scholarly journals On Tree Automata that Certify Termination of Left-Linear Term Rewriting Systems

2005 ◽  
pp. 353-367 ◽  
Author(s):  
Alfons Geser ◽  
Dieter Hofbauer ◽  
Johannes Waldmann ◽  
Hans Zantema
Keyword(s):  
Term Rewriting ◽  
Linear Term ◽  
Tree Automata ◽  
Term Rewriting Systems ◽  
Rewriting Systems

A Characterization of Irreducible Sets Modulo Left-Linear Term Rewriting Systems by Tree Automata

1990 ◽  
Vol 13 (2) ◽  
pp. 211-226
Author(s):  
Z. Fülop ◽  
S. Vágvölgyi
Keyword(s):  
Term Rewriting ◽  
Linear Term ◽  
Tree Automata ◽  
Top Down ◽  
Term Rewriting Systems ◽  
Tree Language ◽  
Rewriting Systems ◽  
Term Rewriting System ◽  
Look Ahead

The concept of top-down tree automata with prefix look-ahead is introduced. It is shown that a tree language is the set of irreducible trees of a left-linear term rewriting system if and only if it can be recognized by a one-state deterministic top-down tree automaton with pre fix look-ahead.

scholarly journals On tree automata that certify termination of left-linear term rewriting systems

2007 ◽  
Vol 205 (4) ◽  
pp. 512-534 ◽  
Author(s):  
Alfons Geser ◽  
Dieter Hofbauer ◽  
Johannes Waldmann ◽  
Hans Zantema
Keyword(s):  
Term Rewriting ◽  
Linear Term ◽  
Tree Automata ◽  
Term Rewriting Systems ◽  
Rewriting Systems

scholarly journals Infinite normal forms for non-linear term rewriting systems

1995 ◽  
Vol 152 (2) ◽  
pp. 285-303
Author(s):  
Paola Inverardi ◽  
Monica Nesi
Keyword(s):  
Normal Forms ◽  
Term Rewriting ◽  
Linear Term ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Non Linear

scholarly journals Modular termination of r-consistent and left-linear term rewriting systems

1995 ◽  
Vol 149 (2) ◽  
pp. 361-374 ◽  
Author(s):  
Manfred Schmidt-Schauß ◽  
Massimo Marchiori ◽  
Sven Eric Panitz
Keyword(s):  
Term Rewriting ◽  
Linear Term ◽  
Term Rewriting Systems ◽  
Rewriting Systems

TWO RELATED ALGORITHMS FOR ROOT-TO-FRONTIER TREE PATTERN MATCHING

2006 ◽  
Vol 17 (06) ◽  
pp. 1253-1272
Author(s):  
LOEK CLEOPHAS ◽  
KEES HEMERIK ◽  
GERARD ZWAAN
Keyword(s):  
Pattern Matching ◽  
Term Rewriting ◽  
Tree Automata ◽  
Term Rewriting Systems ◽  
Missing Link ◽  
Rewriting Systems ◽  
Tree Pattern ◽  
Tree Pattern Matching

Tree pattern matching (TPM) algorithms on ordered, ranked trees play an important role in applications such as compilers and term rewriting systems. Many TPM algorithms appearing in the literature are based on tree automata. For efficiency, these automata should be deterministic, yet deterministic root-to-frontier tree automata (DRFTAS) are less powerful than nondeterministic ones, and no root-to-frontier TPM algorithm using a DRFTA has appeared so far. Hoffmann & O'Donnell presented a root-to-frontier TPM algorithm based on an Aho-Corasick automaton recognizing tree stringpaths. No relationship between this algorithm and algorithms using tree automata has however been described. We show that a specific DRFTA can be used for stringpath matching in a root-to-frontier TPM algorithm. This new algorithm provides a missing link between TPM algorithms using stringpath automata and those using tree automata. We also investigate the correspondence between the automata used by the two algorithms.

scholarly journals Derivational Complexity and Context-Sensitive Rewriting

2021 ◽  
Author(s):  
Salvador Lucas
Keyword(s):  
Normal Forms ◽  
Term Rewriting ◽  
Linear Term ◽  
The Other ◽  
Term Rewriting Systems ◽  
Context Sensitive ◽  
Rewriting Systems ◽  
Other Hand

AbstractContext-sensitive rewriting is a restriction of rewriting where reduction steps are allowed on specific arguments $$\mu (f)\subseteq \{1,\ldots ,k\}$$ μ ( f ) ⊆ { 1 , … , k } of k-ary function symbols f only. Terms which cannot be further rewritten in this way are called $$\mu $$ μ -normal forms. For left-linear term rewriting systems (TRSs), the so-called normalization via$$\mu $$ μ -normalization procedure provides a systematic way to obtain normal forms by the stepwise computation and combination of intermediate $$\mu $$ μ -normal forms. In this paper, we show how to obtain bounds on the derivational complexity of computations using this procedure by using bounds on the derivational complexity of context-sensitive rewriting. Two main applications are envisaged: Normalization via $$\mu $$ μ -normalization can be used with non-terminating TRSs where the procedure still terminates; on the other hand, it can be used to improve on bounds of derivational complexity of terminating TRSs as it discards many rewritings.

A class of ambiguous linear term-rewriting systems on which call-by-need is a normalizing reduction strategy

1987 ◽  
Vol 18 (9) ◽  
pp. 19-30
Author(s):  
Tohru Naoi ◽  
Masafumi Yamashita ◽  
Toshihide Ibaraki ◽  
Namio Honda
Keyword(s):  
Term Rewriting ◽  
Linear Term ◽  
Term Rewriting Systems ◽  
Reduction Strategy ◽  
Rewriting Systems
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