New types of systems of fuzzy relation inequalities and equations, called weakly linear, have been recently introduced in [J. Ignjatović, M. Ćirić, S. Bogdanović, On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081–3113.]. The mentioned paper dealt with homogeneous weakly linear systems, composed of fuzzy relati...

In this paper, we prove that any BL-general fuzzy automaton (BL-GFA) and its quotient have the same behavior. In addition, we obtain the minimal quotient BL-GFA and minimal quotient transformation of the BL-GFA, considering the notion of maximal admissible partition. Furthermore, we show that the number of input symbols and time complexity of the minimal quotient transformation of a BL-GFA are ...

Modular design aims at building complex reactive systems by assembling components, possibly taken off-the-shelf. This approach can be supported by a specification theory in which requirements correspond to specifications while components are models of the specifications. In this article, we consider components which have to fulfill a reachability objective. A difficulty is then induced by the f...

We consider the setting of component-based design for realtime systems with critical timing constraints. Based on our earlier work, we propose a compositional specification theory for timed automata with I/O distinction, which supports substitutive refinement. Our theory provides the operations of parallel composition for composing components at run-time, logical conjunction/disjunction for ind...

The partial derivative automaton (Apd) is usually smaller than other non-deterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptoti...

We present a constructive formalization of the Myhill-Nerode theorem on the minimization of nite automata that follows the account in Hopcroft and Ullman's book Formal Languages and Their Relation to Automata. We chose to formalize this theorem because it illustrates many points critical to formalization of computational mathematics, especially the extraction of an important algorithm from a pr...

A major problem in applying model checking to finite–state systems is the potential combinatorial explosion of the state space arising from parallel composition. Solutions of this problem have been attempted for practical applications using a variety of techniques. Recent work by Andersen [And95] proposes a very promising compositional model checking technique, which has experimentally been sho...

In order to study control problems for hybrid systems, we generalize hybrid automata to hybrid games |say, controller vs. plant. If we specify the continuous dynamics by constant lower and upper bounds, we obtain rectangular games. We show that for rectangular games with objectives expressed in Ltl (linear temporal logic), the winning states for each player can be computed, and winning strategi...

prolonged excessive intake of fluoride during child's growth and development stages has been associated with mental and physical problems. the aim of this study was to investigate the effect of excessive fluoride intake on the intelligence quotient (iq) of children living in five rural areas in makoo/iran.in this cross-sectional study, 293 children aged 6-11 years were selected from five villag...