in this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $l$-setting. this construction is illustrated by an example. we also prove that for an $l$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $l$-subset provided the given $l$-subset possesses sup-property.

We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we prove that the context-free language L1 ∗ = {ab : n ≥ 1}∗ can not be recognized by any rational monoid automaton over a finitely generated permutable monoid. We show that the class of la...

Tiling is a technique used for exploiting medium-grain parallelism in nested loops. It relies on a rst step that detects sets of permutable nested loops. All algorithms developed so far consider the statements of the loop body as a single block, in other words, they are not able to take advantage of the structure of dependences between diierent statements. In this paper, we overcome this limita...

We propose local versions of monotonicity for Boolean and pseudoBoolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives changes in sign on tuples which differ in less than p positions. As it turns out, this parameterized notion provides a hierarchy of monotonicities for pseudo-Boolean (Boolean) functions. Local monotonicities are ...

Partial orders and the clones of functions preserving them have been thoroughly studied in recent years. The topic of this papers is strict orders which are irreflexive, asymmetric and transitive subrelations of partial orders. We call an algebra A = (A,Ω) strictly order primal if for some strict order (A,<) the term functions are precisely the functions which preserve this strict order. Our ap...

Tiling is a technique used for exploitingmedium grain parallelism in nested loops It relies on a rst step that detects sets of permutable nested loops All algorithms developed so far consider the statements of the loop body as a single block in other words they are not able to take advantage of the structure of dependences between di erent statements In this report we overcome this limitation b...