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Match-Bounded String Rewriting Systems [chapter]

Alfons Geser, Dieter Hofbauer, Johannes Waldmann
2003 Lecture Notes in Computer Science  
The problem of existence of a match-bound is still open. Match-boundedness for all strings can be used as an automated criterion for termination, for match-bounded systems are terminating.  ...  In a match-bounded system, match heights are globally bounded. Using recent results on deleting systems, we prove that rewriting by a match-bounded system preserves regular languages.  ...  MATCH-BOUNDED STRING REWRITING SYSTEMS We will now apply the theory of deleting systems to obtain results for match-bounded rewriting.  ... 
doi:10.1007/978-3-540-45138-9_39 fatcat:lh6d32nalrdf5h7mi443qxstyi

Match-Bounded String Rewriting Systems

Alfons Geser, Dieter Hofbauer, Johannes Waldmann
2004 Applicable Algebra in Engineering, Communication and Computing  
The problem of existence of a match-bound is still open. Match-boundedness for all strings can be used as an automated criterion for termination, for match-bounded systems are terminating.  ...  In a match-bounded system, match heights are globally bounded. Using recent results on deleting systems, we prove that rewriting by a match-bounded system preserves regular languages.  ...  MATCH-BOUNDED STRING REWRITING SYSTEMS We will now apply the theory of deleting systems to obtain results for match-bounded rewriting.  ... 
doi:10.1007/s00200-004-0162-8 fatcat:eshe4tyfqrhgrhkgx7k4xjtfvy

Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

Alfons Geser, Dieter Hofbauer, Johannes Waldmann
2005 Journal of automated reasoning  
A string rewriting system is called match-bounded if there is a global upper bound to these numbers.  ...  We show now that the string rewriting systems whose inverse (left and right hand sides exchanged) is match-bounded, have similar exceptional properties.  ...  INVERSE MATCH-BOUNDED STRING REWRITING SYSTEMS Our focus in this article is on string rewriting systems that are inverse match-bounded, i.e., systems obtained from match-bounded ones by exchanging left  ... 
doi:10.1007/s10817-005-9024-8 fatcat:47spcbtif5emdkxuh62o7cal64

On Tree Automata that Certify Termination of Left-Linear Term Rewriting Systems [chapter]

Alfons Geser, Dieter Hofbauer, Johannes Waldmann, Hans Zantema
2005 Lecture Notes in Computer Science  
It is a generalization of the match bound method for string rewriting.  ...  To prove that a term rewriting system terminates we first construct an enriched system over a new signature that simulates the original derivations.  ...  Thanks to Vincent van Oostrom for explaining the connection with the general framework of rewriting labellings.  ... 
doi:10.1007/978-3-540-32033-3_26 fatcat:v7glusrm4rcrffverthjnievum

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

Alfons Geser, Dieter Hofbauer, Johannes Waldmann, Hans Zantema
2007 Information and Computation  
It is a generalization of the match bound method for string rewriting.  ...  To prove that a term rewriting system terminates we first construct an enriched system over a new signature that simulates the original derivations.  ...  Thanks to Vincent van Oostrom for explaining the connection with the general framework of rewriting labellings.  ... 
doi:10.1016/j.ic.2006.08.007 fatcat:phx2dmluobbphglxh6ompinhlq

Termination of Cycle Rewriting [chapter]

Hans Zantema, Barbara König, H. J. Sander Bruggink
2014 Lecture Notes in Computer Science  
Most techniques for proving termination of string rewriting fail for proving termination of cycle rewriting, but match bounds, arctic matrices and tropical matrices can be applied.  ...  Further we show how any terminating string rewriting system can be transformed to a terminating cycle rewriting system, preserving derivational complexity.  ...  Arctic matrices and match bounds have been exploited before for proving bounds on derivational complexity of term rewriting and string rewriting: single applications of these techniques yield linear bounds  ... 
doi:10.1007/978-3-319-08918-8_33 fatcat:owhrz3ditrhoxlbk4yojhfuwva

Synthesising Graphical Theories [article]

Aleks Kissinger
2012 arXiv   pre-print
In this extended abstract, we adapt this technique to diagrammatic theories, expressed as graph rewrite systems, and demonstrate its application by synthesising a graphical theory for studying entangled  ...  It is straightforward to show that m ′ • r −1 is a matching. Definition 2.9. A set of string graph rewrite rules is called a string graph rewrite system.  ...  A string graph rewrite rule L → R is a span of monomorphisms L b1 ←− B b2 −→ R such that b 1 (B) = Bound(L), b 2 (B) = Bound(R) and for all b ∈ B, b 1 (b) ∈ In(L) ⇔ b 2 (b) ∈ In(R).  ... 
arXiv:1202.6079v2 fatcat:bemtn6mwvvcgzp4py4zr2ggepy

