Lazy rewriting is a proper restriction of term rewriting that dynamically restricts the reduction of certain arguments of functions in order to obtain termination. In contrast to context-sensitive rewriting, reductions at such argument positions are not completely forbidden but delayed. Based on the observation that the only existing (non-trivial) approach to prove termination of such lazy rewr...

The concept of graph substitution recently introduced by the authors is applied to term graphs, yielding a uniform framework for uniication, rewriting, and narrowing on term graphs. The notion of substitution allows deenitions of these concepts that are close to the corresponding deenitions in the term world. The rewriting model obtained in this way is equivalent to \collapsed tree rewriting" a...

Constructing a small BDD from a given boolean formula depends on finding a good variable ordering. Finding a good order is NP-complete. In the past, methods based on heuristic analysis and formula (circuit) rewriting have shown to be useful for specific problem domains. We show that these methods need to be integrated: heuristic analysis can drive rewriting, which in turn simplifies analysis. W...

We develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the ‘no-dangling-edge’ condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions – or motif functions ...

A property P of term rewriting systems is persistent if for any many-sorted term rewriting system R, R has the property P i its underlying term rewriting system (R), which results from R by omitting its sort information, has the property P . It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only variables of the same sort. This is the posit...

We study combinations of many-sorted algebraic term rewriting systems and polymorphic lambda term rewriting. Algebraic and lambda terms are mixed by adding the symbols of the algebraic signature to the polymorphic lambda calculus, as higher-order constants. We show that if a many-sorted algebraic rewrite system R is strongly normalizing (terminating, noetherian), then R + β + η + type-β + type-...

String rewriting systems have been originally introduced by Thue [21] in order to study word problems in monoids. A string rewriting system (Σ,R) consists of a set Σ, called the alphabet, and a set R ⊆ Σ∗×Σ∗ of rules. The monoid Σ∗/≡R, obtained by quotienting the free monoid Σ∗ over Σ by the smallest congruence (wrt concatenation) containing R, is called the monoid presented by the rewriting sy...

BDDs provide an established technique for propositional formula manipulation. In this paper we re-develop the basic BDD theory using standard rewriting techniques. Since a BDD is a DAG instead of a tree we need a notion of shared rewriting and develop appropriate theory. A rewriting system is presented by which canonical ROBDDs can be obtained. For this rewriting system a layerwise strategy is ...

Code generators for modern compilers are difficult to construct. To build a code generator that produces correct target code, we require detailed knowledge of the intermediate representation (IR) generated by the compiler’s front-end and intimate knowledge of the instruction set available on the target machine. We then put this knowledge to use by mapping the individual IR instructions to a seq...