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

Paulin Jacobé de Naurois, Virgile Mogbil
2010 Lecture Notes in Computer Science  
We adapt hypergraph 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.  ... 
doi:10.1007/978-3-642-15349-5_9 fatcat:3i7spskt4jgvllmnp57j33kapu

Languages, Rewriting Systems, and Verification of Infinite-State Systems [chapter]

Ahmed Bouajjani
2001 Lecture Notes in Computer Science  
One 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  ... 
doi:10.1007/3-540-48224-5_3 fatcat:ncoisj7wtbgabpjwswi2a4zef4

Algorithms and reductions for rewriting problems [chapter]

Rakesh M. Verma, Michael Rusinowitch, Denis Lugiez
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.  ... 
doi:10.1007/bfb0052369 fatcat:a4jqeyr33ve7jpkcunin6vdg6q

On Computing Reachability Sets of Process Rewrite Systems [chapter]

Ahmed Bouajjani, Tayssir Touili
2005 Lecture Notes in Computer Science  
We consider the problem of symbolic 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.  ... 
doi:10.1007/978-3-540-32033-3_35 fatcat:6phqzdvpfbaidoz7ydv52gmawi

Rewrite Closure for Ground and Cancellative AC Theories [chapter]

Ashish Tiwari
2001 Lecture Notes in Computer Science  
An abstract 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.  ... 
doi:10.1007/3-540-45294-x_28 fatcat:e55i6hexizfpdm5gjj5czc32lu

Well-Structured Pushdown Systems [chapter]

Xiaojuan Cai, Mizuhito Ogawa
2013 Lecture Notes in Computer Science  
As examples, we show that the coverability is decidable 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).  ... 
doi:10.1007/978-3-642-40184-8_10 fatcat:ub37zfwt3nbmdfpnfluusqk7em

Polynomially Bounded Matrix Interpretations

Johannes Waldmann, Marc Herbstritt
2010 International Conference on Rewriting Techniques and Applications  
The criterion can be expressed as a finite domain constraint 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.  ... 
doi:10.4230/lipics.rta.2010.357 dblp:conf/rta/Waldmann10 fatcat:pn6qu6wl7vd2dl5xeumj3ywc3u

On the stabilization of linear neutral delay-differential systems

W.-S. Lu, E. Lee, S. Zak
1986 IEEE Transactions on Automatic Control  
techniques, while the second is the continuous-discrete version of results 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.  ... 
doi:10.1109/tac.1986.1104115 fatcat:trpa2yedljdt7petjjdrjokogy

Decidable models of integer-manipulating programs with recursive parallelism (technical report) [article]

Matthew Hague, Anthony Widjaja Lin
2016 arXiv   pre-print
Since the threads 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.  ... 
arXiv:1605.06868v1 fatcat:fef22ojra5hhvbttpaalf4tidi

Controllability and reachability of 2-D positive systems: a graph theoretic approach

E. Fornasini, M.E. Valcher
2005 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
Upper bounds on the local 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 .  ... 
doi:10.1109/tcsi.2004.842872 fatcat:ely25wsf3jeafhnatshii3f63u

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 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  ... 
doi:10.12700/aph.11.03.2014.03.13 fatcat:65mrv5v3tzdptnegjh3ijrvnfm

Declarative routing

Boon Thau Loo, Joseph M. Hellerstein, Ion Stoica, Raghu Ramakrishnan
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 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.  ... 
doi:10.1145/1080091.1080126 dblp:conf/sigcomm/LooHSR05 fatcat:wfir6japdba25d7kesokkvr5tq

Declarative routing

Boon Thau Loo, Joseph M. Hellerstein, Ion Stoica, Raghu Ramakrishnan
2005 Computer communication review  
We show that our query language is a natural fit 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.  ... 
doi:10.1145/1090191.1080126 fatcat:vhttbhrngbf4pcrxydvh4gbj5i

The reachability problem for ground TRS and some extensions [chapter]

A. Deruyver, R. Gilleron
1989 Lecture Notes in Computer Science  
; modulo associativity, the problem is undecidable; modulo commutativity and associativity, it is decidable 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.  ... 
doi:10.1007/3-540-50939-9_135 fatcat:a7gr7pn6ofaxdgncr5arg4n7j4

Rewriting Models of Boolean Programs [chapter]

Ahmed Bouajjani, Javier Esparza
2006 Lecture Notes in Computer Science  
We show that 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.  ... 
doi:10.1007/11805618_11 fatcat:qjgi46t5vvcttkfe4rgagibvfq
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