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A Survey of Results on Stateless Multicounter Automata

Ibarra O.H., Egecioglu Ö.

Fundamenta Informaticae

2012

Vol. 116, nr 1-4

129-140

A stateless multicountermachine hasm-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, themachine eventually reaches the configurationwhere 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.