The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behaviour of cellular automata in the new topology and show that, under suitable additional hypotheses, they retain certain properties possessed in the usual product top...

Positions and derivatives are two essential notions in the conversion methods from regular expressions to equivalent finite automata. Partial derivative based methods have recently been extended to regular expressions with intersection. In this paper, we present a position automaton construction for those expressions. This construction generalizes the notion of position making it compatible wit...

For set functors preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. And the initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Taylor [16]. Finally, the initial ite...

The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behavior of cellular automata in the new topology and show that, under suitable additional hypotheses, they retain certain properties possessed in the usual product topo...

In this paper, the concepts of somewhat fuzzy automata continuous functions and somewhat fuzzy automata open functions in fuzzy automata topological spaces are introduced and some interesting properties of these functions are studied. In this connection, the concepts of fuzzy automata resolvable spaces and fuzzy automata irresolvable spaces are also introduced and their properties are studied.

9 Let X be a tree and letG=Aut(X), Bass and Tits have given an algorithm to construct the ‘ultimate quotient’ of X by G starting with any quotient of X, an ‘edge-indexed’ graph. Using a sequence of 11 integers that we compute at consecutive steps of the Bass–Tits (BT) algorithm, we give a lower bound on the diameter of the ultimate quotient of a tree by its automorphism group. For a tree X with...

We adapt direct, delayed, and fair simulation to alternating Büchi automata. Unlike with nondeterministic Büchi automata, naive quotients do not preserve the recognized language. As a remedy, we present specifically designed definitions of quotients, namely minimax and semi-elective quotients: minimax quotients, which are simple and have a minimum number of transitions, preserve the recognized ...

We study a sound and complete counterexampleguided abstraction refinement (CEGAR) framework for partially observable Markov decision processes (POMDPs). This framework allows automatic reasoning to find a proper abstraction for POMDPs and reduce model checking complexity. A safety fragment of Probabilistic Computation Tree Logic (PCTL), safePCTL, with the finite horizon is considered as system ...

We present novel techniques for eecient controller synthesis for untimed and timed systems with respect to invariance and reacha-bility properties. In the untimed case, we give algorithms for controller synthesis in the context of nite graphs with controllable and uncontrollable edges, distinguishing between the actions of the system and its environment, respectively. The algorithms are on-they...

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...