We formalize a local model checker in rewriting logic and use it to analyze an infinite-state system in this paper. In order not to pursue infinite computation path endlessly, we perform bounded proof search on the system. Inconclusive proofs occurred in the bounded search are formalized by introducing three-valued logic in our local model checker. We therefore demonstrate how to use rewriting ...

We consider a variant of graph developing system and show various behavior with one type of graph-rewriting. This system is based on rewriting of 3-regular graphs with two possible states per node. We focus on a simple case of fixed number of nodes. The development processes include interaction among rather stable subgraphs. Some simple behaviors, such as clustering and declustering of states, ...

We propose a new formulation for full (weakening and constants included) multiplicative and exponential (MELL) proof nets, allowing a complete set of rewriting rules to parse them. The recognizing grammar deened by such a rewriting system (connuent and strong normalizing on the new proof nets) gives a correctness criterion that we show equivalent to the Danos-Regnier one.

We propose a new formulation for full (weakening and constants included) multiplicative and exponential (MELL) proof nets, allowing a complete set of rewriting rules to parse them. The recognizing grammar deened by such a rewriting system (connuent and strong normalizing on the new proof nets) gives a correctness criterion that we s h o w equivalent to the Danos-Regnier one.

We describe a general decomposition mechanism to express the derivation relation of a word rewriting system R as the composition of a (regular) substitution followed by the derivation relation of a system R′ ∪ D, where R′ is a strict sub-system of R and D is the Dyck rewriting system. From this decomposition, we deduce that the system R (resp. R) preserves regular (resp. context-free) languages...

REPORTRAPPORT Basic process algebra with iteration: completeness of its equational axioms Abstract Bergstra, Bethke & Ponse BBP93] proposed an axiomatisation for Basic Process Algebra extended with (binary) iteration. In this paper, we prove that this axiomatisation is complete with respect to strong bisimulation equivalence. To obtain this result, we will set up a term rewriting system, based ...

In this paper we present a number of necessary conditions for the existence of loops, i.e. reductions of the form t !R c[t ]. We investigate which of the known termination preserving transformation methods also preserve the non-existence of loops. We characterize the existence of loops by overlap closures. We illustrate these methods at new examples of a one-rule term rewriting system and a two...

We present a rewriting system for the linear lambda calculus corresponding to the {!, }-fragment of intuitionistic linear logic. This rewriting system is shown to be strongly normalizing, and Church-Rosser modulo the trivial commuting conversion. Thus it provides a simple decision method for the equational theory of the linear lambda calculus. As an application we prove the strong normalization...

Some personal recollections on the introduction of ‘abstract proof systems’ as a framework for formulating syntax-independent, general results about rule derivability and admissibility. With a particular eye on the inspiration I owe to Roel de Vrijer: the analogy with abstract

Rewriting logic has been revealed as a powerful tool to represent concurrent and state-transitions aspects in a declarative way, providing an adequate environment to specify and execute system representations. Moreover, rewriting logic is reflective, allowing for the definition of operations that transform, combine and manipulate specification modules by making use of the logic itself. Taking a...