Let K be an anti-ideal of a semigroup (S,=, =, ·, θ) with apartness. A construction of the anti-congruence Q(K) and the quasi-antiorder θ, generated by K, are presented. Besides, a construction of the anti-order relation Θ on syntactic semigroup S/Q(K), generated by θ, is given in Bishop’s constructive mathematics.

A notion of open bisimulation is formulated for the spi calculus, an extension of the πcalculus with cryptographic primitives. This notion of open bisimulation is based on the so-called hedged bisimulation, due to Borgström and Nestmann. Open bisimulation is shown to be sound with respect to hedged bisimulation, and futher, open bisimilarity is shown to be a congruence relation on finite spi pr...

Interactions between different sensory modalities can be observed in unimodal areas of the cortex, as revealed by recent neuroimaging studies. A new report by Macaluso and colleagues ( [this issue of Neuron]) shows that crossmodal effects of tactile stimulation in visual cortex critically depend on the spatial congruence of multisensory inputs. This work is discussed in relation to neural and c...

In this paper we discuss the concepts of rough quasi-ideals and rough bi-ideals in a Γ-semigroup. We study some properties of the lower and upper approximations of such ideals with respect to a congruence relation in Γ-semigroup . Mathematics Subject Classification: 03Exx, 28E15

Imai and Iséki [1] introduced the concept of BCK-algebra as a generalization of notions of set difference operation and propositional calculus. The notion of pseudo-BCK algebra was introduced by Georgescu and Iorgulescu [2] as generalization of BCK-algebras not assuming commutativity. Hájek [3] introduced the concept of BL-algebras as the general semantics of basic fuzzy logic (BL-logic). Iorgu...

Algebraic properties and structures of intuitionistic $$L-$$ fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly, we put forward the notion compatible relation, monoid associated with relation can be effectively constructed, construct two monoids different congruence relations given ILFMA, then prove that they isomorphic. Furthermore, u...

In this paper, we introduce a new class algebras related to BCK-algebras and semigroups, called a KS-semigroup and define an ideal of a KS-semigroups and a strong KS-semigroup, and characterizations of ideals is given. Also we define a congruence relation on a KS-semigroups and a quotient KS-semigroups and prove the isomorphism. Mathematics Subject Classification: 06F35, 03G25

Relations among program variables like 1 + 3 · x1 + 5 · x2 ≡ 0 [224] have been called linear congruence relations. Such a relation is valid at a program point iff it is satisfied by all reaching program states. Knowledge about non-trivial valid congruence relations is crucial for various aggressive program transformations. It can also form the backbone of a program correctness proof. In his sem...

By means of a more precise treatment of the congruence relation between n-extensions we show that it is possible to avoid the Schanuel Lemma for proving some results on the functors Ext. An n-extension E from D to C is an exact sequence of the form (1) 0 C El E2 * * En D 0 in an abelian category. The idea to use congruence classes n-extensions as elements of Ext' (D C) is due to Yoneda ([7], [8...