DLOGTIME
Incomputational complexity theory,DLOGTIMEis thecomplexity classof allcomputational problemssolvable in alogarithmicamount ofcomputation timeon a deterministicTuring machine.It must be defined on arandom-access Turing machine,since otherwise the input tape is longer than the range of cells that can be accessed by the machine. It is a very weak model of time complexity: no random-access Turing machine with a smaller deterministic time bound can access the whole input.[1]
Examples
[edit]DLOGTIME includes problems relating to verifying the length of the input,[1]for example the problem "Is the input of even length?",which can be solved in logarithmic time usingbinary search.
Applications
[edit]DLOGTIME-uniformityis important incircuit complexity.[1][2]
References
[edit]- ^abcJohnson, David S. (1990), "A catalog of complexity classes",Handbook of theoretical computer science, Vol. A,Elsevier, Amsterdam, pp. 67–161,MR1127168.See in particularp. 140.
- ^Allender, Eric; Gore, Vivek (1993), "On strong separations from AC0",Advances in computational complexity theory (New Brunswick, NJ, 1990),DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 13, Amer. Math. Soc., Providence, RI, pp. 21–37,MR1255326.See in particularp. 23.