The Experts below are selected from a list of 2151 Experts worldwide ranked by ideXlab platform

Erofeev Evgeny - One of the best experts on this subject based on the ideXlab platform.

  • On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency
    'Open Publishing Association', 2020
    Co-Authors: Tredup Ronny, Erofeev Evgeny
    Abstract:

    Modeling of real-world systems with Petri nets allows to benefit from their generic concepts of parallelism, synchronisation and conflict, and obtain a concise yet expressive system representation. Algorithms for synthesis of a net from a sequential specification enable the well-developed theory of Petri nets to be applied for the system analysis through a net model. The problem of $\tau$-synthesis consists in deciding whether a given Directed Labeled Graph $A$ is isomorphic to the reachability Graph of a Boolean Petri net $N$ of type $\tau$. In case of a positive decision, $N$ should be constructed. For many Boolean types of nets, the problem is NP-complete. This paper deals with a special variant of $\tau$-synthesis that imposes restrictions for the target net $N$: we investigate dependency $d$-restricted tau-synthesis (DR$\tau$S) where each place of $N$ can influence and be influenced by at most d transitions. For a type $\tau$, if tau-synthesis is NP-complete then DR$\tau$S is also NP-complete. In this paper, we show that DR$\tau$S parameterized by $d$ is in XP. Furthermore, we prove that it is W[2]-hard, for many Boolean types that allow unconditional interactions set and reset.Comment: In Proceedings ICE 2020, arXiv:2009.07628. arXiv admin note: substantial text overlap with arXiv:2007.1237

  • On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency (Technical Report)
    2020
    Co-Authors: Tredup Ronny, Erofeev Evgeny
    Abstract:

    The problem of $\tau$-synthesis consists in deciding whether a given Directed Labeled Graph $A$ is isomorphic to the reachability Graph of a Boolean Petri net $N$ of type $\tau$. In case of a positive decision, $N$ should be constructed. For many Boolean types of nets, the problem is NP-complete. This paper deals with a special variant of $\tau$-synthesis that imposes restrictions for the target net $N$: we investigate \emph{dependency $d$-restricted $\tau$-synthesis (DR$\tau$S)} where each place of $N$ can influence and be influenced by at most $d$ transitions. For a type $\tau$, if $\tau$-synthesis is NP-complete then DR$\tau$S is also NP-complete. In this paper, we show that DR$\tau$S parameterized by $d$ is in XP. Furthermore, we prove that it is $W[2]$-hard, for many Boolean types that allow unconditional interactions $set$ and $reset$

Philippe M - One of the best experts on this subject based on the ideXlab platform.

  • A Linear Program to Compare Path-Complete Lyapunov Functions
    'Institute of Electrical and Electronics Engineers (IEEE)', 2017
    Co-Authors: Angeli D, Athanasopoulos N, Rm Jungers, Philippe M
    Abstract:

    We provide an algorithmic procedure allowing to compare stability certificates for discrete-time switching systems and in specific Path-Complete Lyapunov functions (PCLFs). These mathematical objects consist of a set of positive definite functions and a set of Lyapunov inequalities, encoded in a Directed, Labeled Graph. Given two such Graphs, we formulate necessary and sufficient conditions to decide if the existence of a PCLF for the first Graph implies existence of a PCLF for the second Graph, where the corresponding set of functions is constructed by conic combinations of the set of functions related to the first PCLF. The conditions depend only on the topologies of the two Graphs and can be verified by solving a linear program. It is the first systematic approach to compare the conservativeness of PCLFs

  • Path-complete Graphs and common Lyapunov functions
    'Association for Computing Machinery (ACM)', 2017
    Co-Authors: Angeli D, Athanasopoulos N, Rm Jungers, Philippe M
    Abstract:

    A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called pieces, and a Directed, Labeled Graph defining Lyapunov inequalities between these pieces. It provides a stability certificate for discrete-time arbitrary switching systems. In this paper, we prove that the satisfiability of such a criterion implies the existence of a Common Lyapunov Function, expressed as the composition of minima and maxima of the pieces of the Path-Complete Lyapunov function. the converse however is not true even for discrete-time linear systems: we present such a system where a max-of-2 quadratics Lyapunov function exists while no corresponding Path-Complete Lyapunov function with 2 quadratic pieces exists. In light of this, we investigate when it is possible to decide if a Path- Complete Lyapunov function is less conservative than another. By analyzing the combinatorial and algebraic structure of the Graph and the pieces respectively, we provide simple tools to decide when the existence of such a Lyapunov function implies that of another

Tredup Ronny - One of the best experts on this subject based on the ideXlab platform.

