The implications of a specific pseudometric on the collection of languages over a finite alphabet are explored. In distinction from an approach in (Calude et al., 2009) that relates to collections of infinite or bi-infinite sequences, the present work is based on an adaptation of the “Besicovitch” pseudometric introduced by Besicovitch (1932) and elaborated in (Cattaneo et al., 1997) in the con...

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...

We formulate a compositional specification theory for interface automata, where a component model specifies the allowed sequences of input and output interactions with the environment. A trace-based linear-time refinement is provided, which is the weakest preorder preserving substitutivity of components, and is weaker than the classical alternating simulation defined on interface automata. Sinc...

In Dhar’s model of abelian distributed processors, finite automata occupy the vertices of a graph and communicate via the edges. A local commutativity condition ensures that the final output does not depend on the order in which the automata process their inputs. We consider the halting problem for such networks and the critical group, an invariant that governs the behavior of the network on la...

We study the switching aspects of molecular computing from a novel algebraic point of view. Our approach is based on the concept indexed monoidal algebra, which provides an equivalent formalism for compact closed categories being used recently in the literature in connection with quantum computing. The point is to separate syntax, as the algebra G of graphs, from semantics, which is related to ...

We introduce sampled data hybrid automata (SDHA) as a formal model of hybrid systems that result from clock-driven computer control of continuous dynamic sytems. In contrast to standard hybrid automata, the discrete state transitions in the SDHA can occur only at valid sampling times when the guard conditions are evaluated. Sequences of valid sampling times are defined by a clock structure that...

In Dhar’s model of abelian distributed processors, finite automata occupy the vertices of a graph and communicate via the edges. A local commutativity condition ensures that the output of such a network does not depend on the order in which the automata process their inputs. In this paper (the first of a series) we consider the halting problem for such networks and the crticial group, an invari...

This paper concerns computational methods for verifying properties of polyhedral invariant hybrid automata (PIHA), which are hybrid automata with discrete transitions governed by polyhedral guards. To verify properties of the state trajectories for PIHA, the planar switching surfaces are partitioned to define a finite set of discrete states in an approximate quotient transition system (AQTS). S...

A language L is prefix-closed if w ∈ L implies that every prefix of w is in L. It is known that a regular language is prefix-closed if and only if it is accepted by a nondeterministic finite automaton (NFA) with all states final [18]. In the minimal incomplete deterministic finite automaton (DFA) for a prefix-closed language, all the states are final as well. The authors of [18] examined severa...

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 Osius [20] and Taylor [27]. Finally, ...