scholarly journals Graph Path Orderings

10.29007/6hkk ◽  
2018 ◽  
Author(s):  
Nachum Dershowitz ◽  
Jean-Pierre Jouannaud
Keyword(s):  
Building Block ◽  
Finite Set ◽  
Rewrite Rules ◽  
Path Ordering ◽  
The Many ◽  
Recursive Path

We define well-founded rewrite orderings on graphs and show that they can be used to show termination of a set of graph rewrite rules by verifying all their cyclic extensions. We then introduce the graph path ordering inspired by the recursive path ordering on terms and show that it is a well-founded rewrite ordering on graphs for which checking termination of a finite set of graph rewrite rules is decidable. Our ordering applies to arbitrary finite, directed, labeled, ordered multigraphs, hence provides a building block for rewriting with graphs, which should impact the many areas in which computations take place on graphs.

Electron Charge and Current Densities, the Geometrie Phase and Cellular Automata

1993 ◽  
Vol 48 (1-2) ◽  
pp. 134-136
Author(s):  
N. Sukumar ◽  
B. M. Deb ◽  
Harjinder Singh
Keyword(s):  
Current Density ◽  
Electron System ◽  
Time Dependent ◽  
Gauge Potential ◽  
Electronic Charge ◽  
Electronic Density ◽  
Electronic Current ◽  
Finite Set ◽  
The Many ◽  
Electronic Density Distribution

Some consequences of the quantum fluid dynamics formulation are discussed for excited states of atoms and molecules and for time-dependent processes. It is shown that the conservation of electronic current density j(r) allows us to manufacture a gauge potential for each excited state of an atom, molecule or atom in a molecule. This potential gives rise to a tube of magnetic flux carried around by the many-electron system. In time-dependent situations, the evolution of the electronic density distribution can be followed with simple, site-dependent cellular automaton (CA) rules. The CA consists of a lattice of sites, each with a finite set of possible values, here representing finite localized elements of electronic charge and current density (since the charge density rno longer suffices to fully characterize a time-dependent system, it needs to be supplemented with information about the current density j).Our numerical results are presented elsewhere and further developmentis in progress.

scholarly journals On recursive path ordering

1985 ◽  
Vol 40 ◽  
pp. 323-328 ◽  
Author(s):  
M.S. Krishnamoorthy ◽  
P. Narendran
Keyword(s):  
Path Ordering ◽  
Recursive Path

Termination of rewriting in the Calculus of Constructions

2003 ◽  
Vol 13 (2) ◽  
pp. 339-414 ◽  
Author(s):  
DARIA WALUKIEWICZ-CHRZĄSZCZ
Keyword(s):  
Lambda Calculus ◽  
Term Rewriting ◽  
Higher Order ◽  
Strong Normalization ◽  
Term Rewriting System ◽  
Calculus Of Constructions ◽  
Path Ordering ◽  
Higher Order Functions ◽  
Rewriting Rules ◽  
Recursive Path

We show how to incorporate rewriting into the Calculus of Constructions and we prove that the resulting system is strongly normalizing with respect to beta and rewrite reductions. An important novelty of this paper is the possibility to define rewriting rules over dependently typed function symbols. We prove strong normalization for any term rewriting system, such that all function symbols satisfy the, so called, star dependency condition, and every rule is accepted by the Higher Order Recursive Path Ordering (which is an extension of the method created by Jouannaud and Rubio for the setting of the simply typed lambda calculus). The proof of strong normalization is done by using a typed version of reducibility candidates due to Coquand and Gallier. Our criterion is general enough to accept definitions by rewriting of many well-known higher order functions, for example dependent recursors for inductive types or proof carrying functions. This makes it a very good candidate for inclusion in a proof assistant based on the Curry-Howard isomorphism.

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