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Undecidable Properties on Length-Two String Rewriting Systems

Masahiko Sakai, Yi Wang
2008 Electronical Notes in Theoretical Computer Science  
Length-two string rewriting systems are length preserving string rewriting systems that consist of length-two rules.  ...  This paper shows that confluence, termination, left-most termination and right-most termination are undecidable properties for length-two string rewriting systems.  ...  Caron showed that termination is an undecidable property for length preserving string rewriting systems [2] .  ... 
doi:10.1016/j.entcs.2008.03.053 fatcat:6f2pk3yyorbujgamvolr2hxcfe

Some undecidability results concerning the property of preserving regularity

Friedrich Otto
1998 Theoretical Computer Science  
In addition, some undecidability results are presented that generalize results of Gilleron and Tison (1995) from term-rewriting systems to string-rewriting systems.  ...  It follows that the property of being regularity preserving is undecidable for term-rewriting systems, thus answering another question of Gyenizse and VBgviilgyi (1997).  ...  two undecidability results concerning the property of preserving regularity for string-rewriting systems.  ... 
doi:10.1016/s0304-3975(98)00055-3 fatcat:ighxqdcmazhzbm4v7pxenpq7wu

When is an extension of a specification consistent? Decidable and undecidable cases

Friedrich Otto
1991 Journal of symbolic computation  
For the special ease of string-rewriting systems we present decidable and undeeidable eases of this problem.  ...  One can verify that, if R is canonical, then two objects s, t ~ S are congruent if and only if they reduce to the same irreducible object.  ...  In fact, we show that, if R2 is a finite, length-reducing, and confluent string-rewriting system on an alphabet I~2, or if R2 is a finite monadic string-rewriting system on Z2, then it is undecidable in  ... 
doi:10.1016/s0747-7171(08)80150-2 fatcat:nkdhm6qvg5b4raop56t755nzpu

Page 1649 of Mathematical Reviews Vol. , Issue 94c [page]

1994 Mathematical Reviews  
(D-KSSL-MI; Kassel) Some undecidability results for weakly confluent monadic string-rewriting systems.  ...  {For the entire collection see MR 94c:68001.} 94c:68108 68Q42 03D03 03D40 Zhang, Louxin (3-WTRL-C; Waterloo, ON) Some properties of finite special string-rewriting systems. (English summary) J.  ... 

On weakly confluent monadic string-rewriting systems

K. Madlener, P. Narendran, F. Otto, L. Zhang
1993 Theoretical Computer Science  
Zhang, On weakly confluent monadic string-rewriting systems, Theoretical Computer Science 113 (1993) 119-165.  ...  Here a monadic string-rewriting system R on some alphabet z is called weakly confluent if it is confluent on all the congruence classes [a]s, with ao,Su {e}.  ...  For finite length-reducing string-rewriting systems, confluence on a given congruence class is undecidable in general [29] .  ... 
doi:10.1016/0304-3975(93)90213-d fatcat:ba7rvt2rb5fepptcymu4ql6ln4

Open. Closed. Open [chapter]

Nachum Dershowitz
2005 Lecture Notes in Computer Science  
is the best bound on the length of a derivation for a one-rule length-preserving string-rewriting (semi-Thue) system?  ...  Thus termination of string-rewriting systems was provenly undecidable-for an unbounded number of rules.  ... 
doi:10.1007/978-3-540-32033-3_28 fatcat:lrzcrz3y6rb5bpso6zr6bnjkw4

Page 7896 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
Finally, it is shown that it is undecidable in general whether a finite, length-reducing, and confluent string-rewriting system yields a regular set of normal forms for each regular lan- guage.”  ...  Inform. 24 (1995), no. 1-2, 157-175; MR 96k:68106] from term-rewriting systems to string-rewriting systems.  ... 

