An Infinite Pebble Game and Applications

We generalize the well-known pebble game to infinite dag's, and we use this generalization to give new and shorter proofs of results in different areas of computer science (as diverse as "logic of programs" and "formal language theory"). Our applications here include a proof of a theorem due to Salomaa, asserting the existence of a context-free language with infinite index, and a proof of a theorem due to Tiuryn and Erimbetov, asserting that unbounded memory increases the power of logics of programs. The original proofs by Salomaa, Tiuryn, and Erimbetov, are fairly technical. The proofs by Tiuryn and Erimbetov also involve advanced techniques of model theory, namely, back-and-forth constructions based on a variant of Ehrenfeucht-Fraisse games. By contrast, our proofs are not only shorter, but also elementary. All we need is essentially finite induction and, in the case of the Tiuryn-Erimbetov result, the compactness and completeness of first-order logic.

Fast Head Tilt Detection for Human-Computer Interaction

Accurate head tilt detection has a large potential to aid people with disabilities in the use of human-computer interfaces and provide universal access to communication software. We show how it can be utilized to tab through links on a web page or control a video game with head motions. It may also be useful as a correction method for currently available video-based assistive technology that requires upright facial poses. Few of the existing computer vision methods that detect head rotations in and out of the image plane with reasonable accuracy can operate within the context of a real-time communication interface because the computational expense that they incur is too great. Our method uses a variety of metrics to obtain a robust head tilt estimate without incurring the computational cost of previous methods. Our system runs in real time on a computer with a 2.53 GHz processor, 256 MB of RAM and an inexpensive webcam, using only 55% of the processor cycles.