On weighted T-systems

Teruel, Enrique; Chrząstowski-Wachtel, Piotr; Colom, José Manuel; Silva, Manuel

doi:10.1007/3-540-55676-1_20

Cited by 81 publications

(72 citation statements)

References 10 publications

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“…They proved necessary and sufficient conditions for liveness and strict boundedness in their model. Their results as well as those in [19] correspond to those presented in this paper.…”

Section: Related Worksupporting

confidence: 92%

“…In particular, [19] gives necessary and sufficient conditions for strict boundedness of live weighted Marked Graphs (our Theorem 25). Strict boundedness is also the only kind of boundedness which has been investigated formally in the literature on SDFGs themselves; Karp and Miller in their seminal paper [10] introduced computation graphs, which are slightly more general than SDFGs.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Liveness and Boundedness of Synchronous Data Flow Graphs

Ghamarian

Geilen

Basten

et al. 2006

2006 Formal Methods in Computer Aided Design

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“…They proved necessary and sufficient conditions for liveness and strict boundedness in their model. Their results as well as those in [19] correspond to those presented in this paper.…”

Section: Related Worksupporting

confidence: 92%

Section: Related Workmentioning

confidence: 99%

Liveness and Boundedness of Synchronous Data Flow Graphs

Ghamarian

Geilen

Basten

et al. 2006

2006 Formal Methods in Computer Aided Design

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show abstract

“…Rougthly speaking, for any circuit c of a MTWEG, W (c) can be viewed as the production rate of tokens on c. So, if W (c) < 1 for a given circuit, the number of tokens on this circuit decreases after a finite firing sequence and therefore it leads to a deadlock situation [9], [10].…”

Section: B the Normalization Stepmentioning

confidence: 99%

“…Up to now, the time complexity of all the algorithms developed to answer these two fundamental questions is exponential in the worst case [9], [10]. The consequence is that the optimization problems on MTWEG are possibly not in N P : the evaluation of the feasible solutions is not possible in polynomial time, which limits dramatically the existence of efficient algorithms.…”

Section: Introduction and Related Workmentioning

confidence: 99%

A new approach for minimizing buffer capacities with throughput constraint for embedded system design

Benazouz

Marchetti

Munier-Kordon

et al. 2010

ACS/IEEE International Conference on Computer Systems and Applications - AICCSA 2010

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Abstract-The design of streaming (e.g. multimedia or network packet processing) applications must consider several optimizations such as the mimimization of the whole surface of the memory needed on a Chip. The minimum throughput of the output is usually fixed. In this paper, we present an original methodology to solve this problem.The application is modelled using a Marked Timed Weighted Event Graphs (in short MTWEG), which is a subclass of Petri nets. Transitions correspond to specific treatments and the places model buffers for data transfers. It is assumed that transitions are periodically fired with a fixed throughput.The problem is first mathematically modelled using an Integer Linear Program. We then study for a unique buffer the optimum throughput according to the capacity. A first polynomial simple algorithm computing the minimum surface for a fixed throughput is derived when there is no circuit in the initial MTWEG, which corresponds to a wide class of applications. We prove in this case that the capacities of every buffer may be optimized independently.For general MTWEG, the problem is NP-Hard and an original polynomial 2-approximation algorithm is presented. For practical applications, the solution computed is very close to the optimum.

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“…Up to now, the time complexity of all the algorithms developed to answer these two fundamental questions is exponential in the worst case [11], [12]. The consequence is that the optimization problems on MTWEG are possibly not in N P : the evaluation of the feasible solutions is not possible in polynomial time, which limits dramatically the existence of efficient algorithms.…”

Section: Introductionmentioning

confidence: 99%

A polynomial algorithm for the computation of buffer capacities with throughput constraint for embedded system design

Benazouz

Marchetti

Munier-Kordon

et al. 2009

2009 International Conference on Computers &Amp; Industrial Engineering

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Abstract-Marked Timed Weighted Event Graphs (in short MTWEG), which are a sub-class of Petri nets, are widely used for modelling practical industrial problems. In this paper, a central practical problem for the design of streaming (e.g. multimedia or network packet processing) applications is modelled using a MTWEG. The optimization problem tackled here consists then on finding an initial marking minimizing the overall number of tokens for a minimum given throughput.If the firings of the transitions are periodic, this problem is NPcomplete and can be modelled using an Integer Linear Program. A general lower bound on the minimum overall capacity is then proved. If the initial MTWEG has a unique circuit, a polynomial time algorithm based on the resolution of a particular Diophantine equation is presented to solve it exactly. We lastly experiment it on an industrial example.

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On weighted T-systems

Cited by 81 publications

References 10 publications

Liveness and Boundedness of Synchronous Data Flow Graphs

Liveness and Boundedness of Synchronous Data Flow Graphs

A new approach for minimizing buffer capacities with throughput constraint for embedded system design

A polynomial algorithm for the computation of buffer capacities with throughput constraint for embedded system design

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