On the power of communication in alternating machines

Abstract

The synchronized alternating devices are introduced as a generalization of alternating devices. The synchronization enables the communication among parallel processes in alternating computations. A new complexity measure — synchronization complexity is introduced to measure the amount of communication among processes. The basic results covering the reduction theorem for synchronization complexity and simulations among nondeterministic, alternating and synchronized alternating devices are established. There are found very simple devices that, adding synchronized alternation, are as powerful as Turing machines. As opposed to the fact that two-way alternating finite automata recognize only regular languages it is proved that NLOG is exactly the family of languages recognized by two-way synchronized alternating finite automata with parallel complexity 1. Already one-way synchronized alternating finite automata are more powerful than finite automata. However, the log n synchronization adds nothing to any multihead alternating device. Several further results for different types of devices are established. Using simulation through synchronized alternating devices a new simulation result of nondeterministic devices by alternating ones are obtained.