Synchronized Alternating Turing Machines on Four-Dimensional Input Tapes

Synchronized alternating machine is an alternating machine with a special subset of internal states called synchronizing states. This paper introduces a four-dimensional synchronized alternating Turing machine (4-SATM ), and investigates fundamental properties of 4-SATM ’s. The main topics of this paper are: (1) a relationship between the accepting powers of 4-SATM ’s and four-dimensional alternating Turing machines with small space bounds, (2) a relationship between the accepting powers of seven-way and eight-way 4-SATM ’s, (3) a relationship between the accepting powers of 4-SATM ’s and four-dimensional nondeterministic Turing machines. In this paper, we let each sidelength of each input tape of these automata be equivalent in order to increase the theoretical interest. Key–Words: alternation, computational complexity, configuration, four-dimensional Turing machine, synchronization