Variances of solution values that can be calculated in polynomial time may be associated with an instance of the Quadratic Assignment Problem (QAP). The problem of graph isomorphism can be modeled as a QAP, associating each data matrix with each graph. In this work, we look for invariant edge weight functions for the graphs composing the instances in order to try to find quantitative difference...

Combining the the results of A.R. Meyer and L.J. Stockmeyer " The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space " , and K.S. Booth " Iso-morphism testing for graphs, semigroups, and finite automata are polynomiamlly equivalent problems " shows that graph isomorphism is PSPACE-complete. The equivalence problem for regular expressions was shown to be PSPACE-...

We show that Graph Isomorphism is in the complexity class SPP, and hence it is in ⊕P (in fact, it is in ModkP for each k ≥ 2). We derive this result as a corollary of a more general result: we show that a generic problem FIND-GROUP has an FPSPP algorithm. This general result has other consequences: for example, it follows that the hidden subgroup problem for permutation groups, studied in the c...

The greatest characteristic string (GCS) of an undirected graph is a new invariant such that two such graphs are isomorphic if and only if they have the same GCS. We define the invariant, and describe an efficient algorithm for evaluating it. A formal definition of the algorithm is given, and a correctness justification is presented. Timing and operation count studies on an implementation indic...

We study the complexity of isomorphism testing for boolean functions that are represented by decision trees or decision lists. Our results are the following: • Isomorphism testing of rank 1 decision trees is complete for logspace. • For any constant r ≥ 2, isomorphism testing for rank r decision trees is polynomial-time equivalent to Graph Isomorphism. As a consequence of our reduction, we obta...