In recent years there has been a lot of interest in the definition of so-called weakly-relational numeric domains, whose complexity and precision are in between the (non-relational) abstract domain of intervals [9] and the (relational) abstract domain of convex polyhedra [10]. The first weakly-relational domain proposed in the literature is based on systems of constraints of the form x−y ≤ c an...

Independent sets play an important role in matroid theory. In this paper, the definitions of pre-independent fuzzy set system and independent fuzzy set system in L-fuzzy setting are presented. Independent M-fuzzifying set system is introduced and some of its properties are discussed. Further independent (L,M)-fuzzy set system is given and some of its properties are obtained. The relations of th...

In recent years there has been a lot of interest in the definition of so-called weakly-relational numeric domains, whose complexity and precision are in between the (non-relational) abstract domain of intervals [9] and the (relational) abstract domain of convex polyhedra [10]. The first weakly-relational domain proposed in the literature is based on systems of constraints of the form x−y ≤ c an...

In recent years there has been a lot of interest in the definition of so-called weakly-relational numeric domains, whose complexity and precision are in between the (non-relational) abstract domain of intervals [9] and the (relational) abstract domain of convex polyhedra [10]. The first weakly-relational domain proposed in the literature is based on systems of constraints of the form x−y ≤ c an...

Gap-definability and the gap closure operator were defined by S. Fenner, L. Fortnow and S. Kurth (J. Comput. System Sci. 48, 116 148 (1994)). Few complexity classes were known at that time to be gapdefinable. In this paper, we give simple characterizations of both gapdefinability and the gap-closure operator, and we show that many complexity classes are gap-definable, including P, P, PSPACE, EX...

In this paper we systematically explore questions of succinctness in modal logics employed in spatial reasoning. We show that the closure operator, despite being less expressive, is exponentially more succinct than the limit-point operator, and that the μ-calculus is exponentially more succinct than the equally-expressive tangled limit operator. These results hold for any class of spaces contai...

Closure operators are abundant in mathematics; here are a few examples. Given an algebraic structure, such as group, ring, field, lattice, vector space, etc., taking the substructure generated by a set, i.e., the least substructure which includes that set, is a closure operator. Given a binary relation, taking the relation with certain properties, such as reflexive, transitive, equivalence, etc...

In this article we present a fuzzy logic based method for the construction of thoughts of artificial animals (animats). Due to the substantial increase of the processing power of personal computers in the last decade there was a notable progress in the field of animat construction and simulation. Regardless of the achieved results, the coding of the animat’s behaviour is very inaccurate and can...