  • On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency
    'Open Publishing Association', 2020
    Co-Authors: Tredup Ronny, Erofeev Evgeny
    Abstract:

    Modeling of real-world systems with Petri nets allows to benefit from their generic concepts of parallelism, synchronisation and conflict, and obtain a concise yet expressive system representation. Algorithms for synthesis of a net from a sequential specification enable the well-developed theory of Petri nets to be applied for the system analysis through a net model. The problem of $\tau$-synthesis consists in deciding whether a given Directed Labeled Graph $A$ is isomorphic to the reachability Graph of a Boolean Petri net $N$ of type $\tau$. In case of a positive decision, $N$ should be constructed. For many Boolean types of nets, the problem is NP-complete. This paper deals with a special variant of $\tau$-synthesis that imposes restrictions for the target net $N$: we investigate dependency $d$-restricted tau-synthesis (DR$\tau$S) where each place of $N$ can influence and be influenced by at most d transitions. For a type $\tau$, if tau-synthesis is NP-complete then DR$\tau$S is also NP-complete. In this paper, we show that DR$\tau$S parameterized by $d$ is in XP. Furthermore, we prove that it is W[2]-hard, for many Boolean types that allow unconditional interactions set and reset.Comment: In Proceedings ICE 2020, arXiv:2009.07628. arXiv admin note: substantial text overlap with arXiv:2007.1237

  • On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency (Technical Report)
    2020
    Co-Authors: Tredup Ronny, Erofeev Evgeny
    Abstract:

    The problem of $\tau$-synthesis consists in deciding whether a given Directed Labeled Graph $A$ is isomorphic to the reachability Graph of a Boolean Petri net $N$ of type $\tau$. In case of a positive decision, $N$ should be constructed. For many Boolean types of nets, the problem is NP-complete. This paper deals with a special variant of $\tau$-synthesis that imposes restrictions for the target net $N$: we investigate \emph{dependency $d$-restricted $\tau$-synthesis (DR$\tau$S)} where each place of $N$ can influence and be influenced by at most $d$ transitions. For a type $\tau$, if $\tau$-synthesis is NP-complete then DR$\tau$S is also NP-complete. In this paper, we show that DR$\tau$S parameterized by $d$ is in XP. Furthermore, we prove that it is $W[2]$-hard, for many Boolean types that allow unconditional interactions $set$ and $reset$

Angeli D - One of the best experts on this subject based on the ideXlab platform.

  • A Linear Program to Compare Path-Complete Lyapunov Functions
    'Institute of Electrical and Electronics Engineers (IEEE)', 2017
    Co-Authors: Angeli D, Athanasopoulos N, Rm Jungers, Philippe M
    Abstract:

    We provide an algorithmic procedure allowing to compare stability certificates for discrete-time switching systems and in specific Path-Complete Lyapunov functions (PCLFs). These mathematical objects consist of a set of positive definite functions and a set of Lyapunov inequalities, encoded in a Directed, Labeled Graph. Given two such Graphs, we formulate necessary and sufficient conditions to decide if the existence of a PCLF for the first Graph implies existence of a PCLF for the second Graph, where the corresponding set of functions is constructed by conic combinations of the set of functions related to the first PCLF. The conditions depend only on the topologies of the two Graphs and can be verified by solving a linear program. It is the first systematic approach to compare the conservativeness of PCLFs

  • Path-complete Graphs and common Lyapunov functions
    'Association for Computing Machinery (ACM)', 2017
    Co-Authors: Angeli D, Athanasopoulos N, Rm Jungers, Philippe M
    Abstract:

    A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called pieces, and a Directed, Labeled Graph defining Lyapunov inequalities between these pieces. It provides a stability certificate for discrete-time arbitrary switching systems. In this paper, we prove that the satisfiability of such a criterion implies the existence of a Common Lyapunov Function, expressed as the composition of minima and maxima of the pieces of the Path-Complete Lyapunov function. the converse however is not true even for discrete-time linear systems: we present such a system where a max-of-2 quadratics Lyapunov function exists while no corresponding Path-Complete Lyapunov function with 2 quadratic pieces exists. In light of this, we investigate when it is possible to decide if a Path- Complete Lyapunov function is less conservative than another. By analyzing the combinatorial and algebraic structure of the Graph and the pieces respectively, we provide simple tools to decide when the existence of such a Lyapunov function implies that of another

The 20th International Conference - One of the best experts on this subject based on the ideXlab platform.

  • Path-Complete Graphs and Common Lyapunov Functions
    'Association for Computing Machinery (ACM)', 2017
    Co-Authors: Angeli David, Athanasopoulos Nikolaos, Jungers, Raphaël M., Philippe Matthew, The 20th International Conference
    Abstract:

    A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called its pieces, and a Directed, Labeled Graph defining Lyapunov inequalities between these pieces. It provides a stability certificate for discrete-time switching systems under arbitrary switching. In this paper, we prove that the satisfiability of such a criterion implies the existence of a Common Lyapunov Function, expressed as the composition of minima and maxima of the pieces of the Path-Complete Lyapunov function. The converse, however, is not true even for discrete-time linear systems: we present such a system where a max-of-2 quadratics Lyapunov function exists while no corresponding PathComplete Lyapunov function with 2 quadratic pieces exists. In light of this, we investigate when it is possible to decide if a Path-Complete Lyapunov function is less conservative than another. By analyzing the combinatorial and algebraic structure of the Graph and the pieces respectively, we provide simple tools to decide when the existence of such a Lyapunov function implies that of another