak-Rödl Theorem canonizing equivalence relatio...