From Linear Term Rewriting to Graph Rewriting with Preservation of Termination

06/25/2021
by   Roy Overbeek, et al.
0

Encodings of term rewriting systems (TRSs) into graph rewriting systems usually lose global termination, meaning the encodings do not terminate on all graphs. A typical encoding of the terminating TRS rule a(b(x)) -> b(a(x)), for example, may be indefinitely applicable along a cycle of a's and b's. Recently, we introduced PBPO+, a graph rewriting formalism in which rules employ a type graph to specify transformations and control rule applicability. In the present paper, we show that PBPO+ allows for a natural encoding of linear TRS rules that preserves termination globally. This result is a step towards modeling other rewriting formalisms, such as lambda calculus and higher order rewriting, using graph rewriting in a way that preserves properties like termination and confluence. We moreover expect that the encoding can serve as a guide for lifting TRS termination methods to PBPO+ rewriting.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/27/2023

Linear Termination over N is Undecidable

Recently it was shown that it is undecidable whether a term rewrite syst...
research
12/05/2018

Termination of λΠ modulo rewriting using the size-change principle (work in progress)

The Size-Change Termination principle was first introduced to study the ...
research
10/16/2020

Graph Rewriting and Relabeling with PBPO+ (Extended Version)

We extend the powerful Pullback-Pushout (PBPO) approach for graph rewrit...
research
03/14/2023

Termination of Graph Transformation Systems using Weighted Subgraph Counting

We introduce a termination method for the algebraic graph transformation...
research
05/24/2017

Faithful (meta-)encodings of programmable strategies into term rewriting systems

Rewriting is a formalism widely used in computer science and mathematica...
research
07/14/2023

Generalized Weighted Type Graphs for Termination of Graph Transformation Systems

We refine a technique by Bruggink et al. that uses weighted type graphs ...
research
02/27/2018

On Probabilistic Term Rewriting

We study the termination problem for probabilistic term rewrite systems....

Please sign up or login with your details

Forgot password? Click here to reset