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Rewriting Systems for Reachability in Vector Addition Systems with Pairs
[chapter]

2010
*
Lecture Notes in Computer Science
*

We adapt hypergraph

doi:10.1007/978-3-642-15349-5_9
fatcat:3i7spskt4jgvllmnp57j33kapu
*rewriting**system*to a generalization of*Vector**Addition**Systems**with*States (VASS) that we call*vector**addition**systems**with**pairs*(VASP). ...*Reachability**for*the later is well known be equivalent to*reachability**in*Petri nets. ... Introduction*Vector**Addition**Systems**with**Pairs*(VASP) are*Vector**Addition**Systems**with*States (VASS) extended*with**paired*arcs. ...##
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Languages, Rewriting Systems, and Verification of Infinite-State Systems
[chapter]

2001
*
Lecture Notes in Computer Science
*

One

doi:10.1007/3-540-48224-5_3
fatcat:ncoisj7wtbgabpjwswi2a4zef4
*additional*dimension*in*the*rewriting**system*can be used to encode the control states.*For*instance, consider a*system*which manipulates one pushdown stack (resp. one FIFO queue). ... Models of*in*nite-state*systems*The models we consider are de ned as*pairs*(C; ) where the set of con gurations is C = ( ) n , and the transition relation is one of the*rewriting*relations R y ,*with*y ...##
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Algorithms and reductions for rewriting problems
[chapter]

1998
*
Lecture Notes in Computer Science
*

*In*this paper we initiate a study of polynomial-time reductions

*for*some basic decision problems of

*rewrite*

*systems*. ... We also show that there is a family of string

*rewrite*

*systems*

*for*which the word problem is trivially decidable but con uence undecidable, and we show a linear equational theory

*with*decidable word problem ... Rusinowitch

*for*their generous support during his sabbatical year at INRIA Lorraine. The authors thank the reviewers and the committee

*for*constructive comments. ...

##
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On Computing Reachability Sets of Process Rewrite Systems
[chapter]

2005
*
Lecture Notes in Computer Science
*

We consider the problem of symbolic

doi:10.1007/978-3-540-32033-3_35
fatcat:6phqzdvpfbaidoz7ydv52gmawi
*reachability*analysis of a class of term*rewrite**systems*called Process*Rewrite**Systems*(PRS). ... A PRS can be seen as the union of two mutually interdependent sets of term*rewrite*rules: a prefix*rewrite**system*(or, equivalently, a pushdown*system*), and a multiset*rewrite**system*(or, equivalently, ... , an algorithm (resp. semi-algorithm)*for*exact (resp. upperapproximate)*reachability*analysis*for*the class of PRS obtained by combining C*systems**with*prefix*rewrite**systems*. ...##
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Rewrite Closure for Ground and Cancellative AC Theories
[chapter]

2001
*
Lecture Notes in Computer Science
*

An abstract

doi:10.1007/3-540-45294-x_28
fatcat:e55i6hexizfpdm5gjj5czc32lu
*rewrite*closure can be interpreted as a specialized ground tree transducer (*pair*of bottom-up tree automata) and can be used to efficiently decide the*reachability*relation → * I E∪I E − ∪I ... The procedure is extended,*in*a modular way, to deal*with*signatures containing cancellative associative commutative function symbols. ... We would like to thank the anonymous reviewers*for*their helpful comments. ...##
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Well-Structured Pushdown Systems
[chapter]

2013
*
Lecture Notes in Computer Science
*

As examples, we show that the coverability is decidable

doi:10.1007/978-3-642-40184-8_10
fatcat:ub37zfwt3nbmdfpnfluusqk7em
*for*recursive*vector**addition**system**with*states, multi-set pushdown*systems*, and a WSPDS*with*finite control states and well-quasi-ordered stack ... Pushdown*systems*(PDSs) model single-thread recursive programs, and well-structured transition*systems*(WSTSs), such as*vector**addition**systems*, are useful to represent non-recursive multi-thread programs ...*for*Scientific Research(B) (23300008). ...##
###
Polynomially Bounded Matrix Interpretations

2010
*
International Conference on Rewriting Techniques and Applications
*

The criterion can be expressed as a finite domain constraint

doi:10.4230/lipics.rta.2010.357
dblp:conf/rta/Waldmann10
fatcat:pn6qu6wl7vd2dl5xeumj3ywc3u
*system*. It translates to a Boolean constraint*system**with*a size that is polynomial*in*the dimension of the interpretation. ... Matrix interpretations can be used to bound the derivational complexity of*rewrite**systems*. We present a criterion that completely characterizes matrix interpretations that are polynomially bounded. ... A*rewrite**system*R is a set of*pairs*of terms*with*variables, and it defines a*rewrite*relation → R*in*the usual way. ...##
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On the stabilization of linear neutral delay-differential systems

