Traditional automata accept or reject their input, and are therefore Boolean. Lattice automata generalize the traditional setting and map words to values taken from a lattice. In particular, in a fully-ordered lattice, the elements are 0, 1, . . . , n − 1, ordered by the standard ≤ order. Lattice automata, and in particular lattice automata defined with respect to fully-ordered lattices, have i...

A Banaschewski function on a bounded lattice L is an antitone self-map of L that picks a complement for each element of L. We prove a set of results that include the following: • Every countable complemented modular lattice has a Banaschewski function with Boolean range, the latter being unique up to isomorphism. • Every (not necessarily unital) countable von Neumann regular ring R has a map ε ...

We consider n-dimensional Euclidean lattice networks with nearest neighbour coupling architecture. The associated lattice dynamical systems are infinite systems of ordinary differential equations, the cells, indexed by the points in the lattice. A pattern of synchrony is a finite-dimensional flow-invariant subspace for all lattice dynamical systems with the given network architecture. These sub...

A coupled-map lattice showing complex behaviour in presence of a fully negative Lyapunov spectrum is considered. A phase transition from ordered to disordered evolution, upon changing diffusive coupling is studied in detail. Various indicators provide a coherent description of the scenario: the existence of an intermediate transition region characterized by an irregular alternancy of periodic a...

We study the structural stability of coupled map lattice models of hyperbolic type under certain metrics. We prove the existence of equilibrium states for continuous functions on lattice models under the conditions of weak interaction and translation invariance. We also study the uniqueness and ergodic properties of these equilibrium states for HH older continuous functions.

Exact results are obtained for a lattice gas on the 3-12 lattice with twoand three-site interactions. By using a decoration transformation, we map the lattice gas into one on the honeycomb lattice with pure two-site interactions. This procedure permits us to draw exact results for the original 3-12 lattice gas. In particular, we obtain its exact two-phase boundary, and confirm the fact that an ...

This paper examines the application of lattice adaptation techniques to speaker-dependent models for the purpose of conversational telephone speech transcription. Given sufficient training data per speaker, it is feasible to build adapted speakerdependent models using lattice MLLR and lattice MAP. Experiments on iterative and cascaded adaptation are presented. Additionally various strategies fo...

We compare the behavior of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and twopoint correlation with increasing truncated lattice size. This suggests that spatiotemporal embedding techniques...