The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Heike Wehrheim - One of the best experts on this subject based on the ideXlab platform.
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towards a thread local Proof Technique for starvation freedom
Integrated Formal Methods, 2016Co-Authors: Gerhard Schellhorn, Oleg Travkin, Heike WehrheimAbstract:Today, numerous elaborate algorithms for the effective synchronization of concurrent processes operating on shared memory exist. Of particular importance for the verification of such concurrent algorithms are thread-local Proof Techniques, which allow to reason about the sequential program of one process individually. While thread-local verification of safety properties has received a lot of attention in recent years, this is less so for liveness properties, in particular for liveness under the assumption of fairness. In this paper, we propose a new thread-local Proof Technique for starvation freedom. Starvation freedom states that under a weakly fair schedule every process will eventually make progress. We contrast our new Proof Technique with existing global Proof Techniques based on ranking functions, and employ it exemplarily for the Proof of starvation freedom of ticket locks, the standard locking algorithm of the Linux kernel.
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IFM - Towards a Thread-Local Proof Technique for Starvation Freedom
Lecture Notes in Computer Science, 2016Co-Authors: Gerhard Schellhorn, Oleg Travkin, Heike WehrheimAbstract:Today, numerous elaborate algorithms for the effective synchronization of concurrent processes operating on shared memory exist. Of particular importance for the verification of such concurrent algorithms are thread-local Proof Techniques, which allow to reason about the sequential program of one process individually. While thread-local verification of safety properties has received a lot of attention in recent years, this is less so for liveness properties, in particular for liveness under the assumption of fairness. In this paper, we propose a new thread-local Proof Technique for starvation freedom. Starvation freedom states that under a weakly fair schedule every process will eventually make progress. We contrast our new Proof Technique with existing global Proof Techniques based on ranking functions, and employ it exemplarily for the Proof of starvation freedom of ticket locks, the standard locking algorithm of the Linux kernel.
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A Sound and Complete Proof Technique for Linearizability of Concurrent Data Structures
ACM Transactions on Computational Logic, 2014Co-Authors: Gerhard Schellhorn, John Derrick, Heike WehrheimAbstract:Efficient implementations of data structures such as queues, stacks or hash-tables allow for concurrent access by many processes at the same time. To increase concurrency, these algorithms often completely dispose with locking, or only lock small parts of the structure. Linearizability is the standard correctness criterion for such a scenario—where a concurrent object is linearizable if all of its operations appear to take effect instantaneously some time between their invocation and return. The potential concurrent access to the shared data structure tremendously increases the complexity of the verification problem, and thus current Proof Techniques for showing linearizability are all tailored to specific types of data structures. In previous work, we have shown how simulation-based Proof conditions for linearizability can be used to verify a number of subtle concurrent algorithms. In this article, we now show that conditions based on backward simulation can be used to show linearizability of every linearizable algorithm, that is, we show that our Proof Technique is both sound and complete. We exemplify our approach by a linearizability Proof of a concurrent queue, introduced in Herlihy and Wing's landmark paper on linearizability. Except for their manual Proof, none of the numerous other approaches have successfully treated this queue. Our approach is supported by a full mechanisation: both the linearizability Proofs for case studies like the queue, and the Proofs of soundness and completeness have been carried out with an interactive prover, which is KIV.
Gerhard Schellhorn - One of the best experts on this subject based on the ideXlab platform.
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towards a thread local Proof Technique for starvation freedom
Integrated Formal Methods, 2016Co-Authors: Gerhard Schellhorn, Oleg Travkin, Heike WehrheimAbstract:Today, numerous elaborate algorithms for the effective synchronization of concurrent processes operating on shared memory exist. Of particular importance for the verification of such concurrent algorithms are thread-local Proof Techniques, which allow to reason about the sequential program of one process individually. While thread-local verification of safety properties has received a lot of attention in recent years, this is less so for liveness properties, in particular for liveness under the assumption of fairness. In this paper, we propose a new thread-local Proof Technique for starvation freedom. Starvation freedom states that under a weakly fair schedule every process will eventually make progress. We contrast our new Proof Technique with existing global Proof Techniques based on ranking functions, and employ it exemplarily for the Proof of starvation freedom of ticket locks, the standard locking algorithm of the Linux kernel.
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IFM - Towards a Thread-Local Proof Technique for Starvation Freedom
Lecture Notes in Computer Science, 2016Co-Authors: Gerhard Schellhorn, Oleg Travkin, Heike WehrheimAbstract:Today, numerous elaborate algorithms for the effective synchronization of concurrent processes operating on shared memory exist. Of particular importance for the verification of such concurrent algorithms are thread-local Proof Techniques, which allow to reason about the sequential program of one process individually. While thread-local verification of safety properties has received a lot of attention in recent years, this is less so for liveness properties, in particular for liveness under the assumption of fairness. In this paper, we propose a new thread-local Proof Technique for starvation freedom. Starvation freedom states that under a weakly fair schedule every process will eventually make progress. We contrast our new Proof Technique with existing global Proof Techniques based on ranking functions, and employ it exemplarily for the Proof of starvation freedom of ticket locks, the standard locking algorithm of the Linux kernel.
