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Match-Bounded String Rewriting Systems
[chapter]
2003
Lecture Notes in Computer Science
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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
2004
Applicable Algebra in Engineering, Communication and Computing
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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
2005
Journal of automated reasoning
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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]
2005
Lecture Notes in Computer Science
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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
2007
Information and Computation
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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]
2014
Lecture Notes in Computer Science
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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]
2012
arXiv
pre-print
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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
1994
Theoretical Computer Science
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., 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
2004
Theoretical Computer Science
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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]
2003
Lecture Notes in Computer Science
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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
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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
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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
2014
Electronic Proceedings in Theoretical Computer Science
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2012 pre-print arXiv:1204.6695v2 fatcat:lh6pvauohrhiblosc5r475xdviOther Versions
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
2020
Proceedings of the 2020 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation - PEPM 2020
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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]
2015
Lecture Notes in Computer Science
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2015 pre-print arXiv:1504.02716v1 fatcat:3zk3xnjnkjeuhb4ofw6laac4qqOther Versions
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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