Pseudo-natural algorithms for the word problem for finitely presented monoids and groups
Journal of Symbolic Computation
Journal of Symbolic Computation
Termination proofs and the length of derivations
RTA-89 Proceedings of the 3rd international conference on Rewriting Techniques and Applications
String-rewriting systems
Termination proofs by multiset path orderings imply primitive recursive derivation lengths
Theoretical Computer Science - Selected papers of the Second International Conference on algebraic and logic programming, Nancy, France, October 1–3, 1990
Infinite string rewrite systems and complexity
Journal of Symbolic Computation
Computable analysis: an introduction
Computable analysis: an introduction
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
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We study the derivational complexities of string rewriting systems. We discuss the following fundamental question: which functions can be derivational complexities of terminating finite string rewriting systems? They are recursive, but for any recursive function, there is a derivational complexity larger than it. We relate them to the time functions of Turing machines. In particular, we show that the functions n^@a(@a2) and @a^n(@a1) for a real number @a are equivalent to the derivational complexity of some finite string rewriting systems if the computational complexity of @a is relatively low (for example, @a is rational, algebraic, @p or e). On the other hand, they cannot be equivalent to any derivational complexities if the complexity of @a is high.