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Reachability in Dynamical Systems with Rounding [article]

Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, Amaury Pouly, David Purser, Markus A. Whiteland
<span title="2020-09-28">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step.  ...  in the behaviour of the orbit 𝒪=<[x], [M[x]],[M[M[x]]],...>, i.e., the trajectory of a linear dynamical system in which the state is rounded after each step.  ...  How rounded orbits can be simulated by actual orbits of the dynamical system is investigated in [20, 29] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2009.13353v1">arXiv:2009.13353v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xbogzzin65hsjhsxlnyw4ifgpa">fatcat:xbogzzin65hsjhsxlnyw4ifgpa</a> </span>
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Reachability in Dynamical Systems with Rounding

Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, Amaury Pouly, David Purser, Markus A. Whiteland, Nitin Saxena, Sunil Simon
<span title="2020-12-04">2020</span>
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step.  ...  interested in the behaviour of the orbit 𝒪 = ⟨[x], [M[x]],[M[M[x]]],... ⟩, i.e., the trajectory of a linear dynamical system in which the state is rounded after each step.  ...  As the rounding is refined, some properties 36:4 Reachability in Dynamical Systems with Rounding of the discretized orbits follow probabilistic laws asymptotically, as shown in [16, 17] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.fsttcs.2020.36">doi:10.4230/lipics.fsttcs.2020.36</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gqutkk4k25gqfgafcbqaw4shiy">fatcat:gqutkk4k25gqfgafcbqaw4shiy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201212091256/https://drops.dagstuhl.de/opus/volltexte/2020/13277/pdf/LIPIcs-FSTTCS-2020-36.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/02/e2/02e23a17e90a4e579b03beaa468610fe8fb0ed39.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.fsttcs.2020.36"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Verified Reachability Analysis of Continuous Systems [chapter]

Fabian Immler
<span title="">2015</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This work presents the formal verification of an algorithm for reachability analysis in continuous systems.  ...  It is proved to be sound with respect to the existing formalization of ODEs in Isabelle/HOL.  ...  Introduction Many real-world systems with continuous dynamics can be modeled with ordinary differential equations (ODEs).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-46681-0_3">doi:10.1007/978-3-662-46681-0_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c4n2otyxrndu7pz7nwjbldggvq">fatcat:c4n2otyxrndu7pz7nwjbldggvq</a> </span>
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Beyond HyTech: Hybrid Systems Analysis Using Interval Numerical Methods [chapter]

Thomas A. Henzinger, Benjamin Horowitz, Rupak Majumdar, Howard Wong-Toi
<span title="">2000</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We h a ve designed a new algorithm, which is capable of directly verifying hybrid systems with general continuous dynamics, such as linear and nonlinear di erential equations.  ...  W e consider three examples: a thermostat with delay, a t wo-tank water system, and an air-tra c collision avoidance protocol.  ...  Introduction In a hybrid system, digital controllers interact with a continuous environment.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-46430-1_14">doi:10.1007/3-540-46430-1_14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eha3ugeevzfwdcqzbw24dmywnq">fatcat:eha3ugeevzfwdcqzbw24dmywnq</a> </span>
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Model-Checking Parameterized Concurrent Programs Using Linear Interfaces [chapter]

Salvatore La Torre, P. Madhusudan, Gennaro Parlato
<span title="">2010</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
a k round schedule.  ...  iteratively considering the program under k roundrobin schedules, for increasing values of k, using a novel compositional construct called linear interfaces that summarize the effect of a block of threads in  ...  Denote with S the following system of equations: 1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-14295-6_54">doi:10.1007/978-3-642-14295-6_54</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uf2ryxxmkvcffi367mjmcsaywy">fatcat:uf2ryxxmkvcffi367mjmcsaywy</a> </span>
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Recent progress in continuous and hybrid reachability analysis

Eugene Asarin, Thao Dang, Goran Frehse, Antoine Girard, Colas Le Guernic, Oded Maler
<span title="">2006</span> <i title="IEEE"> 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control </i> &nbsp;
Set-based reachability analysis computes all possible states a system may attain, and in this sense provides knowledge about the system with a completeness, or coverage, that a finite number of simulation  ...  Due to its inherent complexity, the application of reachability analysis has been limited so far to simple systems, both in the continuous and the hybrid domain.  ...  LHA readily model systems with simple dynamics such as timed protocols with drifting clocks, or production systems with tanks and buffers [3] . A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cacsd-cca-isic.2006.4776877">doi:10.1109/cacsd-cca-isic.2006.4776877</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hipfmslmorgtzjm56vw3rmrpju">fatcat:hipfmslmorgtzjm56vw3rmrpju</a> </span>
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Page 5114 of Mathematical Reviews Vol. , Issue 83m [page]

<span title="">1983</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
For example, in k=66 rounds, our algorithm will sort any n-element linearly ordered set with O(n'-'°) comparisons.”  ...  It is assumed that any property of a system can be defined by giving a set of ‘target’ states and a type of reachability.  ... 
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A Distributed Approach for Monitoring Multicast Service Availability

Kamil Sarac, Kevin C. Almeroth
<span title="">2004</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3izr2b7idfhjrp7ojmgew3mlbm" style="color: black;">Journal of Network and Systems Management</a> </i> &nbsp;
With the deployment of native multicast in commercial networks, multicast is getting closer to becoming a ubiquitous service in the Internet.  ...  We believe our work provides insight into the issues and considerations in designing and developing multicast reachability monitoring systems.  ...  It is a common piece in many network management systems. Most Network Operation Center (NOC) personnel are comfortable with SNMP and most are familiar with SNMP-based systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1023/b:jons.0000043684.78854.fd">doi:10.1023/b:jons.0000043684.78854.fd</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5ow65dbvkrd6ppkdlze6z4wvze">fatcat:5ow65dbvkrd6ppkdlze6z4wvze</a> </span>
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The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

