Verifying time complexity of Turing machines

Verifying time complexity of Turing machines

We show that, for all reasonable functions T (n) = o(n log n), we can algorithmically verify whether a given one-tape Turing machine runs in time at most T (n). This is a tight bound on the order of growth for the function T because we prove that, for T (n) ≥ (n+1) and T (n) = Ω(n log n), there exists no algorithm that would verify whether a given one-tape Turing machine runs in time at most T ...

Space Complexity in Infinite Time Turing Machines

1 9 M ay 2 01 4 Verifying Time Complexity of Deterministic Turing Machines ∗

We show that, for all reasonable functions T (n) = o(n log n), we can algorithmically verify whether a given one-tape Turing machine runs in time at most T (n). This is a tight bound on the order of growth for the function T because we prove that, for T (n) ≥ (n+1) and T (n) = Ω(n log n), there exists no algorithm that would verify whether a given one-tape Turing machine runs in time at most T ...

Verifying whether One-Tape Turing Machines Run in Linear Time

We discuss the following family of problems, parameterized by integersC ≥ 2 andD ≥ 1: Does a given one-tape q-state Turing machine make at mostCn+D steps on all computations on all inputs of length n, for all n? Assuming a fixed tape and input alphabet, we show that these problems are co-NP-complete and we provide good lower bounds. Specifically, these problems can not be solved in o(q(C−1)/4) ...

Turing Machines and Understanding Computational Complexity

We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.