Insertion Operations on Deterministic Reversal-Bounded Counter Machines ⇤

Several insertion operations are studied applied to languages accepted by one-way and two-way deterministic reversal-bounded multicounter machines. These operations are defined by the ideals obtained from relations such as the prefix, infix, sux and outfix relations. The insertion of regular languages and other languages into deterministic reversal-bounded multicounter languages is also studied. The question of whether the resulting languages can always be ac-cepted by deterministic machines with the same number of turns on the input tape, the same number of counters, and reversals on the counters is investi-gated. In addition, the question of whether they can always be accepted by increasing either the number of input tape turns, counters, or counter reversals is addressed. The results in this paper form a complete characterization based on these parameters. Towards these new results, a new technique is created for simultaneously showing a language cannot be accepted by both one-way deter-ministic reversal-bounded multicounter machines, and by two-way deterministic machines with one reversal-bounded counter