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A Sound and Complete Proof Technique for Linearizability of Concurrent Data Structures
ACM Transactions on Computational Logic, 2014Co-Authors: Gerhard Schellhorn, John Derrick, Heike WehrheimAbstract:Efficient implementations of data structures such as queues, stacks or hash-tables allow for concurrent access by many processes at the same time. To increase concurrency, these algorithms often completely dispose with locking, or only lock small parts of the structure. Linearizability is the standard correctness criterion for such a scenario—where a concurrent object is linearizable if all of its operations appear to take effect instantaneously some time between their invocation and return. The potential concurrent access to the shared data structure tremendously increases the complexity of the verification problem, and thus current Proof Techniques for showing linearizability are all tailored to specific types of data structures. In previous work, we have shown how simulation-based Proof conditions for linearizability can be used to verify a number of subtle concurrent algorithms. In this article, we now show that conditions based on backward simulation can be used to show linearizability of every linearizable algorithm, that is, we show that our Proof Technique is both sound and complete. We exemplify our approach by a linearizability Proof of a concurrent queue, introduced in Herlihy and Wing's landmark paper on linearizability. Except for their manual Proof, none of the numerous other approaches have successfully treated this queue. Our approach is supported by a full mechanisation: both the linearizability Proofs for case studies like the queue, and the Proofs of soundness and completeness have been carried out with an interactive prover, which is KIV.
Oleg Travkin - One of the best experts on this subject based on the ideXlab platform.
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towards a thread local Proof Technique for starvation freedom
Integrated Formal Methods, 2016Co-Authors: Gerhard Schellhorn, Oleg Travkin, Heike WehrheimAbstract:Today, numerous elaborate algorithms for the effective synchronization of concurrent processes operating on shared memory exist. Of particular importance for the verification of such concurrent algorithms are thread-local Proof Techniques, which allow to reason about the sequential program of one process individually. While thread-local verification of safety properties has received a lot of attention in recent years, this is less so for liveness properties, in particular for liveness under the assumption of fairness. In this paper, we propose a new thread-local Proof Technique for starvation freedom. Starvation freedom states that under a weakly fair schedule every process will eventually make progress. We contrast our new Proof Technique with existing global Proof Techniques based on ranking functions, and employ it exemplarily for the Proof of starvation freedom of ticket locks, the standard locking algorithm of the Linux kernel.
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IFM - Towards a Thread-Local Proof Technique for Starvation Freedom
Lecture Notes in Computer Science, 2016Co-Authors: Gerhard Schellhorn, Oleg Travkin, Heike WehrheimAbstract:Today, numerous elaborate algorithms for the effective synchronization of concurrent processes operating on shared memory exist. Of particular importance for the verification of such concurrent algorithms are thread-local Proof Techniques, which allow to reason about the sequential program of one process individually. While thread-local verification of safety properties has received a lot of attention in recent years, this is less so for liveness properties, in particular for liveness under the assumption of fairness. In this paper, we propose a new thread-local Proof Technique for starvation freedom. Starvation freedom states that under a weakly fair schedule every process will eventually make progress. We contrast our new Proof Technique with existing global Proof Techniques based on ranking functions, and employ it exemplarily for the Proof of starvation freedom of ticket locks, the standard locking algorithm of the Linux kernel.
Rudiger Urbanke - One of the best experts on this subject based on the ideXlab platform.
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Spatial Coupling as a Proof Technique and Three Applications
IEEE Transactions on Information Theory, 2016Co-Authors: Andrei Giurgiu, Nicolas Macris, Rudiger UrbankeAbstract:The aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic properties of graphical models are easier to prove in the case of spatial coupling. In such cases, one can then use the so-called interpolation method to transfer known results for the spatially coupled case to the uncoupled one. Our main use of this framework is for Low-density parity check (LDPC) codes, where we use interpolation to show that the average entropy of the codeword conditioned on the observation is asymptotically the same for spatially coupled as for uncoupled ensembles. We give three applications of this result for a large class of LDPC ensembles. The first one is a Proof of the so-called Maxwell construction stating that the MAP threshold is equal to the area threshold of the BP GEXIT curve. The second is a Proof of the equality between the BP and MAP GEXIT curves above the MAP threshold. The third application is the intimately related fact that the replica symmetric formula for the conditional entropy in the infinite block length limit is exact.
