We propose a rewriting system for parsing full multiplicative and exponential proof structures. The recognizing grammar deened by such a rewriting system (connuent and strong normalizing) gives a correctness criterion that we show equivalent to the Danos-Regnier one.

We define a compilation scheme for a constructor-based strongly-sequential graph rewriting system which shortcuts some needed steps. The object code, what the compiler produces on input the rewriting system, is another constructor-based graph rewriting system that is normalizing for the original system when using an innermost strategy. Hence, the object code can be easily implemented by eager f...

Given a constructor term rewriting system defining injective functions, the inversion compiler proposed by Nishida, Sakai and Sakabe generates a confluent conditional term rewriting system, and unravels the conditional system into an unconditional term rewriting system. In general, the unconditional system is not confluent and thus not computationally equivalent to the conditional system. In th...

The ground term reachability problem consists in determining whether a given variable-free term t can be transformed into a given variable-free term t′ by the application of rules from a term rewriting system R. The joinability problem, on the other hand, consists in determining whether there exists a variable-free term t′′ which is reachable both from t and from t′. Both problems have proven t...

We consider commutative string rewriting systems (Vector Addition Systems, Petri nets), i.e., string rewriting systems in which all pairs of letters commute. We are interested in reachability: given a rewriting system R and words v and w, can v be rewritten to w by applying rules from R? A famous result states that reachability is decidable for commutative string rewriting systems. We show that...

The starting point of this paper is McMillan’s complete finite prefix of an unfolding that has been obtained from a Petri net or a process algebra expression. The paper addresses the question of how to obtain the (possibly infinite) system behaviour from the complete finite prefix. An algorithm is presented to derive from the prefix a graph rewriting system that can be used to construct the unf...

We define four families of word-rewriting systems: the prefix/suffix systems and the left/right systems. The rewriting of prefix systems generalizes the prefix rewriting of systems: a system is prefix (suffix) if a left hand side and a right hand side are overlapping only by prefix (suffix). The rewriting of right systems generalizes the mechanism of transducers: a system is right (left) if a l...

We define a type inference system for Nominal Rewriting where the types associated to terms are polymorphic (built from a set of base data sorts, type variables, and user-defined type constructors). In contrast with standard term rewriting systems or the λ-calculus, a typing environment for nominal rewriting includes type information for atoms, variables and function symbols. We give a syntax-d...