scholarly journals Tame combings, almost convexity and rewriting systems for groups

1997 ◽  
Vol 225 (2) ◽  
pp. 263-276 ◽  
Author(s):  
Susan M. Hermiller ◽  
John Meier
Keyword(s):  
Rewriting Systems ◽  
Almost Convexity

scholarly journals A uniform model for almost convexity and rewriting systems

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Mark Brittenham ◽  
Susan Hermiller
Keyword(s):  
Topological Property ◽  
Finitely Generated ◽  
Rewriting Systems ◽  
Finite Presentation ◽  
Finitely Generated Groups ◽  
Inductive Procedure ◽  
Van Kampen Diagrams ◽  
Uniform Model ◽  
Almost Convexity

AbstractWe introduce a topological property for finitely generated groups, called stackable, that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define algorithmically stackable groups, for which this procedure is an algorithm. This property gives a common model for algorithms arising from both rewriting systems and almost convexity for groups.

Tree Rewriting Systems, Combinatory Weak Reduction Systems and Type Free Languages1

1982 ◽  
Vol 5 (3-4) ◽  
pp. 279-299
Author(s):  
Alberto Pettorossi
Keyword(s):  
Combinatory Logic ◽  
Rewriting Systems ◽  
Tree Transducers ◽  
Tree Languages ◽  
One To One ◽  
The One ◽  
Weak Reduction

In this paper we consider combinators as tree transducers: this approach is based on the one-to-one correspondence between terms of Combinatory Logic and trees, and on the fact that combinators may be considered as transformers of terms. Since combinators are terms themselves, we will deal with trees as objects to be transformed and tree transformers as well. Methods for defining and studying tree rewriting systems inside Combinatory Weak Reduction Systems and Weak Combinatory Logic are also analyzed and particular attention is devoted to the problem of finiteness and infinity of the generated tree languages (here defined). This implies the study of the termination of the rewriting process (i.e. reduction) for combinators.

scholarly journals Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System

2021 ◽  
Vol 178 (3) ◽  
pp. 173-185
Author(s):  
Arthur Adinayev ◽  
Itamar Stein
Keyword(s):  
Isomorphism Problem ◽  
Complete Characterization ◽  
Hasse Diagram ◽  
Subgraph Isomorphism ◽  
Rewriting Systems ◽  
Rewriting System ◽  
String Rewriting ◽  
Reduction Graph

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible.

PATTERN MATCHING CODE MINIMIZATION IN REWRITING-BASED PROGRAMMING LANGUAGES

2002 ◽  
Vol 13 (06) ◽  
pp. 873-887
Author(s):  
NADIA NEDJAH ◽  
LUIZA DE MACEDO MOURELLE
Keyword(s):  
Programming Languages ◽  
Pattern Matching ◽  
Term Rewriting ◽  
Directed Acyclic Graphs ◽  
Tree Automaton ◽  
Minimal Tree ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Acyclic Graphs ◽  
Space Requirements

We compile pattern matching for overlapping patterns in term rewriting systems into a minimal, tree matching automata. The use of directed acyclic graphs that shares all the isomorphic subautomata allows us to reduce space requirements. These are duplicated in the tree automaton. We design an efficient method to identify such subautomata and avoid duplicating their construction while generating the dag automaton. We compute some bounds on the size of the automata, thereby improving on previously known equivalent bounds for the tree automaton.

Rewriting Systems Over Indexed Multisets

2013 ◽  
Vol 57 (1) ◽  
pp. 165-179 ◽  
Author(s):  
O. Agrigoroaiei ◽  
G. Ciobanu
Keyword(s):  
Rewriting Systems
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