Characterizations of CD Grammar Systems Working in Competence Mode by Multicounter Machine Resources

Abstract

In this paper we focus on characterizations of cooperating distributed grammar systems (henceforth CDGSs) working in { ≤ k, = k, ≥ k }-competence mode, k ≥ 1, defined in [1], by means of time, space and several other resources of a multicounter machine such as number of counters, reversals or 0-tests. We show that CDGSs working in { ≤ k, = k, ≥ k}-competence mode, k ≥ 1, can be simulated by one-way nondeterministic multicounter machines in linear time and space, with a linear-bounded number of reversals. If we impose restrictions on the capacity of each counter to perform 0-testings, we find that CDGSs working in { ≤ 1, = 1} ∪ { ≥ k | k ≥ 1}-competence mode can be simulated by one-way partially blind multicounter machines in quasirealtime. It is known from [8] that quasirealtime partially blind multicounter machines accept the family of Petri net languages. Consequently, various decision problems for partially blind multicounter machines are decidable. With respect to them, several decidability results, for CDGSs working in competence mode, grammars and systems with regulated rewriting, that emerge from the above simulations are presented, too.