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We present several new results on minimal space requirements to recognize a nonregular language: (i) realtime nondeterministic Turing machines can recognize a nonregular unary language within weak log log n space, (ii) log log n is a tight space lower bound for accepting general nonregular languages on weak realtime pushdown automata, (iii) there exist unary nonregular languages accepted by realtime alternating one-counter automata within weak log n space, (iv) there exist nonregular languages accepted by two-way deterministic pushdown automata within strong log log n space, and, (v) there exist unary nonregular languages accepted by two-way one-counter automata using quantum and classical states with middle log n space and bounded error.

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