Spatial Representation and Navigation in a Bio-inspired Robot

A biologically inspired computational model of rodent repre-sentation?based (locale) navigation is presented. The model combines visual input in the form of realistic two dimensional grey-scale images and odometer signals to drive the firing of simulated place and head direction cells via Hebbian synapses. The space representation is built incrementally and on-line without any prior information about the environment and consists of a large population of location-sensitive units (place cells) with overlapping receptive fields. Goal navigation is performed using reinforcement learning in continuous state and action spaces, where the state space is represented by population activity of the place cells. The model is able to reproduce a number of behavioral and neuro-physiological data on rodents. Performance of the model was tested on both simulated and real mobile Khepera robots in a set of behavioral tasks and is comparable to the performance of animals in similar tasks

On locally checkable properties

Abstract. The large computational price of formal verification of general ωregular properties has led to the study of restricted classes of properties, and to the development of verification methodologies for them. Examples that have been widely accepted by the industry include the verification of safety properties, and bounded model checking. We introduce and study another restricted class of properties – the class of locally checkable properties. For an integer k ≥ 1, a language L ⊆ Σ ω is k-checkable if there is a language R ⊆ Σ k (of “allowed subwords”) such that a word w belongs to L iff all the subwords of w of length k belong to R. A property is locally checkable if its language is k-checkable for some k. Locally checkable properties, which are a special case of safety properties, are common in the specification of systems. In particular, one can often bound an eventuality constraint in a property by a fixed time frame. The practical importance of locally checkable properties lies in the low memory demand for their run-time verification. A monitor for a k-checkable property needs only a record of the last k computation cycles. Furthermore, even if a large number of k-checkable properties are monitored, the monitors can share their memory, resulting in memory demand that do not depend on the number of properties monitored. This advantage of locally checkable properties makes them particularly suitable for run-time verification. In the paper, we define locally checkable languages, study their relation to other restricted classes of properties, study the question of deciding whether a property is locally checkable, and study the relation between the size of the property (specified by an LTL formula or an automaton) and the smallest k for which the property is k-checkable.