We present a new method for proving termination of term rewriting systems automatically. It is a generalization of the match bound method for string rewriting. To prove that a term rewriting system terminates on a given regular language of terms, we first construct an enriched system over a new signature that simulates the original derivations. The enriched system is an infinite system over an ...

Many applicative programming languages are based on the call-by-value lambda calculus. For these languages tools such as compilers, pa.rtial evaluators, and other transformation systems often make use of rewriting systems that incorporate some form of beta reduction. For purposes of automatic rewriting it is important to develop extensions of beta-value reduction and to develop methods for guar...

In earlier work, we have shown that for confluent term rewrite systems, innermost polynomial runtime complexity induces polytime computability of the functions defined. In this paper, we generalise this result to full rewriting. For that, we again exploit graph rewriting. We give a new proof of the adequacy of graph rewriting for full rewriting that allows for a precise control of the resources...

In the theory of graph rewriting, the use of coalescing rules, i.e., of rules which besides deleting and generating graph items, can coalesce some parts of the graph, turns out to be quite useful for modelling purposes, but, at the same time, problematic for the development of a satisfactory partial order concurrent semantics for rewrites. Rewriting over graphs with equivalences, i.e., (typed h...

Recently, many techniques have been introduced that allow the (automated) classification of the runtime complexity of term rewrite systems (TRSs for short). In earlier work, the authors have shown that for confluent TRSs, innermost polynomial runtime complexity induces polytime computability of the functions defined. In this paper, we generalise the above result to full rewriting. Following our...

A partial monoid P is a set with a partial multiplication × (and total identity 1P ) which satisfies some associativity axiom. The partial monoid P may be embedded in the free monoid P ∗ and the product × is simulated by a string rewriting system on P ∗ that consists in evaluating the concatenation of two letters as a product in P , when it is defined, and a letter 1P as the empty word ǫ. In th...

The efficiency of syntactic analysis by using a set of rewriting rules is greatly influenced by the order or the arrangement of the rules for the application. There are some trials which subdivide the set of rules into subsets and specify the sequence of rule applications, thus avoiding the useless rule applicagions [i]. But the subdivision of the rule set and the specification of the sequence ...

Invertible transformations can be used for realizing a system where development is done in different views, keeping the views consistent with a common model. A method to realize such a system is called automatic Model-View-Controller engineering (MVARE). In this thesis important properties of general MVARE are identified and discussed. The invertibility of a number of rewriting techniques is di...

This work is devoted to an interpretation and computation of the first homology groups of the small category given by a rewriting system. It is shown that the elements of the first homology group may be regarded as the equivalence classes of the flows in a graph of the rewriting system. This is applied to calculating the homology groups of asynchronous transition systems and Petri nets. Example...