Finite-Turn Repetitive Checking Automata and Sequential/ Parallel Matrix Languages

A class of machines capable of recognizing two-dimensional sequential/parallel matrix languages is introduced. It is called "finite-turn repetitive checking automata" (FTRCA). This checking automaton is provided with three READ-WRITE heads, one READ only head, and a control register in its memory to keep track of the internal transition states and the stack symbols. The value of the register ranges from 0 to a finite positive integer k and can repetitively appear as many times as necessary. A one-to-one correspondence is established between the class of FIRCA and (R:R)ML–the smallest class of the sequential/parallel matrix languages. Several closure properties are also investigated.