Can real-time deterministic multicounter automata recognize the marked palindrome language?
I realized that in Fischer, Meyer, and Rosenberg (1968) Theorem 1.3, it is proven that "The language of marked palindrome is not recognizable by any one-way $k-CM$ which operates in time less than $T(n) = 2^{(n/2k)}$." 

The same result also appears in Petersen (2009).