Modes of convergence for term graph rewriting
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Modes of convergence for term graph rewriting. / Bahr, Patrick.
In: Logical Methods in Computer Science, Vol. 8, No. 2, 6, 2012.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Modes of convergence for term graph rewriting
AU - Bahr, Patrick
PY - 2012
Y1 - 2012
N2 - Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order respectively a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term rewriting.We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the modes of convergence on term graphs are conservative extensions of the corresponding modes of convergence on terms and are preserved under unravelling term graphs to terms. Moreover, we show that many of the properties known from infinitary term rewriting are preserved. This includes the intrinsic completeness of both modes of convergence and the fact that convergence via the partial order is a conservative extension of the metric convergence.
AB - Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order respectively a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term rewriting.We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the modes of convergence on term graphs are conservative extensions of the corresponding modes of convergence on terms and are preserved under unravelling term graphs to terms. Moreover, we show that many of the properties known from infinitary term rewriting are preserved. This includes the intrinsic completeness of both modes of convergence and the fact that convergence via the partial order is a conservative extension of the metric convergence.
KW - Faculty of Science
KW - term graph rewriting
KW - infinitary rewriting
KW - weak convergence
KW - partial order
KW - metric
KW - semilattice
KW - completeness
KW - soundness
U2 - 10.2168/LMCS-8(2:6)2012
DO - 10.2168/LMCS-8(2:6)2012
M3 - Journal article
VL - 8
JO - Logical Methods in Computer Science
JF - Logical Methods in Computer Science
SN - 1860-5974
IS - 2
M1 - 6
ER -
ID: 38429534