Abstract. Robotics researchers will be aware of Dexter Kozen's contributions to algebraic algorithms, which have enabled the widespread use of the theory of real closed fields and polynomial arithmetic for motion planning. However, Dexter has also made several important contributions to the theory of information invariants, and produced some of the most profound results in this field. These are first embodied in his 1978 paper On the Power of the Compass, with Manuel Blum. This work has had a wide impact in robotics and nanoscience.Starting with Dexter's insights, robotics researchers have explored the problem of determining the information requirements to perform robot tasks, using the concept of information invariants. This represents an attempt to characterize a family of complicated and subtle issues concerned with measuring robot task complexity.In this vein, several measures have been proposed [14] to measure the information complexity of a task: (a) How much internal state should the robot retain? (b) How many cooperating robots are required, and how much communication between them is necessary? (c) How can the robot change (side-effect) the environment in order to record state or sensory information to perform a task? (d) How much information is provided by sensors? and (e) How much computation is required by the robot? We have considered how one might develop a kind of "calculus" on (a) -(e) in order to compare the power of sensor systems analytically. To this end, information invariants is a theory whereby one sensor can be "reduced" to another (much in the spirit of computation-theoretic reductions), by adding, deleting, and reallocating (a) -(e) among collaborating autonomous robots. As we show below, this work steers using Dexter's compass.
The Power of the CompassIn 1978, Blum and Kozen wrote a ground-breaking paper on maze-searching automata [2,38]. This chapter is devoted to a discussion of their results, On The Power of the Compass [2], and we interpret their results in the context of autonomous mobile robots and information invariants. Transformation, Universal Reduction, etc.); these are described in Section 3.3. Small roman numerals (i), (ii) denote resources for information invariants in massively-parallel distributed manipulation and nanoscience (Section 3.2).
The Scales Fall from My EyesFrom 1987-1997, I taught at Cornell, just down the hall from Dexter. My health was excellent. Every morning I drank Pepsi before teaching large undergraduate programming lectures. Each afternoon I drank espresso and wrote papers, while watching the sun set over Lake Cayuga from my office (which was the largest lair, with the best view, in Upson Hall). In the evenings I would eat dinner with Dan Huttenlocher or Ramin Zabih, and at night I played in Dexter's band, The Steamin' Weenies. I tended a large flock of enthusiastic graduate students and post-docs working on robotics. In 1990, my student Jim Jennings and I posed the following: Question 1.[35] "Let us consider a rational reconstruction of mobile robot...