Roth’s equivalence problem in unit regular rings

The Equivalence Problem over Finite Rings

We investigate the computational complexity of deciding whether or not a given polynomial , presented as the sum of monomials, is identically 0 over a ring. It is proved that if the factor by the Jacobson-radical is not commutative, then the problem is coNP-complete.

Commuting $pi$-regular rings

R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.

The Equivalence Problem for LL - and L / ? - Regular Grammars

The equivalence problem for context-free grammars is “given two arbitrary grammars, do they generate the same language ?” Since this is undecidable in general attention has been restricted to decidable subclasses of the context-free grammars. For example, the classes of U(k) grammars and real-time strict deterministic grammars. In this paper it is shown that the equivalence problem for U-regula...

The Equivalence Problem for LL- and LR-Regular Grammars

Questions whether or not two grammars belonging to a family of grammars generate the same language have extensively been studied in the literature. These problems are called equivalence problems and if there exists an algorithm which for each pair of grammars of this family gives an answer to this question then the equivalence problem for this family of grammars is said to be decidable. Otherwi...

Normal Ideals in Regular Rings