Thue systems as rewriting systems

Ronald V. Book
1987 Journal of symbolic computation  
The emphasis is on Thue systems with the Chureh-Rosser property, where the notion of reduction is based on length-decreasing rewriting rules.  ...  This paper is a survey of recent results on Thue systems, where the systems are viewed as rewriting systems on strings over a finite alphabet.  ...  For example, one might investigate the types of groups or monoids that are finitely generated but are presented by infinite regular or infinite context-free Church-Rosser Thue systems.  ... 
doi:10.1016/s0747-7171(87)80021-4 fatcat:pqx6qbrwmngcdfsj6mabwfrxce

On S-Regular Prefix-Rewriting Systems and Automatic Structures [chapter]

Friedrich Otto
1999 Lecture Notes in Computer Science  
Accordingly we consider s-regular pre xrewriting systems showing that even for fairly restricted systems of this form con uence is undecidable in general.  ...  Underlying the notion of an automatic structure is that of a synchronously regular (s-regular for short) set of pairs of strings.  ...  Hence, the undecidability of con uence for length-reducing f-regular string-rewriting systems yields this result O'D u83].  ... 
doi:10.1007/3-540-48686-0_42 fatcat:ovze6wudrja2bjyp37ee7fllby

On Problems Dual to Unification [article]

Zümrüt Akçam, Daniel S. Hono II, Paliath Narendran
2017 arXiv   pre-print
We also prove that the common term problem is undecidable for dwindling string rewriting systems.  ...  In this paper, we investigate a problem dual to the unification problem, namely the Common Term (CT) problem for string rewriting systems.  ...  [13] proved that the CT problem is undecidable even for convergent and length-reducing string rewriting systems.  ... 
arXiv:1706.05607v2 fatcat:tammzeefcnajhgwmalldrzn6ay

FDT is undecidable for finitely presented monoids with solvable word problems [chapter]

Friedrich Otto, Andrea Sattler-Klein
1997 Lecture Notes in Computer Science  
This improves upon the undecidability result of R. Cremanns and F. Otto (1996) , which was based on the undecidability of the word problem for the nitely presented monoids considered.  ...  Exploiting a new technique for proving undecidability results developed by A.  ...  Then S 1 n is an in nite, length-reducing, and canonical string-rewriting system on 1 by Theorem 4.1.  ... 
doi:10.1007/bfb0036200 fatcat:ihqndqszgzhulgshuqcrs7cxvi

Page 466 of Mathematical Reviews Vol. , Issue 89A [page]

1989 Mathematical Reviews  
In general it is undecidable whether or not a given finite string- rewriting system R is confluent on a given congruence class [w],, even when only length-reducing systems are considered.  ...  In this area one has to decide whether two canonical term rewriting systems have the same set of irreducible ground terms.  ... 

Linear bounded automata and rewrite systems : Influence of initial configurations on decision properties [chapter]

A-C Caron
1991 Lecture Notes in Computer Science  
We prove that termination is undecidable for non-length-increashlg string rewriting systems, using linear-bounded automala.  ...  On the other hand, we prove the undecidability of confluence for terminating rewriting systems when temas begin by a fixed symbol.  ...  length-preserving string rewriting systems.  ... 
doi:10.1007/3-540-53982-4_5 fatcat:2y753c4nqbdivmpiylkqncpyoy

On deciding the confluence of a finite string-rewriting system on a given congruence class

Friedrich Otto
1987 Journal of computer and system sciences (Print)  
In general it is undecidable whether or not a given finite string-rewriting system R is confluent on a given congruence class [w]~, even when only length-reducing systems are considered.  ...  A string-rewriting system R on alphabet C induces a congruence ++ 2 on the free monoid 27 generated by Z, and hence, the set M, of congruence classes modulo -2 is a monoid.  ...  Then RL is a finite length-reducing string-rewriting system on A.  ... 
doi:10.1016/0022-0000(87)90017-1 fatcat:uuahdoiqerd7lmkymitfrgngd4

Simple termination is difficult

Aart Middeldorp, Bernhard Gramlich
1995 Applicable Algebra in Engineering, Communication and Computing  
We show that simple termination is an undecidable property, even for one-rule systems. This contradicts a result by Jouannaud and Kirchner.  ...  The proof is based on the ingenious construction of Dauchet who showed the undecidability of termination for one-rule systems.  ...  On the other hand, Caron [1] recently showed that termination is an undecidable property of length-preserving string rewriting systems-systems in which the left-hand side and the right-hand side of each  ... 
doi:10.1007/bf01225647 fatcat:v3wttyottfczvawhn6amvik55i
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