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 Lin Our proof uses an Ehrenfeucht Fra ss e game for transitive closure logic with counting Gr a IL As a corresponding upper bound we show that tree canonization is expressible in FO COUNT lo...

We show that, for k constant, k-tree isomorphism can be decided in logarithmic space by giving a logspace canonical labeling algorithm. The algorithm computes a unique tree decomposition, uses colors to fully encode the structure of the original graph in the decomposition tree and invokes Lindell’s tree canonization algorithm. As a consequence, the isomorphism, the automorphism, as well as the ...

In recent results the complexity of isomorphism testing on graphs of bounded treewidth is improved to TC [GV06] and further to LogCFL [DTW10]. The computation of canonical forms or a canonical labeling provides more information than isomorphism testing. Whether canonization is in NC or even TC was stated as an open question in [Köb06]. Köbler and Verbitsky [KV08] give a TC canonical labeling al...

We show that the class of chordal claw-free graphs admits LREC=-definable canonization. LREC= is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This operator can be evaluated in logarithmic space. It follows that there exists a logarithmic-space canonization algorithm for the class of chordal claw-free graphs, and tha...

In recent results the complexity of isomorphism testing on graphs of bounded treewidth is improved to TC [GV06] and further to LogCFL [DTW10]. The computation of canonical forms or a canonical labeling provides more information than isomorphism testing. Whether canonization is in NC or even TC was stated as an open question in [Köb06]. Köbler and Verbitsky [KV08] give a TC canonical labeling al...

Motivated by a Tukey classification problem we develop here a new topological Ramsey space R1 that in its complexity comes immediately after the classical is a natural Ellentuck space [5]. 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 is analogous to the Pudlak-Rödl Theorem canonizin...

As organizations reach higher levels of business process management maturity, they often find themselves maintaining very large process model repositories, representing valuable knowledge about their operations. A common practice within these repositories is to create new process models, or extend existing ones, by copying and merging fragments from other models. We contend that if these duplic...

Symmetries of combinatorial objects are known to complicate search algorithms, but such obstacles can often be removed by detecting symmetries early and discarding symmetric subproblems. Canonical labeling of combinatorial objects facilitates easy equivalence checking through quick matching. All existing canonical labeling software also finds symmetries, but the fastest symmetry-finding softwar...

Abstract The first four (out of eight) books Daniello Bartoli’s (1608–85) officially commissioned Istoria della Compagnia di Gesù , dedicated to Asia were devoted recounting the miraculous deeds Francis Xavier (1506–52). A century after his death, and thirty years canonization, was still an influential role model for all Jesuits (especially those who desired become missionaries in “Indies”). Ba...