Multiple Equality Sets and Post Machines

Abstract Equality sets of finite sets of homomorphisms are studied as part of formal language theory. Some particular equality sets, called Merge k ( k -COPY), are investigated. These languages are combinatorially difficult, and are full semiAFL generators of the recursively enumerable sets, and are semiAFL generators of the class MULTI-RESET, provided k ⩾ 3. To accomplish this characterization, equality sets are related to multihead and multitape Post machines operating in real time. A Post machine has a one-way input tape and Post tapes as storage tapes, which in the multihead version are scanned from left to right by a write head and several read heads. By simulating Post machines by multiple reset machines, and vice versa, several new characterisations of the class MULTI-RESET are obtained, and it is shown that for multihead and multitape Post machines linear time is no more powerful than real time, and two Post tapes or, alternatively, three heads on one Post tape are as powerful as any finite number of heads or tapes. Finally, some complexity bounds for equality sets and Post machines are discussed.

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