How many queries are needed to learn?
Journal of the ACM (JACM)
An Overview of the Theory of Computational Complexity
Journal of the ACM (JACM)
Unary Pushdown Automata and Auxiliary Space Lower Bounds
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Nondeterministic one-tape off-line turing machines and their time complexity
Journal of Automata, Languages and Combinatorics
Theory of one-tape linear-time Turing machines
Theoretical Computer Science
Theoretical Computer Science
| Hi-index | 0.01 |
Any sequential machine M represents a function fM from input sequences to output symbols. A function f is representable if some finite-state sequential machine represents it. The function fM is called an n-th order approximation to a given function f if fM is equal to f for all input sequences of length less than or equal to n. It is proved that, for an arbitrary nonrepresentable function f, there are infinitely many n such that any sequential machine representing an nth order approximation to f has more than n/2 + 1 states. An analogous result is obtained for two-way sequential machines and, using these and related results, lower bounds are obtained for two-way sequential machines and, using these and related results, lower bounds are obtained on the amount of work tape required online and offline Turing machines that compute nonrepresentable functions.