On termination of one rule rewrite systems

Pierre Lescanne
1994 Theoretical Computer Science  
., On termination of one rule rewrite systems, Theoretical Computer Science 132 (1994) 3955401.  ...  A match of P is any string y such y=Ctlclil ... sli,=fll~i, ... pi,. Modified Post's correspondence problem is to determine, given a system, whether this system has a match.  ...  Fig. 1 gives its associated one-rule rewrite system. and that these rewrites contribute to build a match for the given Post's correspondence system.  ... 
doi:10.1016/0304-3975(94)00029-8 fatcat:blq7jlcworac7kkkl3kdfel3be

Deleting string rewriting systems preserve regularity

Dieter Hofbauer, Johannes Waldmann
2004 Theoretical Computer Science  
A string rewriting system is called deleting if there exists a partial ordering on its alphabet such that each letter in the right-hand side of a rule is less than some letter in the corresponding left-hand  ...  We show that the rewrite relation induced by a deleting system can be represented as the composition of a finite substitution (into an extended alphabet), a rewrite relation of an inverse context-free  ...  Match-bounded rewriting An important application of deleting rewriting systems is in match-bounded rewriting, see [9, 10] .  ... 
doi:10.1016/j.tcs.2004.04.009 fatcat:kjhbjtx4obcqbbxvglxq42yuui

Deleting String Rewriting Systems Preserve Regularity [chapter]

Dieter Hofbauer, Johannes Waldmann
2003 Lecture Notes in Computer Science  
A string rewriting system is called deleting if there exists a partial ordering on its alphabet such that each letter in the right-hand side of a rule is less than some letter in the corresponding left-hand  ...  We show that the rewrite relation induced by a deleting system can be represented as the composition of a finite substitution (into an extended alphabet), a rewrite relation of an inverse context-free  ...  Match-bounded rewriting An important application of deleting rewriting systems is in match-bounded rewriting, see [9, 10] .  ... 
doi:10.1007/3-540-45007-6_27 fatcat:o2sx5sjwrrdz3bdwoonxd4hu2m

Page 2767 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
A term rewriting system is an abstract reduction system that rewrites objects with a term structure. “In Chapter 3 we describe how we can represent logic in type theory.  ...  We conclude with some easily com- puted bounds on the size of the automata, thereby improving on previously known equivalent bounds for the tree automaton.”  ... 

Page 8086 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Summary: “We present a finite, special, and confluent string- rewriting system for which the word matching problem is unde- cidable.  ...  problem is undecidable for finite special string-rewriting systems that are confluent.  ... 

Pattern graph rewrite systems

Aleks Kissinger, Alex Merry, Matvey Soloviev
2014 Electronic Proceedings in Theoretical Computer Science  
Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems.  ...  In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where  ...  A span of string graphs L i 1 ←− I i 2 −→ R is called a rewrite rule, written L R, if • I is a point graph and i 1 restricts to a bijection I ∼ = Bound(L) and i 2 to I ∼ = Bound(R), • for all p ∈ I, i  ... 
doi:10.4204/eptcs.143.5 fatcat:juelbsr5drcmrombpa43mtg2yy

High-fidelity metaprogramming with separator syntax trees

Rodin T. A. Aarssen, Tijs van der Storm
2020 Proceedings of the 2020 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation - PEPM 2020  
Concrete syntax trees (CSTs) preserve all layout information, but transformation systems or parsers that support CSTs are rare and can be cumbersome to use.  ...  Systems such as ASF+SDF [3] , TXL [4] , and Rascal [8] support CSTs, which preserve all layout of the source program; additionally, such systems support concrete syntax patterns to allow rewrite rules  ...  left-hand side variables to bound subterms: -subsititute the yield of the bound variables in env in the right-hand side of R (with the substitution algorithm described below); -parse the resulting string  ... 
doi:10.1145/3372884.3373162 dblp:conf/pepm/AarssenS20 fatcat:gbfak6v5wndh3i3ptbcjuxysvu

Equational Reasoning with Context-Free Families of String Diagrams [chapter]

Aleks Kissinger, Vladimir Zamdzhiev
2015 Lecture Notes in Computer Science  
We show that the language-membership and match-enumeration problems are decidable for these grammars, and hence that there is an algorithm for rewriting string graphs according to B-ESG rewrite patterns  ...  A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout rewriting.  ...  bounded.  ... 
doi:10.1007/978-3-319-21145-9_9 fatcat:kmmncweyfrdzrcbd3dlt6tnn7u
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