Confluence Problems for Trace Rewriting Systems

Confluence Problems for Trace Rewriting

On the Confluence of Trace Rewriting Systems

In [NO88], a particular trace monoid M is constructed such that for the class of length–reducing trace rewriting systems over M , confluence is undecidable. In this paper, we show that this result holds for every trace monoid, which is neither free nor free commutative. Furthermore we will present a new criterion for trace rewriting systems that implies decidability of confluence.

Confluence of Curried Term-Rewriting Systems

Reduction Systems Definition An Abstract Reduction System short ARS consists of a set A and a sequence i of binary relations on A labelled by some set I We often drop the label if I is a singleton We write A j P if the ARS A A i i I has the property P Further we write A j P Q i A j P and A j Q An ARS A A has the diamond property A j i It has the Church Rosser property is con uent A j CR i A j G...

Proving Confluence of Term Rewriting Systems Automatically

We have developed an automated confluence prover for term rewriting systems (TRSs). This paper presents theoretical and technical ingredients that have been used in our prover. A distinctive feature of our prover is incorporation of several divide–and–conquer criteria such as those for commutative (Toyama, 1988), layer-preserving (Ohlebusch, 1994) and persistent (Aoto & Toyama, 1997) combinatio...

Formalizing the Confluence of Orthogonal Rewriting Systems

Orthogonality is a discipline of programming that in a syntactic manner guarantees determinism of functional specifications. Essentially, orthogonality avoids, on the one side, the inherent ambiguity of non determinism, prohibiting the existence of different rules that specify the same function and that may apply simultaneously (non-ambiguity), and, on the other side, it eliminates the possibil...