We propose a dynamic graph-based relational learning approach using graph-rewriting rules to analyze how biological networks change over time. The analysis of dynamic biological networks is necessary to understand life at the systemlevel, because biological networks continuously change their structures and properties while an organism performs various biological activities to promote reproducti...

Rewriting with associativity, commutativity and identity has been an open problem for a long time. In 1989, Baird, Peterson and Wilkerson introduced the notion of constrained rewriting, to avoid the problem of non-termination inherent to the use of identities. We build up on this idea in two ways: by giving a complete set of rules for completion modulo these axioms; by showing how to build appr...

The description of a single state of a modelled system is often complex in practice, but few procedures for synthesis address this problem in depth. We study systems in which a state is described by an arbitrary finite structure, and changes of the state are represented by structure rewriting rules, a generalisation of term and graph rewriting. Both the environment and the controller are allowe...

Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of rewriting is presented in detail. LCF provides a family of rewriting functions, and operators to combine them. A succession of functions is described, from ...

We address the problem of an efficient rewriting strategy for general term rewriting systems. Several strategies have been proposed over the last two decades for rewriting, the most efficient of all being the natural rewriting strategy [9]. All the strategies so far, including natural rewriting, assume that the given term rewriting system is a left-linear constructor system. Although these rest...

A simple method is proposed for testing equivalence in a restricted domain of two given term rewriting systems. By using the Church-Rosser property and the teachability of term rewriting systems, the method allows us to prove equivalence of these systems without the explicit use of induction; this proof usually requires some kind of induction. The method proposed is a general extension of induc...

As term-rewriting has matured, with applications in areas such as automatic program transformation, the necessity of programmed control for applying rules has become apparent. Early term-rewriting systems used a xed strategy, such as innermost-leftmost matching, choosing among possibly overlapping rules nondeterministically. This mode of control is su cient for a con uent, terminating system of...