Remarks on Separating Words

On the gap between separating words and separating their reversals

A deterministic finite automaton (DFA) separates two strings w and x if it accepts w and rejects x. The minimum number of states required for a DFA to separate w and x is denoted by sep(w, x). The present paper shows that the difference ∣∣sep(w, x)− sep(w, xR)∣∣ is unbounded for a binary alphabet; here w stands for the mirror image of w. This solves an open problem stated in [Demaine, Eisenstat...

On Partitions Separating Words

Partitions {Lk}k=1 of A + into m pairwise disjoint languages L1, L2, . . . , Lm such that Lk = L + k for k = 1, 2, . . . , m are considered. It is proved that such a closed partition of A+ can separate the words u1, u2, . . . , um ∈ A+ (i.e. each Lk contains exactly one word of the sequence u1, u2, . . . , um) if and only if for each pair i, j of distinct elements in {1, 2, . . . , m}, the word...

Some Remarks on Regular Words

SOME REMARKS ON ALMOST UNISERIAL RINGS AND MODULES

In this paper we study almost uniserial rings and modules. An R−module M is called almost uniserial if any two nonisomorphic submodules are linearly ordered by inclusion. A ring R is an almost left uniserial ring if R_R is almost uniserial. We give some necessary and sufficient condition for an Artinian ring to be almost left uniserial.

Semantic Adequacy in Translation: Strategies employed in the English renderings of Sa'di's wittical remarks of The Rose Garden (Golistan)

Translating literary works is a difficult task, especially when it comes to cultural elements. It gets more difficult when words have ambiguities and multiple layers of meaning. The present study sought to examine the adequacy of witticism in the English renderings of Sa'di's clever remarks in Golistan (The Rose Garden). To this purpose, the researchers selected three English translations of Go...