An abstract theory of sensor eventification

Unlike traditional cameras, event cameras measure changes in light intensity and report differences. This paper examines the conditions necessary for other traditional sensors to admit eventified versions that provide adequate information despite outputting only changes. The requirements depend upon the regularity of the signal space, which we show may depend on several factors including structure arising from the interplay of the robot and its environment, the input-output computation needed to achieve its task, as well as the specific mode of access (synchronous, asynchronous, polled, triggered). Further, there are additional properties of stability (or non-oscillatory behavior) that can be desirable for a system to possess and that we show are also closely related to the preceding notions. This paper contributes theory and algorithms (plus a hardness result) that addresses these considerations while developing several elementary robot examples along the way.Comment: 21 pages, 14 figure

A fixed-parameter tractable algorithm for combinatorial filter reduction

What is the minimal information that a robot must retain to achieve its task? To design economical robots, the literature dealing with reduction of combinatorial filters approaches this problem algorithmically. As lossless state compression is NP-hard, prior work has examined, along with minimization algorithms, a variety of special cases in which specific properties enable efficient solution. Complementing those findings, this paper refines the present understanding from the perspective of parameterized complexity. We give a fixed-parameter tractable algorithm for the general reduction problem by exploiting a transformation into minimal clique covering. The transformation introduces new constraints that arise from sequential dependencies encoded within the input filter -- some of these constraints can be repaired, others are treated through enumeration. Through this approach, we identify parameters affecting filter reduction that are based upon inter-constraint couplings (expressed as a notion of their height and width), which add to the structural parameters present in the unconstrained problem of minimal clique covering.Comment: 8 pages, 4 figure