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Match-Bounded String Rewriting Systems
[chapter]

2003
*
Lecture Notes in Computer Science
*

The problem of existence of a

doi:10.1007/978-3-540-45138-9_39
fatcat:lh6d32nalrdf5h7mi443qxstyi
*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*. ...##
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Match-Bounded String Rewriting Systems

2004
*
Applicable Algebra in Engineering, Communication and Computing
*

The problem of existence of a

doi:10.1007/s00200-004-0162-8
fatcat:eshe4tyfqrhgrhkgx7k4xjtfvy
*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*. ...##
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Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

2005
*
Journal of automated reasoning
*

A

doi:10.1007/s10817-005-9024-8
fatcat:47spcbtif5emdkxuh62o7cal64
*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 ...##
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On Tree Automata that Certify Termination of Left-Linear Term Rewriting Systems
[chapter]

2005
*
Lecture Notes in Computer Science
*

It is a generalization of the

doi:10.1007/978-3-540-32033-3_26
fatcat:v7glusrm4rcrffverthjnievum
*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. ...##
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On tree automata that certify termination of left-linear term rewriting systems

2007
*
Information and Computation
*

It is a generalization of the

doi:10.1016/j.ic.2006.08.007
fatcat:phx2dmluobbphglxh6ompinhlq
*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. ...##
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Termination of Cycle Rewriting
[chapter]

2014
*
Lecture Notes in Computer Science
*

Most techniques for proving termination of

doi:10.1007/978-3-319-08918-8_33
fatcat:owhrz3ditrhoxlbk4yojhfuwva
*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*...##
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Synthesising Graphical Theories
[article]

2012
*
arXiv
*
pre-print

In this extended abstract, we adapt this technique to diagrammatic theories, expressed as graph

arXiv:1202.6079v2
fatcat:bemtn6mwvvcgzp4py4zr2ggepy
*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). ...##
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On termination of one rule rewrite systems

1994
*
Theoretical Computer Science
*

., On termination of one rule

doi:10.1016/0304-3975(94)00029-8
fatcat:blq7jlcworac7kkkl3kdfel3be
*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*. ...##
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Deleting string rewriting systems preserve regularity

2004
*
Theoretical Computer Science
*

A

doi:10.1016/j.tcs.2004.04.009
fatcat:kjhbjtx4obcqbbxvglxq42yuui
*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] . ...##
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Deleting String Rewriting Systems Preserve Regularity
[chapter]

2003
*
Lecture Notes in Computer Science
*

A

doi:10.1007/3-540-45007-6_27
fatcat:o2sx5sjwrrdz3bdwoonxd4hu2m
*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] . ...##
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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.” ...##
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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. ...##
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Pattern graph rewrite systems

2014
*
Electronic Proceedings in Theoretical Computer Science
*

Dixon, Duncan and Kissinger introduced

doi:10.4204/eptcs.143.5
fatcat:juelbsr5drcmrombpa43mtg2yy
*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 ...##
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High-fidelity metaprogramming with separator syntax trees

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

doi:10.1145/3372884.3373162
dblp:conf/pepm/AarssenS20
fatcat:gbfak6v5wndh3i3ptbcjuxysvu
*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*...##
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Equational Reasoning with Context-Free Families of String Diagrams
[chapter]

2015
*
Lecture Notes in Computer Science
*

We show that the language-membership and

doi:10.1007/978-3-319-21145-9_9
fatcat:kmmncweyfrdzrcbd3dlt6tnn7u
*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*. ...
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