We give new general methods for constructing small non-deterministic 4nite automata (NFA) from arbitrary ones. Given an NFA, we compute the largest right-invariant equivalence on the set of states and then merge the equivalent states to obtain a smaller automaton. When applying this method to position automata, we get a way to convert regular expressions into NFAs which are always smaller than ...

We prove that any noetherian quasi-excellent scheme of characteristic zero admits a strong desingularization which is functorial with respect to all regular morphisms. We show that as an easy formal consequence of this result one obtains strong functorial desingularization for many other spaces of characteristic zero including quasi-excellent stacks and formal schemes, and complex and non-archi...

A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

We investigate a generalization of Hopf algebra slq (2) by weakening the invertibility of the generator K, i.e. exchanging its invertibility KK = 1 to the regularity KKK = K. This leads to a weak Hopf algebra wslq (2) and a J-weak Hopf algebra vslq (2) which are studied in detail. It is shown that the monoids of group-like elements of wslq (2) and vslq (2) are regular monoids, which supports th...

For an anti-congruence q we say that it is regular anti-congruence on semigroup (S,=, =, ·, α) ordered under anti-order α if there exists an antiorder θ on S/q such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anti-congruence q is regular if there exists a quasi-antiorder σ on S under α such that q = σ ∪ σ−1. Besides, for regular anti-congruence q on S, a constr...

The fundamental properties of the class QUASI of quasi-relabeling relations are investigated. A quasi-relabeling relation is a tree relation that is de ned by a tree bimorphism (φ,L, ψ), where φ and ψ are quasi-relabeling tree homomorphisms and L is a regular tree language. Such relations admit a canonical representation, which immediately also yields that QUASI is closed under nite union. Howe...

In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.

Abstract In this paper, we have introduced anti fuzzy quasi-ideals, anti fuzzy bi-(generalized bi-) ideals and anti fuzzy left (right, two-sided) ideals in LA-semigroup. Further we have characterized an intra-regular LA-semigroup by the properties of their anti fuzzy left (right, two-sided) ideals, anti fuzzy bi(generalized bi-)ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals. Fur...

Biglieri showed that a diagram with N states can be used to compute the generating function for any trellis code with N states. Rouanne & Costello and Zehavi & Wolf showed that for quasi-regular trellis codes, an N -state diagram produces the correct generating function. Schlegel showed that application of a standard FSM (finite-state-machine) minimization algorithm reduces quasi-regular trelli...

A result of Steinberg's on the existence of rational regular unipotent elements in quasi-split simple algebraic groups over fields of arbitrary characteristic is partially extended to the case of non-quasi-split groups.