An important case of hybrid systems are the rectangular automata. First, rectangular dynamics can naturally and arbitrarily closely approximate more general, nonlinear dynamics. Second, rectangular automata are the most general type of hybrid systems for which model checking |in particular, Ltl model checking| is decidable. However, on one hand, the original proofs of decidability did not sugge...

We report here on the structure of reversible quantum cellular automata with the additional restriction that these are also Clifford operations. This means that tensor products of Weyl operators (projective representation of a finite abelian symplectic group) are mapped to multiples of tensor products of Weyl operators. Therefore Clifford quantum cellular automata are induced by symplectic cell...

Hybrid systems are interacting systems of digital automata and continuous plants subject to disturbances. The digital automata are used to force the state trajectory of the continuous plant to obey a performance specification. For the basic concepts and notation for hybrid systems, see Kohn and Nerode (1993), and other papers in the same volume. Here we introduce tools for analyzing enforcing v...

In the last 20 years or so, chemists and molecular biologists have synthesized some novel DNA polyhedra. Polyhedral links were introduced to model DNA polyhedra and study topological properties of DNA polyhedra. As a very powerful invariant of oriented links, the Homfly polynomial of some of such polyhedral links with small number of crossings has been obtained. However, it is a challenge to co...

We explore natural classes of finitely generated semigroups that have word problem decidable by synchronous or asynchronous two-tape finite state automata. Synchronous two-tape automata decide regular word problems and asynchronous automata decide rational word problems. We argue that asynchronous two-tape automata are a more suitable choice than synchronous two-tape automata and show that the ...

Feature selection is of great importance in Quantitative Structure-Activity Relationship (QSAR) analysis. This problem has been solved using some meta-heuristic algorithms such as: GA, PSO, ACO, SA and so on. In this work two novel hybrid meta-heuristic algorithms i.e. Sequential GA and LA (SGALA) and Mixed GA and LA (MGALA), which are based on Genetic algorithm and learning automata for QSAR f...

Correctness of many hybrid and distributed systems require stability and convergence guarantees. Unlike the standard induction principle for verifying invariance, a theory for verifying stability or convergence of automata is currently not available. In this paper, we formalize one such theory proposed by Tsitsiklis [25]. We build on the existing PVS metatheory for untimed, timed, and hybrid in...

In this paper, we introduce the formalism of duration-constrained regular expressions to model real-time and hybrid systems, which is an extension of regular expressions with duration constraints. It is equivalent in expressive power to a class of linear hybrid automata called loop-closed automata in which any variable tested in a loop is reset or tested to exact values in the same loop. Based ...

ion methods are used to simplify models and make their analysis more tractable. Several equivalence relations have been studied for subclasses of hybrid systems. For example, it can be shown that transition systems of timed automata admit finite state abstractions, called region graphs, that are time-abstract bisimilar, see [AD94] for details. Those equivalence results are used to prove decidab...

We present a hybrid architecture of recurrent neural networks (RNNs) inspired by hidden Markov models (HMMs). We train the hybrid architecture using genetic algorithms to learn and represent dynamical systems. We train the hybrid architecture on a set of deterministic finite-state automata strings and observe the generalization performance of the hybrid architecture when presented with a new se...