Finite Set Of Operations Research Articles

GENCLO AND TERMEQUIV ARE EXPTIME-COMPLETE

In 1999, Bergman et al. showed that the following two problems are EXPTIME-complete: GENCLO, which decides whether an operation on a finite set A belongs to a clone generated by a finite set of operations on A; and TERMEQUIV, which decides whether two algebras on the same finite set and with finitely many fundamental operations are term-equivalent. However, the proof of one of the key statements was not correct. Using the techniques proposed by Bergman et al., in this paper we present the correct proof.

The Set of Finite Operators is Nowhere Dense

AbstractA bounded linear operator A on a complex, separable, infinite dimensional Hilbert space is called finite if for each . It is shown that the class of all finite operators is a closed nowhere dense subset of