Infinite String Rewrite Systems and Complexity

Complexity Analysis of Precedence Terminating Infinite Graph Rewrite Systems

The general form of safe recursion (or ramified recurrence) can be expressed by an infinite graph rewrite system including unfolding graph rewrite rules introduced by Dal Lago, Martini and Zorzi, in which the size of every normal form by innermost rewriting is polynomially bounded. Every unfolding graph rewrite rule is precedence terminating in the sense of Middeldorp, Ohsaki and Zantema. Altho...

DAN-based string rewrite computational systems

We describe a DNA computing system called programmed mutagenesis. prove that it is universal, and present experimental results from a prototype computation. DNA is a material with important characteristics, such as possessing all the information necessary for self-reproduction in the presence of appropriate enzymes and components, simple natural evolution mechanism, and miniature scale, all of ...

Automated Complexity Analysis of Term Rewrite Systems

Automation of Recursive Path Ordering for Infinite Labelled Rewrite Systems

Semantic labelling is a transformational technique for proving termination of Term Rewriting Systems (TRSs). Only its variant with finite sets of labels was used so far in tools for automatic termination proving and variants with infinite sets of labels were considered not to be suitable for automation. We show that such automation can be achieved for semantic labelling with natural numbers, in...

Recursive Path Ordering for Infinite Labelled Rewrite Systems

Semantic labelling is a transformational technique for proving termination of Term Rewriting Systems (TRSs). Only its variant with finite sets of labels was used so far in tools for automatic termination proving and variants with infinite sets of labels were considered not to be suitable for automation. We show that such automation can be achieved for semantic labelling with natural numbers, in...