Pieter Collins, Alexandre Goldsztejn
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
This paper introduces a new algorithm dedicated to the rigorous reachability analysis of nonlinear dynamical systems.  ...  The algorithm is initially presented in the context of discrete time dynamical systems, and then extended to continuous time dynamical systems driven by ODEs.  ...  Reachability Algorithm for Discrete Time Dynamical Systems Let us consider the discrete-time dynamical system (2) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2008.12.033">doi:10.1016/j.entcs.2008.12.033</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bfrrquyy7rcizbk3gycs263j6u">fatcat:bfrrquyy7rcizbk3gycs263j6u</a> </span>
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Analysis Method of Dynamic Extensible Service Model Based on Petri-Net

Can Zhang, Jing Jiang, Cheng Fan, Jie Sun, Rui Min Yang
<span title="">2013</span> <i title="Trans Tech Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6p2bt2u2i5dhli23v3xjch4yre" style="color: black;">Advanced Materials Research</a> </i> &nbsp;
A dynamic application customization and extensible service composition model is proposed in this paper.  ...  It is a big challenge to realize the dynamic change of the network environment and users demands.  ...  In addition, it is very convenient that the reachability tree is used to analyze the dynamic feature of system reachability, boundednes, liveness, etc.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4028/www.scientific.net/amr.765-767.1618">doi:10.4028/www.scientific.net/amr.765-767.1618</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dlect7nn3jeidllkcmlbons4de">fatcat:dlect7nn3jeidllkcmlbons4de</a> </span>
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SEER: Scalable Energy Efficient Relay Schemes in MANETs [chapter]

Lin-Fei Sung, Cheng-Lin Wu, Yi-Kai Chiang, Shyh-In Hwang
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
However, the radio signals are likely to overlap with each other in a geographical area.  ...  Thus, a good energy-efficient relay scheme should be able to further maximize the system lifetime without sacrificing the reachability of broadcasting.  ...  However, using predefined fixed probability p falls in a dilemma between reachability, the number of rebroadcasting messages, and the system lifetime as node movement.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11823285_97">doi:10.1007/11823285_97</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fxu5jb6ldfalxblmsrtzwrodb4">fatcat:fxu5jb6ldfalxblmsrtzwrodb4</a> </span>
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PHAVer: Algorithmic Verification of Hybrid Systems Past HyTech [chapter]

Goran Frehse
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Affine dynamics are handled by on-the-fly overapproximation and partitioning of the state space based on user-provided constraints and the dynamics of the system.  ...  In 1995, HyTech broke new ground as a potentially powerful tool for verifying hybrid systems. But due to practical and systematic limitations it is only applicable to relatively simple systems.  ...  Acknowledgments The author is most grateful for the numerous inspiring discussions with Prof. Bruce Krogh, whose insightful guidance was indispensable, and to Prof. Frits W. Vaandrager and Prof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-31954-2_17">doi:10.1007/978-3-540-31954-2_17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ux7wm556wrfj7ir7xkssjwrj5y">fatcat:ux7wm556wrfj7ir7xkssjwrj5y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811220259/https://users.ece.cmu.edu/~krogh/otherNSFpapers/Fre08.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/67/16/67166e2211ce47c42bf0b87eb36c0c07026660ce.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-31954-2_17"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

PHAVer: algorithmic verification of hybrid systems past HyTech

Goran Frehse
<span title="2008-01-08">2008</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zzy5ovlifvatfirg4js7u4uetq" style="color: black;">International Journal on Software Tools for Technology Transfer (STTT)</a> </i> &nbsp;
Affine dynamics are handled by on-the-fly overapproximation and partitioning of the state space based on user-provided constraints and the dynamics of the system.  ...  In 1995, HyTech broke new ground as a potentially powerful tool for verifying hybrid systems. But due to practical and systematic limitations it is only applicable to relatively simple systems.  ...  Acknowledgments The author is most grateful for the numerous inspiring discussions with Prof. Bruce Krogh, whose insightful guidance was indispensable, and to Prof. Frits W. Vaandrager and Prof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10009-007-0062-x">doi:10.1007/s10009-007-0062-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ohyfhbxobvaxho6ziyxg75wlju">fatcat:ohyfhbxobvaxho6ziyxg75wlju</a> </span>
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Sequentializing Parameterized Programs

Salvatore La Torre, P. Madhusudan, Gennaro Parlato
<span title="2012-07-15">2012</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
Sequentialization is achieved using the concept of a linear interface that captures the effect an unbounded block of processes have on the shared state in a k-round schedule.  ...  We exhibit assertion-preserving (reachability preserving) transformations from parameterized concurrent shared-memory programs, under a k-round scheduling of processes, to sequential programs.  ...  Let A be a parameterized multi-stack pushdown system and k ∈ N. Reachability up to k-round-robin schedules in A reduces to reachability in A k .  ... 
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Modeling a New AQM Model for Internet Chaotic Behavior Using Petri Nets

José M. Amigó, Guillem Duran, Ángel Giménez, José Valero, Oscar Martinez Bonastre
<span title="2021-06-24">2021</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/smrngspzhzce7dy6ofycrfxbim" style="color: black;">Applied Sciences</a> </i> &nbsp;
This innovative AQM is based on a discrete dynamical model of random early detection (RED) for controlling bifurcations and chaos in Internet congestion control.  ...  This article focuses on modeling with Petri nets (PNs) a new scheme of AQM.  ...  We are also grateful to José Ramón García Valdés, network administrator of the Miguel Hernández University communication network, for his support to run and supervise the network parameters discussed in  ... 
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