Equivalence classes generated by sequence training.

Equivalence Classes of Permutations under Various Relations Generated by Constrained Transpositions

We consider a large family of equivalence relations on the symmetric group of permutations of n that generalize those discovered by Knuth in his study of the RobinsonSchensted correspondence. In our most general setting, two permutations are equivalent if one can be obtained from the other by a sequence of pattern-replacing moves of prescribed form; however, we limit our focus to patterns where...

Some equivalence classes of operators on B(H)

The graph of equivalence classes and Isoclinism of groups

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

Veriication by State Spaces with Equivalence Classes

This paper demonstrates the potential of veriication based on state spaces reduced by equivalence relations. The basic observation is that quite often, some states of a system are similar, i.e., they induce similar behaviours. Similarity can be formally expressed by deen-ing equivalence relations on the set of states and the set of actions of a system under consideration. A state space can be c...

The Variety Generated by Equivalence Algebras

Every equivalence relation can be made into a groupoid with the same underlying set if we define the multiplication as follows: xy = x if x, y are related; otherwise, xy = y. The groupoids, obtained in this way, are called equivalence algebras. We find a finite base for the equations of equivalence algebras. The base consists of equations in four variables, and we prove that there is no base co...