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Stefano Tonetta - One of the best experts on this subject based on the ideXlab platform.

  • Infinite-state invariant checking with IC3 and predicate Abstraction
    Formal Methods in System Design, 2016
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We address the problem of verifying invariant properties on infinite-state Systems. We present a novel approach, IC3ia , for generalizing the IC3 invariant checking algorithm from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit Abstraction, a form of predicate Abstraction that expresses Abstract paths without computing explicitly the Abstract System. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search. The proposed approach has two key advantages. First, unlike previous SMT generalizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available and are often highly inefficient. Second, compared to a direct exploration of the concrete transition System, the use of Abstraction gives a significant performance improvement, as our experiments demonstrate.

  • ic3 modulo theories via implicit predicate Abstraction
    Tools and Algorithms for Construction and Analysis of Systems, 2014
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses Abstract transitions without computing explicitly the Abstract System and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search.

  • ic3 modulo theories via implicit predicate Abstraction
    arXiv: Logic in Computer Science, 2013
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses Abstract tran- sitions without computing explicitly the Abstract System and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discov- ering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search. The proposed approach has two key advantages. First, unlike current SMT gener- alizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available, and can moreover be inefficient. Second, compared to a direct exploration of the concrete transition System, the use of Abstraction gives a significant performance improve- ment, as our experiments demonstrate.

Alessandro Cimatti - One of the best experts on this subject based on the ideXlab platform.

  • Infinite-state invariant checking with IC3 and predicate Abstraction
    Formal Methods in System Design, 2016
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We address the problem of verifying invariant properties on infinite-state Systems. We present a novel approach, IC3ia , for generalizing the IC3 invariant checking algorithm from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit Abstraction, a form of predicate Abstraction that expresses Abstract paths without computing explicitly the Abstract System. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search. The proposed approach has two key advantages. First, unlike previous SMT generalizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available and are often highly inefficient. Second, compared to a direct exploration of the concrete transition System, the use of Abstraction gives a significant performance improvement, as our experiments demonstrate.

  • ic3 modulo theories via implicit predicate Abstraction
    Tools and Algorithms for Construction and Analysis of Systems, 2014
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses Abstract transitions without computing explicitly the Abstract System and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search.

  • ic3 modulo theories via implicit predicate Abstraction
    arXiv: Logic in Computer Science, 2013
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses Abstract tran- sitions without computing explicitly the Abstract System and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discov- ering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search. The proposed approach has two key advantages. First, unlike current SMT gener- alizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available, and can moreover be inefficient. Second, compared to a direct exploration of the concrete transition System, the use of Abstraction gives a significant performance improve- ment, as our experiments demonstrate.

Alberto Griggio - One of the best experts on this subject based on the ideXlab platform.

  • Infinite-state invariant checking with IC3 and predicate Abstraction
    Formal Methods in System Design, 2016
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We address the problem of verifying invariant properties on infinite-state Systems. We present a novel approach, IC3ia , for generalizing the IC3 invariant checking algorithm from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit Abstraction, a form of predicate Abstraction that expresses Abstract paths without computing explicitly the Abstract System. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search. The proposed approach has two key advantages. First, unlike previous SMT generalizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available and are often highly inefficient. Second, compared to a direct exploration of the concrete transition System, the use of Abstraction gives a significant performance improvement, as our experiments demonstrate.

  • ic3 modulo theories via implicit predicate Abstraction
    Tools and Algorithms for Construction and Analysis of Systems, 2014
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses Abstract transitions without computing explicitly the Abstract System and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search.

  • ic3 modulo theories via implicit predicate Abstraction
    arXiv: Logic in Computer Science, 2013
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses Abstract tran- sitions without computing explicitly the Abstract System and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discov- ering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search. The proposed approach has two key advantages. First, unlike current SMT gener- alizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available, and can moreover be inefficient. Second, compared to a direct exploration of the concrete transition System, the use of Abstraction gives a significant performance improve- ment, as our experiments demonstrate.

Sergio Mover - One of the best experts on this subject based on the ideXlab platform.

  • Infinite-state invariant checking with IC3 and predicate Abstraction
    Formal Methods in System Design, 2016
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We address the problem of verifying invariant properties on infinite-state Systems. We present a novel approach, IC3ia , for generalizing the IC3 invariant checking algorithm from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit Abstraction, a form of predicate Abstraction that expresses Abstract paths without computing explicitly the Abstract System. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search. The proposed approach has two key advantages. First, unlike previous SMT generalizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available and are often highly inefficient. Second, compared to a direct exploration of the concrete transition System, the use of Abstraction gives a significant performance improvement, as our experiments demonstrate.

  • ic3 modulo theories via implicit predicate Abstraction
    Tools and Algorithms for Construction and Analysis of Systems, 2014
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses Abstract transitions without computing explicitly the Abstract System and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search.

  • ic3 modulo theories via implicit predicate Abstraction
    arXiv: Logic in Computer Science, 2013
    Co-Authors: Alessandro Cimatti, Alberto Griggio, Sergio Mover, Stefano Tonetta
    Abstract:

    We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition Systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses Abstract tran- sitions without computing explicitly the Abstract System and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the Abstract state space, discovering inductive clauses over the Abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current Abstraction allows for a spurious counterexample, it is refined by discov- ering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search. The proposed approach has two key advantages. First, unlike current SMT gener- alizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available, and can moreover be inefficient. Second, compared to a direct exploration of the concrete transition System, the use of Abstraction gives a significant performance improve- ment, as our experiments demonstrate.

Jiongmin Yong - One of the best experts on this subject based on the ideXlab platform.

  • regularity analysis for an Abstract System of coupled hyperbolic and parabolic equations
    Journal of Differential Equations, 2015
    Co-Authors: Jianghao Hao, Zhuangyi Liu, Jiongmin Yong
    Abstract:

    Abstract In this paper, we provide a complete regularity analysis for the following Abstract System of coupled hyperbolic and parabolic equations { u t t = − A u + γ A α w , w t = − γ A α u t − k A β w , u ( 0 ) = u 0 , u t ( 0 ) = v 0 , w ( 0 ) = w 0 , where A is a self-adjoint, positive definite operator on a complex Hilbert space H , and ( α , β ) ∈ [ 0 , 1 ] × [ 0 , 1 ] . We are able to decompose the unit square of the parameter ( α , β ) into three parts where the semigroup associated with the System is analytic, of specific order Gevrey classes, and non-smoothing, respectively. Moreover, we will show that the orders of Gevrey class is sharp, under proper conditions.

  • regularity analysis for an Abstract System of coupled hyperbolic and parabolic equations
    arXiv: Analysis of PDEs, 2014
    Co-Authors: Jianghao Hao, Zhuangyi Liu, Jiongmin Yong
    Abstract:

    In this paper, we provide a complete regularity analysis for an Abstract System of coupled hyperbolic and parabolic equations in a complex Hilbert space. We are able to decompose the unit square of the parameters into three parts where the semigroup associated with the System is analytic, of specific order Gevrey classes, and non-smoothing, respectively. Moreover, we will show that the orders of Gevrey class are sharp, under proper conditions.