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Patrice Godefroid - One of the best experts on this subject based on the ideXlab platform.

  • LTL Generalized Model checking revisited
    International Journal on Software Tools for Technology Transfer, 2011
    Co-Authors: Patrice Godefroid, Nir Piterman
    Abstract:

    Given a 3-valued abstraction of a program (possibly generated using static program analysis and predicate abstraction) and a temporal logic formula, Generalized Model checking (GMC) checks whether there exists a concretization of that abstraction that satisfies the formula. In this paper, we revisit Generalized Model checking for linear time (LTL) properties. First, we show that LTL GMC is 2EXPTIME-complete in the size of the formula and polynomial in the Model, where the degree of the polynomial depends on the formula, instead of EXPTIME-complete and quadratic as previously believed. The standard definition of GMC depends on a definition of concretization which is tailored for branching-time Model checking. We then study a simpler linear completeness preorder for relating program abstractions. We show that LTL GMC with this weaker preorder is only EXPSPACE-complete in the size of the formula, and can be solved in linear time and logarithmic space in the size of the Model. Finally, we identify classes of formulas for which the Model complexity of standard GMC is reduced.

  • VMCAI - LTL Generalized Model Checking Revisited
    Lecture Notes in Computer Science, 2008
    Co-Authors: Patrice Godefroid, Nir Piterman
    Abstract:

    Given a 3-valued abstraction of a program (possibly generated using static program analysis and predicate abstraction) and a temporal logic formula, Generalized Model checking (GMC) checks whether there exists a concretization of that abstraction that satisfies the formula. In this paper, we revisit Generalized Model checking for linear time (LTL) properties. First, we show that LTL GMC is 2EXPTIME-complete in the size of the formula and polynomial in the Model, where the degree of the polynomial depends on the formula, instead of EXPTIME-complete and quadratic as previously believed. The standard definition of GMC depends on a definition of concretization which is tailored for branching-time Model checking. We then study a simpler linear completeness preorder for relating program abstractions. We show that LTL GMC with this weaker preorder is only EXPSPACE-complete in the size of the formula, and can be solved in linear time and logarithmic space in the size of the Model. Finally, we identify classes of formulas for which the Model complexity of standard GMC is reduced.

  • CAV - Automatic Abstraction Using Generalized Model Checking
    Computer Aided Verification, 2002
    Co-Authors: Patrice Godefroid, Radha Jagadeesan
    Abstract:

    Generalized Model checking is a framework for reasoning about partial state spaces of concurrent reactive systems. The state space of a system is only "partial" (partially known) when a full state-space exploration is not computationally tractable, or when abstraction techniques are used to simplify the system's representation. In the context of automatic abstraction, Generalized Model checking means checking whether there exists a concretization of an abstraction that satisfies a temporal logic formula. In this paper, we showh owgen eralized Model checking can extend existing automatic abstraction techniques (such as predicate abstraction) for Model checking concurrent/reactive programs and yield the three following improvements: (1) any temporal logic formula can be checked (not just universal properties as with traditional conservative abstractions), (2) correctness proofs and counterexamples are both guaranteed to be sound, and (3) verification results can be more precise. We study the cost needed to improve precision by presenting new upper and lower bounds for the complexity of Generalized Model checking in the size of the abstraction.

  • Automatic abstraction using Generalized Model checking
    Lecture Notes in Computer Science, 2002
    Co-Authors: Patrice Godefroid, Radha Jagadeesan
    Abstract:

    Generalized Model checking is a framework for reasoning about partial state spaces of concurrent reactive systems. The state space of a system is only partial (partially known) when a full state-space exploration is not computationally tractable, or when abstraction techniques are used to simplify the system's representation. In the context of automatic abstraction, Generalized Model checking means checking whether there exists a concretization of an abstraction that satisfies a temporal logic formula. In this paper, we show how Generalized Model checking can extend existing automatic abstraction techniques (such as predicate abstraction) for Model checking concurrent/reactive programs and yield the three following improvements: (1) any temporal logic formula can be checked (not just universal properties as with traditional conservative abstractions), (2) correctness proofs and counter-examples are both guaranteed to be sound, and (3) verification results can be more precise. We study the cost needed to improve precision by presenting new upper and lower bounds for the complexity of Generalized Model checking in the size of the abstraction.