1986
*
IEEE Transactions on Automatic Control
*

techniques, while the second is the continuous-discrete version of results

doi:10.1109/tac.1986.1104115
fatcat:trpa2yedljdt7petjjdrjokogy
*in*[6] derived using maximum principle techniques. ... Examination of these two feedback control laws reveals that the first is the continuous-discrete version of the continuous results presented*in*[ 1 ] and [ l l ] originally derived using dynamic programming ... ACKNOWLEDGMENT The authors would like to thank the reviewer*for*the constructive remarks. ...##
###
Decidable models of integer-manipulating programs with recursive parallelism (technical report)
[article]

2016
*
arXiv
*
pre-print

Since the threads

arXiv:1605.06868v1
fatcat:fef22ojra5hhvbttpaalf4tidi
*in*each program configuration are structured*in*a hierarchical fashion, our model is state-extended ground-tree*rewrite**systems*equipped*with*shared unbounded integer counters that can ...*systems**with*counters. ... Another variant of*vector**addition**systems**with*recursion are pushdown*vector**addition**systems*, where a single (sequential) stack and several global counters are permitted. ...##
###
Controllability and reachability of 2-D positive systems: a graph theoretic approach

2005
*
IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications
*

Upper bounds on the local

doi:10.1109/tcsi.2004.842872
fatcat:ely25wsf3jeafhnatshii3f63u
*reachability*index*for*some special classes of positive*systems*are finally derived. ... While the global*reachability*index is bounded by the*system*dimension , the local*reachability*index may far exceed the*system*dimension. ... If so is an th monomial*vector*and,*for**systems**with*scalar inputs is an th monomial*vector*Notice, finally, that all*pairs*are necessarily distinct, but the case may occur that*for*. ...##
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On the Reachability of Linear Time Varying Systems

2014
*
Acta Polytechnica Hungarica
*

Developing an adequate version of the Cauchy formula, a necessary and suffiecient condition

doi:10.12700/aph.11.03.2014.03.13
fatcat:65mrv5v3tzdptnegjh3ijrvnfm
*for*complete*reachability*of generalized LTV*systems*is obtained*in*terms of a generalized Gram matrix. ...*In*this paper*system*properties of generalized linear time varying (LTV)*systems*are discussed where,*in**addition*to the control, its certain derivatives also appear both*in*the dynamics and the observation ... that is a*vector**in*the image space of the Kalman-matrix, gen Kdoes not equal the*reachable*subspace of the general*system*over [0, ] By the classical Lagrange lemma, if the above holds*for*every ...##
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Declarative routing

2005
*
Proceedings of the 2005 conference on Applications, technologies, architectures, and protocols for computer communications - SIGCOMM '05
*

We show that our query language is a natural fit

doi:10.1145/1080091.1080126
dblp:conf/sigcomm/LooHSR05
fatcat:wfir6japdba25d7kesokkvr5tq
*for*routing, and can express a variety of well-known routing protocols*in*a compact and clean fashion. ...*In*this paper, we explore a new point*in*this design space that aims to strike a better balance between the extensibility and robustness of a routing infrastructure. ... Consequently, the communication overhead of each*additional*query*for**Pair*-Share-Mix2 is reduced compared to*Pair*-Share-Mix. ...##
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Declarative routing

2005
*
Computer communication review
*

We show that our query language is a natural fit

doi:10.1145/1090191.1080126
fatcat:vhttbhrngbf4pcrxydvh4gbj5i
*for*routing, and can express a variety of well-known routing protocols*in*a compact and clean fashion. ...*In*this paper, we explore a new point*in*this design space that aims to strike a better balance between the extensibility and robustness of a routing infrastructure. ... Consequently, the communication overhead of each*additional*query*for**Pair*-Share-Mix2 is reduced compared to*Pair*-Share-Mix. ...##
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The reachability problem for ground TRS and some extensions
[chapter]

1989
*
Lecture Notes in Computer Science
*

; modulo associativity, the problem is undecidable; modulo commutativity and associativity, it is decidable

doi:10.1007/3-540-50939-9_135
fatcat:a7gr7pn6ofaxdgncr5arg4n7j4
*with*complexity of*reachability*problem*for**vector**addition**systems*. ... ~S~A~ The*reachability*problem*for*term*rewriting**systems*(TRS) is the problem of deciding,*for*a given TRS S and two terms M and N, whether M can reduce to N by applying the rules of S. ... (i) and (ii)*For*RGAC, we have a negative answer*for*(i) and a positive answer*for*(ii)*with*the complexity of the teachability problem*for**vector**addition**systems*. ...##
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Rewriting Models of Boolean Programs
[chapter]

2006
*
Lecture Notes in Computer Science
*

We show that

doi:10.1007/11805618_11
fatcat:qjgi46t5vvcttkfe4rgagibvfq
*rewrite**systems*can be used to give semantics to imperative programs*with*boolean variables, a class of programs used*in*software model-checking as over-or underapproximations of real programs ... We study the classes of*rewrite**systems*induced by programs*with*different features like procedures, concurrency, or dynamic thread creation, and survey a number of results on their word problem and their ... Analysis String-*rewriting**systems**with*prefix-*rewriting*have an interesting story. ...
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