More Problems in Rewriting

Complete Growth Series of Coxeter Groups with more than Three Generators

String rewriting for double coset systems

In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not suffer this restriction and we present some examples of infinite double coset systems which can now easily be solved using our approach. Even when both enumerati...

Conditional Narrowing Modulo in Rewriting Logic and Maude

This work studies the relationship between verifiable and computable answers for reachability problems in rewrite theories with an underlying membership equational logic. These problems have the form (∃x̄)s(x̄) →∗ t(x̄), with x̄ some variables, or a conjunction of several of these subgoals. A calculus that solves this kind of problems has been developed and proved correct. Given a reachability prob...

Primitive Rewriting

Undecidability results in rewriting have usually been proved by reduction from undecidable problems of Turing machines or, more recently, from Post’s Correspondence Problem. Another natural candidate for proofs regarding term rewriting is Recursion Theory, a direction we promote in this contribution. We present some undecidability results for “primitive” term rewriting systems, which encode pri...

Confluence of Shallow Right-Linear Rewrite Systems

We show that confluence of shallow and right-linear term rewriting systems is decidable. This class of rewriting system is expressive enough to include nontrivial nonground rules such as commutativity, identity, and idempotence. Our proof uses the fact that this class of rewrite systems is known to be regularity-preserving, which implies that its reachability and joinability problems are decida...

Referree’s Report Isoperimetric Regions in Spaces

This is a very nice paper, looking at isoperimetric problems in various surfaces, though the paper’s title indicates it considers isoperimetric problems in general spaces. It would be a much better and unified paper, in particular more accessible to undergraduates, if the abstract and title reflected that the results center on abstract surfaces rather than abstract spaces. I would recommend tha...