Stefan Michael Kahrs - Modularity of Convergence and Strong Convergence in Infinitary Rewriting

lmcs:878 - Logical Methods in Computer Science, September 6, 2010, Volume 6, Issue 3 - https://doi.org/10.2168/LMCS-6(3:18)2010
Modularity of Convergence and Strong Convergence in Infinitary Rewriting

Authors: Stefan Michael Kahrs

Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term Rewriting Systems that all reduction sequences converge to a limit. Strong Convergence requires in addition that redex positions in a reduction sequence move arbitrarily deep. In this paper it is shown that both Convergence and Strong Convergence are modular properties of non-collapsing Infinitary Term Rewriting Systems, provided (for convergence) that the term metrics are granular. This generalises known modularity results beyond metric \infty.


Volume: Volume 6, Issue 3
Published on: September 6, 2010
Accepted on: June 25, 2015
Submitted on: September 18, 2009
Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory,F.4.2


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