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Deciding confluence of certain term rewriting systems in polynomial time

Guillem Godoy, Ashish Tiwari, Rakesh Verma
2004 Annals of Pure and Applied Logic  
The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems.  ...  The same approach also shows the decidability of confluence for shallow and linear term rewriting systems.  ...  The research of the third author was supported in part by the National Science Foundation under grants CCR-9732186, CCR-0306475, and DUE-0313880.  ... 
doi:10.1016/j.apal.2004.04.005 fatcat:bbegyqguzzdwpdf6dls4k5odo4

Deciding confluence of certain term rewriting systems in polynomial time

A. Tiwari
Proceedings 17th Annual IEEE Symposium on Logic in Computer Science  
We present a polynomial time algorithm for deciding confluence of ground term rewrite systems.  ...  We generalize the decision procedure to get a polynomial time algorithm, assuming that the maximum arity of a symbol in the signature is a constant, for deciding confluence of rewrite systems where each  ...  We thank Rakesh Verma for pointing us to [4] , Guillem Godoy for pointing out an error in the second part of this paper, and the referees for their comments.  ... 
doi:10.1109/lics.2002.1029852 dblp:conf/lics/Tiwari02 fatcat:2xsdmetho5biradjm6n2s7cp2y

Page 4273 of Mathematical Reviews Vol. , Issue 95g [page]

1995 Mathematical Reviews  
It decides the nonterminal separation (NTS) property of context-free grammars in polynomial time.  ...  A straight- forward generalization of the algorithm decides the NTS property of extended context-free grammars (but not in polynomial time).”  ... 

Page 1592 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
Using the Peterson-Stickel algorithm we show that confluence is decidable for right-linear monadic term rewriting systems.  ...  {For the entire collection see MR 92b:68018.} 92c:68099 68Q42 03B35 03D05 Salomaa, Kai (SF-TURK) Decidability of confluence and termination of monadic term rewriting systems.  ... 

Rewriting in Practice [chapter]

Ashish Tiwari
2011 Lecture Notes in Computer Science  
We discuss applications of rewriting in three different areas: design and analysis of algorithms, theorem proving and term rewriting, and modeling and analysis of biological processes.  ...  Several decidable criterion have been recently developed for checking confluence of restricted classes of term rewriting systems [19, 21, 22, 20] .  ...  In term rewriting, the objects are equivalence classes of terms, representations of these objects are the terms themselves, and orderings are certain binary relations on terms.  ... 
doi:10.1007/978-3-642-21691-6_3 fatcat:fa4763xizjhhbjt7vwxikz54wu

Semantic confluence tests and completion methods

David A. Plaisted
1985 Information and Control  
We present semantic methods for showing that a term-rewriting system is confluent. We also present methods for completing a given term-rewriting system to obtain an equivalent confluent system.  ...  The concept of "ground confluence" is discussed; methods for demonstrating ground confluence are also given. We give decision procedures for some sub-problems that arise in this method.  ...  Then if the equation x q = X is added to the term-rewriting system, and the equation x + x + "" + x = 0 is added, where x is repeated p times, the irreducible forms of polynomials will still be identical  ... 
doi:10.1016/s0019-9958(85)80005-x fatcat:ddzpvfno45d2vcke3hzkzpqazy

Page 6213 of Mathematical Reviews Vol. , Issue 95j [page]

1995 Mathematical Reviews  
Solvability of this system lies in NP and can be decided in O(polylog(n)) time using 2°) processors.  ...  Comput. 5 (1976), no. 4, 618-623; MR 56 #13549], solvability of a linear system can be decided in this model in O(polylog(n)) time using a polynomial number of processors.  ... 

Page 1589 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
Summary: “Generally speaking, the confluence property is not pre- served when term rewriting systems (TRSs) are combined, even if they are canonical.  ...  David Pokrass Jacobs (1-CLEM-C) 93¢:68047 68Q42 Zhang, Xu Bo (PRC-ASBJ-SF) Some results on the confluence property of combined term rewriting systems. J. Comput. Sci. Tech.  ... 

Author Index

2004 Annals of Pure and Applied Logic  
., The complexity of first-order and monadic second-order logic revisited (1-3) 3-31 Godoy, G., Tiwari, A. and Verma, R., Deciding confluence of certain term rewriting systems in polynomial time (1-3)  ...  -H.L., An approach to deciding the observational equivalence of Algol-like languages (1-3) 125-171 Otto, M., Modal and guarded characterisation theorems over finite transition systems (1-3) 173-205 Plotkin  ... 
doi:10.1016/s0168-0072(04)00115-0 fatcat:uvctnxmfzzddfeuo3fyozfjm3q

Page 4104 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
Summary: “Polynomial orderings can be used for proving the ter- mination of term rewriting systems.  ...  Summary: “We investigate the system obtained by adding an alge- braic rewriting system R to an untyped lambda calculus in which terms are formed using the function symbols from R as constants.  ... 

Page 6557 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
In the survey, the author discusses the following sub- classes of @,i: @wp := {Ms| the word problem for S is decidable}, @poly := {Ms| the word problem for S is decidable in polynomial time}, @con := {  ...  Ms| S is finite and convergent}, #2, := {Ms| Z= {a,b}}, @2wp := {Ms| 2 = {a,b}, the word problem for S is decidable}, @2poly = {Ms| 2 = {a,b}, the word problem for S is decidable in polynomial time}, @  ... 

Some results about confluence on a given congruence class [chapter]

Friedrich Otto
1987 Lecture Notes in Computer Science  
On the other hand, for certain subclasses of these systems confluence on a given congruence class is decidable.  ...  It is undecidable in general whether or not a term-rewriting system is confluent on a given congruence class.  ...  The author wants to thank Ron Book for bringing this problem to his attention, and for many fruitful discussions regarding the various results presented in this paper.  ... 
doi:10.1007/3-540-17220-3_13 fatcat:3lrnrib5zza6vndtefatyh6mii

On weakly confluent monadic string-rewriting systems

K. Madlener, P. Narendran, F. Otto, L. Zhang
1993 Theoretical Computer Science  
It is investigated as to how far the various decidability results for finite, monadic, and confluent string-rewriting systems can be carried over to the class of finite monadic string-rewriting systems  ...  After establishing that the property of weak confluence is tractable for finite monadic string-rewriting systems, we prove that many decision problems that are tractable for finite, monadic, and confluent  ...  validation problem is decidable in polynomial time.  ... 
doi:10.1016/0304-3975(93)90213-d fatcat:ba7rvt2rb5fepptcymu4ql6ln4

Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems

Max Dauchet, Thierry Heuillard, Pierre Lescanne, Sophie Tison
1990 Information and Computation  
The aim of this paper is to propose an algorithm to decide the confluence of finite ground term rewrite systems.  ...  It is well known that the confluence is not decidable for general term rewrite systems, but this paper proves it is for ground term rewrite systems following a conjecture made by Huet and Oppen in their  ...  The aim of this paper is to propose an algorithm to decide the confluence of finite ground term rewrite systems.  ... 
doi:10.1016/0890-5401(90)90015-a fatcat:qvkzgcapyzgq7ndqm4e3kmkf2e

Page 2658 of Mathematical Reviews Vol. , Issue 87e [page]

1987 Mathematical Reviews  
We prove here the decidability of confluence for ground term rewriting systems.  ...  (F-LILL) Decidability of confluence for ground term rewriting systems. Fundamentals of computation theory (Cottbus, 1985), 80-89, Lecture Notes in Comput. Sci., 199, Springer, Berlin-New York, 1985.  ... 
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