Wireless Parallel Computing and Its Links to Descriptive Complexity

Abstract. Wireless Parallel Turing Machine (WPTM) is a new computational model recently introduced and studied by the authors. Its design captures important features of wireless mobile computing. In this paper we survey the results related to the descriptive complexity aspects of the new model. In particular, we show a tight relationship of wireless parallel computing to alternating and synchronized alternating Turing machines. This relationship opens, e.g., the road to circuit complexity by offering an elegant WPTM characterization of bounded uniform circuit families, such as NC and NC i. The structural properties of computational graphs of WPTM computations inspire definitions of new complexity measures capturing important aspects of wireless computations: energy consumption and the number of broadcasting channels used during computation. These measures do not seem to have direct counterparts in alternating computations. We mention some results related to these new structural measures, e.g., a polynomial time–bounded complexity hierarchy based on channel complexity, lying between P and PSPACE which seems to be incomparable to the standard polynomial–time alternating hierarchy