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We examine inkdots placed on the input string as a way of providing advice tofinite automata, and establish the relations between this model and thepreviously studied models of advised finite automata. The existence of aninfinite hierarchy of classes of languages that can be recognized with the helpof increasing numbers of inkdots as advice is shown. The effects of differentforms of advice on the succinctness of the advised machines are examined. Wealso study randomly placed inkdots as advice to probabilistic finite automata,and demonstrate the superiority of this model over its deterministic version.Even very slowly growing amounts of space can become a resource of meaningfuluse if the underlying advised model is extended with access to secondarymemory, while it is famously known that such small amounts of space are notuseful for unadvised one-way Turing machines.

Inkdots as advice for finite automata