  • TIME - Generalized Model checking
    12th International Symposium on Temporal Representation and Reasoning (TIME'05), 1
    Co-Authors: Patrice Godefroid
    Abstract:

    Three-valued Models, in which properties of a system are either true, false or unknown, have recently been advocated as a better representation for reactive program abstractions generated by automatic techniques such as predicate abstraction. Indeed, for the same cost, Model checking three-valued abstractions (also called may/must abstractions) can be used to both prove and disprove any temporal-logic property, whereas traditional conservative abstractions can only prove universal properties. Also, verification results can be more precise with Generalized Model checking, which checks whether there exists a concretization of an abstraction satisfying a temporal-logic formula. Generalized Model checking generalizes both Model checking (when the Model is complete) and satisfiability (when everything in the Model is unknown), probably the two most studied problems related to temporal logic and verification. In this talk, the main ideas behind this framework, namely Models for three-valued abstractions, completeness preorders (to measure the level of completeness of such Models), three-valued temporal logics and Generalized Model checking was presented . The algorithms and complexity bounds for three-valued Model checking and Generalized Model-checking for various temporal logics, was also discussed. The applications to program verification via automatic abstraction, was then discussed. Examples of programs and properties that can be verified by Generalized Model checking but not with current abstraction-based verification tools, was shown. Classes of temporal-logic formulas for which Model checking is guaranteed to always have the same precision as Generalized Model checking, was also presented. The final topic is a brief discussion of three-valued abstractions for reasoning about open systems and about games in general, as well as completeness issues (i.e., given an infinite-state program and a property, is there a finite-state abstraction of that program that satisfies this property?).

Nir Piterman - One of the best experts on this subject based on the ideXlab platform.

  • LTL Generalized Model checking revisited
    International Journal on Software Tools for Technology Transfer, 2011
    Co-Authors: Patrice Godefroid, Nir Piterman
    Abstract:

    Given a 3-valued abstraction of a program (possibly generated using static program analysis and predicate abstraction) and a temporal logic formula, Generalized Model checking (GMC) checks whether there exists a concretization of that abstraction that satisfies the formula. In this paper, we revisit Generalized Model checking for linear time (LTL) properties. First, we show that LTL GMC is 2EXPTIME-complete in the size of the formula and polynomial in the Model, where the degree of the polynomial depends on the formula, instead of EXPTIME-complete and quadratic as previously believed. The standard definition of GMC depends on a definition of concretization which is tailored for branching-time Model checking. We then study a simpler linear completeness preorder for relating program abstractions. We show that LTL GMC with this weaker preorder is only EXPSPACE-complete in the size of the formula, and can be solved in linear time and logarithmic space in the size of the Model. Finally, we identify classes of formulas for which the Model complexity of standard GMC is reduced.

  • VMCAI - LTL Generalized Model Checking Revisited
    Lecture Notes in Computer Science, 2008
    Co-Authors: Patrice Godefroid, Nir Piterman
    Abstract:

    Given a 3-valued abstraction of a program (possibly generated using static program analysis and predicate abstraction) and a temporal logic formula, Generalized Model checking (GMC) checks whether there exists a concretization of that abstraction that satisfies the formula. In this paper, we revisit Generalized Model checking for linear time (LTL) properties. First, we show that LTL GMC is 2EXPTIME-complete in the size of the formula and polynomial in the Model, where the degree of the polynomial depends on the formula, instead of EXPTIME-complete and quadratic as previously believed. The standard definition of GMC depends on a definition of concretization which is tailored for branching-time Model checking. We then study a simpler linear completeness preorder for relating program abstractions. We show that LTL GMC with this weaker preorder is only EXPSPACE-complete in the size of the formula, and can be solved in linear time and logarithmic space in the size of the Model. Finally, we identify classes of formulas for which the Model complexity of standard GMC is reduced.

Daniel Hubert - One of the best experts on this subject based on the ideXlab platform.

  • Comparison of the Generalized and bi-Maxwellian multimoment multispecies approaches of the terrestrial polar wind
    Journal of Geophysical Research Space Physics, 2000
    Co-Authors: François Leblanc, Daniel Hubert, Pierre-louis Blelly
    Abstract:

    A comparison between two multimoment approaches is provided in the context of an application to the terrestrial polar wind. We compare the bi-Maxwellian 16-moment approach with the 16-moment Generalized Model, which has been built in order to account for the suprathermal part of the velocity distribution function better than the previous multimoment approaches. This comparison has shown a general similarity between the two approaches and has shown that the better adapted closure assumption of the set of transport equations of the Generalized Model generates a higher acceleration. Moreover, the better determination of the collisional energy transfers generates a smaller increase of the temperature of the supersonic species that generally agrees with the adiabatic cooling assumption predicted by Monte Carlo or direct resolution of the Fokker Planck equation. The Generalized Model also provides the typical profiles of the velocity distribution function from the original collision-dominated region to the collisionless region. These profiles are in good agreement with the Monte Carlo and collision kinetic resolution in the collision-dominated region and in the lower part of the transition region.

