A Survey of Results on Stateless Multicounter Automata

A stateless multicounter machine has m-counters operating on a one-way input delimited by left and right end markers. A move of the machine depends only on the symbol under the input head and the sign pattern of the counters. An input string is accepted if, when the input head is started on the left end marker with all counters zero, the machine eventually reaches the configuration where the input head is on the right end marker with all the counters again zero. We bring together a number of results on stateless multicounter automata of various different types: deterministic, nondeterministic, realtime (the input head moves right at every step), or non-realtime. We investigate realtime and non-realtime machines in both deterministic and nondeterministic cases with respect to the number of counters and reversals. In addition to hierarchy results, we also consider closure properties and the connections to stateless multihead automata.