Normal forms and normal theories in conditional rewriting

Two Normal Forms for Rewriting P Systems

On the Modularity of Normal Forms in Rewriting

The last open problem regarding the modularity of the fundamental properties of Term Rewriting Systems concerns the property of uniqueness of normal forms w r t reduction UN In this article we solve this open problem showing that UN is modular for left linear Term Rewriting Systems The novel pile and delete technique here introduced allows for quite a short proof and is of independent interest ...

Unique Normal Forms in Infinitary Weakly Orthogonal Term Rewriting

We present some contributions to the theory of infinitary rewriting for weakly orthogonal term rewrite systems, in which critical pairs may occur provided they are trivial. We show that the infinitary unique normal form property (UN∞) fails by a simple example of a weakly orthogonal TRS with two collapsing rules. By translating this example, we show that UN∞ also fails for the infinitary λβη-ca...

Normal Forms and Reduction for Theories of Binary Relations

We consider equational theories of binary relations, in a language expressing composition, converse, and lattice operations. We treat the equations valid in the standard model of sets and also define a hierarchy of equational axiomatisations stratifying the standard theory. By working directly with a presentation of relation-expressions as graphs we are able to define a notion of reduction whic...

Elementary Deduction Problem for Locally Stable Theories with Normal Forms

We present an algorithm to decide the intruder deduction problem (IDP) for a class of locally stable theories enriched with normal forms. Our result relies on a new and efficient algorithm to solve a restricted case of higher-order associative-commutative matching, obtained by combining the Distinct Occurrences of AC-matching algorithm and a standard algorithm to solve systems of linear Diophan...