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...

The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [4] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. In this paper we describe a family of...

We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in Σ 2 . In the case of linear matroids, which are represented over polynomially growing fields, we note that the problem is unlikely to be Σ 2 -complete and is coNPhard. We show that when the rank of the matroid is bounded by a constant, linear matroid isomorphism and matroid isomorphism a...

We address the question of whether two multiplayer strategic games are equivalent and the computationalcomplexity of deciding such a property. We introduce two notions of isomorphisms, strong and weak. Each oneof those isomorphisms preserves a different structure of the game. Strong isomorphism are defined to preservethe utility functions and Nash equilibria. Weak isomorphism preser...

Automatic structures are finitely presented structures where the universe and all relations can be recognized by finite automata. It is known that the isomorphism problem for automatic structures is complete for Σ 1 , the first existential level of the analytical hierarchy. Positive results on ordinals and on Boolean algebras raised hope that the isomorphism problem is simpler for transitive re...

Algorithms to decide isomorphism of modules have been honed continually over the last 30 years, and their range of applicability has been extended to include modules over a wide range of rings. Highly efficient computer implementations of these algorithms form the bedrock of systems such as GAP and Magma, at least in regard to computations with groups and algebras. By contrast, the fundamental ...

We introduce a nonlocal game that captures and extends the notion of graph isomorphism. This game can be won in the classical case if and only if the two input graphs are isomorphic. Thus, by considering quantum strategies we are able to define the notion of quantum isomorphism. We also consider the case of more general non-signalling strategies, and show that such a strategy exists if and only...

double system of exponents with complex-valued coefficients is considered. under some conditions on the coefficients, we prove that if this system forms a basis for the morrey-lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.