Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...

Hybrid systems are dynamical systems with the ability to describe mixed discretecontinuous evolution of a wide range of systems. Consequently, at first glance, hybrid systems appear powerful but recalcitrant, neither yielding to analysis and reasoning through a purely continuous-time modeling as with systems of differential equations, nor open to inferential processes commonly used for discrete...

Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalised powe...

Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis of real-time systems whose correctness depends on relative magnitudes of different delays. Conseque...

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...

in this paper, our focus of attention is the proper propagationof fuzzy degrees in determinization of $nondeterministic$ $fuzzy$$finite$ $tree$ $automata$ (nffta). initially, two determinizationmethods are introduced which have some limitations (one inbehavior preserving and other in type of fuzzy operations). inorder to eliminate these limitations and increasing theefficiency of ffta, we defin...

A regular event is star-free if it can be denoted by a regular expression involving only Boolean operations and concatenation (dot). The family of star-free events can be constructed by alternately applying Boolean operations and concatenation. This approach leads to a hierarchy of star-free events, and to the definition of "dot-depth" of a star-free event which appears to be useful as a measur...