We study various complexity properties of suffix-free regular languages. The quotient complexity of a regular language L is the number of left quotients of L; this is the same as the state complexity of L, which is the number of states in a minimal deterministic finite automaton (DFA) accepting L. A regular language L′ is a dialect of a regular language L if it differs only slightly from L (for...

A language L is prefix-closed if w ∈ L implies that every prefix of w is in L. It is known that a regular language is prefix-closed if and only if it is accepted by a nondeterministic finite automaton (NFA) with all states final [18]. In the minimal incomplete deterministic finite automaton (DFA) for a prefix-closed language, all the states are final as well. The authors of [18] examined severa...

¡v in this paper we consider a strongly regular relation ƒá on hypermodules so that the quotient is amodule (with abelian group) over a fundamental commutative ring. also, we state necessary and sufficientconditions so that the relation ƒá is transitive, and finally we prove that ƒá is transitive on hypermodules.

For a compact space X we consider extending endomorphisms of the algebra C(X) to be endomorphisms of Arens-Hoffman and Cole extensions of C(X). Given a non-linear, monic polynomial p ∈ C(X)[t], with C(X)[t]/pC(X)[t] semi-simple, we show that if an endomorphism of C(X) extends to the Arens-Hoffman extension with respect to p, then it also extends to the simple Cole extension with respect to p. W...

A weakly distance-regular digraph is thick if its attached scheme regular. In this paper, we show that each commutative has a subdigraph such the corresponding quotient falls into six families of digraphs up to isomorphism.

We propose linear systems of hedge language equations (LSH) as a formalism to represent regular hedge languages. These linear systems are suitable for several computations in the algebra of regular hedge languages. We indicate algorithms to translate between representations by hedge automata and LSH, and for the computation of LSH for the intersection, quotient, left and right factors of regula...

In this paper, we are going to introduce a fundamental relation on \(H_{v}BE\)-algebra and investigate some of properties, also construct new \((H_{v})BE\)-algebras via relation. We show that quotient any regular regulation is an quotient, strongly \(BE\)-algebra. Furthermore consider under what conditions relations transitive.