  • A Generalized Model for the Proton Expansion in Astrophysical Winds. III. The Collisional Transfers and Their Properties
    The Astrophysical Journal, 2000
    Co-Authors: François Leblanc, Daniel Hubert, Pierre-louis Blelly
    Abstract:

    This is the third and last of a series of papers that present a new theoretical approach to Modeling the expansion of the solar and terrestrial polar winds by solving the Fokker-Planck equation. The Coulomb collisional transfers between the different species that compose these winds are presented after the velocity distribution function and the set of transport equations associated with the Generalized Model. The method and the assumptions used to calculate these terms are described. They are derived from generic expressions, which must be numerically estimated for specific applications. Their new properties are analyzed in the context of the terrestrial polar wind, and their potential importance in the processes of heating and acceleration of the solar wind is discussed. Because the Generalized Model is adapted to reproduce the high suprathermal part of the velocity distribution function currently observed in the solar wind, we also emphasize the role of this contribution in the collisional transfers. In the terrestrial polar wind, the region of energy transfer between H+ and O+ ions is thinner than previously predicted. In the solar wind, the region of energy transfer between electrons and protons in the inner corona is larger than previously thought. The role of the thermal and mirror forces and the mechanisms of isotropization of the electrons are underlined.

  • A Generalized Model for the Proton Expansion in Astrophysical Winds. I. The Velocity Distribution Function Representation
    The Astrophysical Journal, 1997
    Co-Authors: François Leblanc, Daniel Hubert
    Abstract:

    We construct a new approach to Model the velocity distribution function (VDF) for the protons in stellar atmosphere expansions or planetary polar winds. The Generalized Grad method of construction is used, and comparisons with the bi-Maxwellian polynomial expansion Model are made in applications to the solar wind in the context of the measurements made by the Helios probes between 0.3 and 1 AU. A fitting procedure based on a sum of two Maxwellian functions is used to check the convergence property of both polynomial expansions and to calculate the predicted polynomial expansion profiles along the magnetic field orientation for typical proton VDFs in the solar wind. The Generalized Model is better adapted than the bi-Maxwellian polynomial expansion function to reproduce the long-tail features of a majority of the observed proton VDFs; moreover, our Model does not display negative values of the VDF, contrary to the bi-Maxwellian expansion for normalized heat flux larger than unity. A 16 moment approximation, which corresponds to a third order of development, allows us to provide an associated set of Generalized transport equations better closed than the equivalent system associated with a bi-Maxwellian polynomial expansion.

François Leblanc - One of the best experts on this subject based on the ideXlab platform.

  • Comparison of the Generalized and bi-Maxwellian multimoment multispecies approaches of the terrestrial polar wind
    Journal of Geophysical Research Space Physics, 2000
    Co-Authors: François Leblanc, Daniel Hubert, Pierre-louis Blelly
    Abstract:

    A comparison between two multimoment approaches is provided in the context of an application to the terrestrial polar wind. We compare the bi-Maxwellian 16-moment approach with the 16-moment Generalized Model, which has been built in order to account for the suprathermal part of the velocity distribution function better than the previous multimoment approaches. This comparison has shown a general similarity between the two approaches and has shown that the better adapted closure assumption of the set of transport equations of the Generalized Model generates a higher acceleration. Moreover, the better determination of the collisional energy transfers generates a smaller increase of the temperature of the supersonic species that generally agrees with the adiabatic cooling assumption predicted by Monte Carlo or direct resolution of the Fokker Planck equation. The Generalized Model also provides the typical profiles of the velocity distribution function from the original collision-dominated region to the collisionless region. These profiles are in good agreement with the Monte Carlo and collision kinetic resolution in the collision-dominated region and in the lower part of the transition region.