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and now to something completely different spatial coupling as a Proof Technique
International Symposium on Information Theory, 2013Co-Authors: Andrei Giurgiu, Nicolas Macris, Rudiger UrbankeAbstract:The aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic properties of graphical models are easier to prove in the case of spatial coupling. In such cases, one can then use the so-called interpolation method to transfer results known for the spatially coupled case to the uncoupled one. Our main application of this framework is to LDPC codes, where we use interpolation to show that the average entropy of the codeword conditioned on the observation is asymptotically the same for spatially coupled as for uncoupled ensembles. We use this fact to prove the so-called Maxwell conjecture for a large class of ensembles. In a first paper last year, we have successfully implemented this strategy for the case of LDPC ensembles where the variable node degree distribution is Poisson. In the current paper we now show how to treat the practically more relevant case of general left degree distributions. In particular, regular ensembles fall within this framework. As we will see, a number of technical difficulties appear when compared to the simpler case of Poisson-distributed degrees. For our arguments to hold we need symmetry to be present. For coding, this symmetry follows from the channel symmetry; for general graphical models the required symmetry is called Nishimori symmetry.
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Spatial Coupling as a Proof Technique
arXiv: Information Theory, 2013Co-Authors: Andrei Giurgiu, Nicolas Macris, Rudiger UrbankeAbstract:The aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic properties of graphical models are easier to prove in the case of spatial coupling. In such cases, one can then use the so-called interpolation method to transfer results known for the spatially coupled case to the uncoupled one. Our main application of this framework is to LDPC codes, where we use interpolation to show that the average entropy of the codeword conditioned on the observation is asymptotically the same for spatially coupled as for uncoupled ensembles. We use this fact to prove the so-called Maxwell conjecture for a large class of ensembles. In a first paper last year, we have successfully implemented this strategy for the case of LDPC ensembles where the variable node degree distribution is Poisson. In the current paper we now show how to treat the practically more relevant case of general variable degree distributions. In particular, regular ensembles fall within this framework. As we will see, a number of technical difficulties appear when compared to the simpler case of Pois son- distributed degrees. For our arguments to hold we need symmetry to be present. For coding, this symmetry follows from the channel symmetry; for general graphical models the required symmetry is called Nishimori symmetry.
Rossella Petreschi - One of the best experts on this subject based on the ideXlab platform.
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graphs that are not pairwise compatible a new Proof Technique extended abstract
International Workshop on Combinatorial Algorithms, 2018Co-Authors: Pierluigi Baiocchi, Tiziana Calamoneri, Angelo Monti, Rossella PetreschiAbstract:A graph \(G=(V,E)\) is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers \(d_{min}\) and \(d_{max}\), \(d_{min} \le d_{max}\), such that each node \(u \in V\) is uniquely associated to a leaf of T and there is an edge \((u,v) \in E\) if and only if \(d_{min} \le d_{T} (u, v) \le d_{max}\), where \(d_{T} (u, v)\) is the sum of the weights of the edges on the unique path \(P_{T}(u,v)\) from u to v in T. Understanding which graph classes lie inside and which ones outside the PCG class is an important issue. Despite numerous efforts, a complete characterization of the PCG class is not known yet. In this paper we propose a new Proof Technique that allows us to show that some interesting classes of graphs have empty intersection with PCG. We demonstrate our Technique by showing many graph classes that do not lie in PCG. As a side effect, we show a not pairwise compatibility planar graph with 8 nodes (i.e. \(C^2_8\)), so improving the previously known result concerning the smallest planar graph known not to be PCG.
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IWOCA - Graphs that Are Not Pairwise Compatible: A New Proof Technique (Extended Abstract)
Lecture Notes in Computer Science, 2018Co-Authors: Pierluigi Baiocchi, Tiziana Calamoneri, Angelo Monti, Rossella PetreschiAbstract:A graph \(G=(V,E)\) is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers \(d_{min}\) and \(d_{max}\), \(d_{min} \le d_{max}\), such that each node \(u \in V\) is uniquely associated to a leaf of T and there is an edge \((u,v) \in E\) if and only if \(d_{min} \le d_{T} (u, v) \le d_{max}\), where \(d_{T} (u, v)\) is the sum of the weights of the edges on the unique path \(P_{T}(u,v)\) from u to v in T. Understanding which graph classes lie inside and which ones outside the PCG class is an important issue. Despite numerous efforts, a complete characterization of the PCG class is not known yet. In this paper we propose a new Proof Technique that allows us to show that some interesting classes of graphs have empty intersection with PCG. We demonstrate our Technique by showing many graph classes that do not lie in PCG. As a side effect, we show a not pairwise compatibility planar graph with 8 nodes (i.e. \(C^2_8\)), so improving the previously known result concerning the smallest planar graph known not to be PCG.
