What is known complexity of language {a | a = x^2}, is it possible there exist deterministic Turing machine (one input tape and one work tape) that accept this language in linear time?
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"linear time" - I'd bet a no. Regexps are linear time in input size, and they are utterly insufficient for this task. Even recognizing palindromes is quadratic, IIRC – John Dvorak May 15 '17 at 20:41
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https://arxiv.org/abs/cs/0310046, https://math.stackexchange.com/q/84040/14578, https://cs.stackexchange.com/q/17975/755 – D.W. May 15 '17 at 21:14