  • A Generalized Model for the Proton Expansion in Astrophysical Winds. III. The Collisional Transfers and Their Properties
    The Astrophysical Journal, 2000
    Co-Authors: François Leblanc, Daniel Hubert, Pierre-louis Blelly
    Abstract:

    This is the third and last of a series of papers that present a new theoretical approach to Modeling the expansion of the solar and terrestrial polar winds by solving the Fokker-Planck equation. The Coulomb collisional transfers between the different species that compose these winds are presented after the velocity distribution function and the set of transport equations associated with the Generalized Model. The method and the assumptions used to calculate these terms are described. They are derived from generic expressions, which must be numerically estimated for specific applications. Their new properties are analyzed in the context of the terrestrial polar wind, and their potential importance in the processes of heating and acceleration of the solar wind is discussed. Because the Generalized Model is adapted to reproduce the high suprathermal part of the velocity distribution function currently observed in the solar wind, we also emphasize the role of this contribution in the collisional transfers. In the terrestrial polar wind, the region of energy transfer between H+ and O+ ions is thinner than previously predicted. In the solar wind, the region of energy transfer between electrons and protons in the inner corona is larger than previously thought. The role of the thermal and mirror forces and the mechanisms of isotropization of the electrons are underlined.

  • A Generalized Model for the Proton Expansion in Astrophysical Winds. I. The Velocity Distribution Function Representation
    The Astrophysical Journal, 1997
    Co-Authors: François Leblanc, Daniel Hubert
    Abstract:

    We construct a new approach to Model the velocity distribution function (VDF) for the protons in stellar atmosphere expansions or planetary polar winds. The Generalized Grad method of construction is used, and comparisons with the bi-Maxwellian polynomial expansion Model are made in applications to the solar wind in the context of the measurements made by the Helios probes between 0.3 and 1 AU. A fitting procedure based on a sum of two Maxwellian functions is used to check the convergence property of both polynomial expansions and to calculate the predicted polynomial expansion profiles along the magnetic field orientation for typical proton VDFs in the solar wind. The Generalized Model is better adapted than the bi-Maxwellian polynomial expansion function to reproduce the long-tail features of a majority of the observed proton VDFs; moreover, our Model does not display negative values of the VDF, contrary to the bi-Maxwellian expansion for normalized heat flux larger than unity. A 16 moment approximation, which corresponds to a third order of development, allows us to provide an associated set of Generalized transport equations better closed than the equivalent system associated with a bi-Maxwellian polynomial expansion.

Radha Jagadeesan - One of the best experts on this subject based on the ideXlab platform.

  • CAV - Automatic Abstraction Using Generalized Model Checking
    Computer Aided Verification, 2002
    Co-Authors: Patrice Godefroid, Radha Jagadeesan
    Abstract:

    Generalized Model checking is a framework for reasoning about partial state spaces of concurrent reactive systems. The state space of a system is only "partial" (partially known) when a full state-space exploration is not computationally tractable, or when abstraction techniques are used to simplify the system's representation. In the context of automatic abstraction, Generalized Model checking means checking whether there exists a concretization of an abstraction that satisfies a temporal logic formula. In this paper, we showh owgen eralized Model checking can extend existing automatic abstraction techniques (such as predicate abstraction) for Model checking concurrent/reactive programs and yield the three following improvements: (1) any temporal logic formula can be checked (not just universal properties as with traditional conservative abstractions), (2) correctness proofs and counterexamples are both guaranteed to be sound, and (3) verification results can be more precise. We study the cost needed to improve precision by presenting new upper and lower bounds for the complexity of Generalized Model checking in the size of the abstraction.

  • Automatic abstraction using Generalized Model checking
    Lecture Notes in Computer Science, 2002
    Co-Authors: Patrice Godefroid, Radha Jagadeesan
    Abstract:

    Generalized Model checking is a framework for reasoning about partial state spaces of concurrent reactive systems. The state space of a system is only partial (partially known) when a full state-space exploration is not computationally tractable, or when abstraction techniques are used to simplify the system's representation. In the context of automatic abstraction, Generalized Model checking means checking whether there exists a concretization of an abstraction that satisfies a temporal logic formula. In this paper, we show how Generalized Model checking can extend existing automatic abstraction techniques (such as predicate abstraction) for Model checking concurrent/reactive programs and yield the three following improvements: (1) any temporal logic formula can be checked (not just universal properties as with traditional conservative abstractions), (2) correctness proofs and counter-examples are both guaranteed to be sound, and (3) verification results can be more precise. We study the cost needed to improve precision by presenting new upper and lower bounds for the complexity of Generalized Model checking in the size of the abstraction.