We investigate the complexity of the syntactic isomorphism problem of CNF Boolean Formulas (CSFI): given two CNF Boolean formulas φ(a1, . . . , an) and φ(b1, . . . , bn) decide whether there exists a permutation of clauses, a permutation of literals and a bijection between their variables such that φ(a1, . . . , an) and φ(b1, . . . , bn) become syntactically identical. We first show that the CS...

We give a new upper bound for the Group and Quasigroup Isomorphism problems when the input structures are given explicitly by multiplication tables. We show that these problems can be computed by polynomial size nondeterministic circuits of unbounded fan-in with O(log log n) depth and O(log n) nondeterministic bits, where n is the number of group elements. This improves the existing upper bound...

With the emergence of the big data concept, the big graph database model has become very popular since it provides strong modeling for complex applications and fast querying, especially for the cases that require costly join operations in RDBMs. However, it is a big challenge to find all exact matches of a query graph in a big graph database, which is known as the subgraph isomorphism problem. ...

This paper addresses the problem of finding a class of representative itemsets up to subitemset isomorphism. An efficient algorithm is of practical importance in the domain of optimal sorting networks. Although only exponential algorithms for solving the problem exist in the literature, the complexity classification of the problem has never been addressed. In this paper, we present a complexity...

Graph isomorphism checking can be used in graph-based model checking to achieve symmetry reduction. Instead of one-to-one comparing the graph representations of states, canonical forms of state graphs can be computed. These canonical forms can be used to store and compare states. However, computing a canonical form for a graph is computationally expensive. Whether computing a canonical represen...

We study the complexity of the Graph Isomorphism problem on graph classes that are characterized by a finite number of forbidden induced subgraphs, focusing mostly on the case of two forbidden subgraphs. We show hardness results and develop techniques for the structural analysis of such graph classes, which applied to the case of two forbidden subgraphs give the following results: A dichotomy i...

The isomorphism problem is neither known to be NP-complete nor polynomial. Yet it is crucial for managing large conceptual graph sets. In order to speed up the conceptual graph isomorphism test, we associate to graphs a textual code that is invariant under isomorphism: a structural or ltering code. The structural code of a given graph is based on the computation by a structural function of an i...

We show that the number of variables and quantifier depth needed to distinguish a pair graphs by first-order logic sentences exactly match complexity measures clause width refute corresponding graph isomorphism formula in propositional narrow resolution. Using this connection, we obtain upper lower bounds for refuting formulas (normal) In particular, if k is minimum two with n vertices each, th...

In this lecture, I will present three results related to Strongly Regular Graphs. 1. An algorithm for testing isomorphism of SRGs that runs in time 2 O(√ n log n). 2. A proof that f and g, the dimensions of the eigenspaces, are both at least √ n. The problem of testing isomorphism of graphs is often reduced to the problem of giving each vertex in a graph a unique name. If we have a way of doing...