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Papers by Hanne Gottliebsen
We present early work on a PVS implementation of a model of simple control as signal flow graphs ... more We present early work on a PVS implementation of a model of simple control as signal flow graphs to enable formal verification of input/output behaviour of the control system. As has been shown by Rutten, Signal flow graphs can be described using Escardo's coinductive stream calculus, which includes a definition of differentiation for streams over the real numbers and the use of differential equations. The basics of coinductive stream calculus has been implemented in PVS.
Formal Aspects of Computing, 2013
Real number theorem proving has many uses, particularly for verification of safety critical syste... more Real number theorem proving has many uses, particularly for verification of safety critical systems and systems for which design errors may be costly. We discuss a chain of developments building on real number theorem proving in PVS. This leads from the verification of aspects of an air traffic control system, through work on the integration of computer algebra and automated theorem proving to a new tool, NRV, first presented here that builds on the capabilities of Maple and PVS to provide a verified and automatic analysis of Nichols plots. This automates a standard technique used by control engineers and greatly improves assurance compared with the traditional method of visual inspection of the Nichols plots.
New concepts for automating air traffic management functions at small non-towered airports raise ... more New concepts for automating air traffic management functions at small non-towered airports raise serious safety issues associated with the software implementations and their underlying key algorithms. The criticality of such software systems necessitates that strong guarantees of the safety be developed for them. In this paper we present a formal method for modeling and verifying such systems using the PVS theorem proving system. The method is demonstrated on a preliminary concept of operation for the Small Aircraft Transportation System (SATS) project at NASA Langley.
New concepts for automating air traffic management functions at small non-towered airports raise ... more New concepts for automating air traffic management functions at small non-towered airports raise serious safety issues associated with the software implementations and their underlying key algorithms. The criticality of such software systems necessitates that strong guarantees of the safety be developed for them. In this paper we present a formal method for modeling and verifying such systems using the PVS theorem proving system. The method is demonstrated on a preliminary concept of operation for the Small Aircraft Transportation System (SATS) project at NASA Langley.
Lecture Notes in Computer Science, 2000
In this paper we present a library of transcendental functions such as exp, log, cos, sin and tan... more In this paper we present a library of transcendental functions such as exp, log, cos, sin and tan and also an automated continuity checker for real valued functions, both done using PVS. Our aim is to develop theorem proving support for computer algebra systems, and other applications which rely on mathematical analysis. The focus of the paper is on the
We present early work on a PVS implementation of a model of simple control as signal flow graphs ... more We present early work on a PVS implementation of a model of simple control as signal flow graphs to enable formal verification of input/output behaviour of the control system. As has been shown by Rutten, Signal flow graphs can be described using Escardo's coinductive stream calculus, which includes a definition of differentiation for streams over the real numbers and the use of differential equations. The basics of coinductive stream calculus has been implemented in PVS.
Maple is a popular and powerful computer algebra system, but it could not guarantee the correctne... more Maple is a popular and powerful computer algebra system, but it could not guarantee the correctness of all answers. PVS provides formal proofs to guarantee the correctness of answers, but it cannot be used efficiently without specific knowl edge of the system. To combine the advantages of PVS and Maple, an interface is built between the systems so that
Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99, 1999
We assess the current state of research in the application of computer aided formal reasoning to ... more We assess the current state of research in the application of computer aided formal reasoning to computer algebra, and argue that embedded verification support allows users to enjoy its benefits without wrestling with technicalities. We illustrate this claim by considering symbolic definite integration, and present a verifiable symbolic definite integral table look up: a system which matches a query comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of lemmas about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. We present the full model of such a system as well as a description of our prototype implementation showing the efficacy of such a system: for example, the prototype is able to obtain correct answers in cases where computer algebra systems [CAS] do not. We extend upon Fateman's web-based table by including parametric limits of integration and queries with side conditions.
Lecture Notes in Computer Science, 1999
We present a veri ed symbolic de nite integral table lookup: a system which matches a query, comp... more We present a veri ed symbolic de nite integral table lookup: a system which matches a query, comprising a de nite integral with parameters and side conditions, against an entry in a veri ed table and uses a call to a library of facts about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. Our system is able to obtain correct answers in cases where standard techniques implemented in computer algebra systems fail.
Lecture Notes in Computer Science, 2001
We describe an interface between version 6 of the Maple computer algebra system with the PVS auto... more We describe an interface between version 6 of the Maple computer algebra system with the PVS automated theorem prover. The interface is designed to allow Maple users access to the robust and checkable proof environment of PVS. We also extend this environment by the provision of a library of proof strategies for use in real analysis. We demonstrate examples using the interface and the real analysis library. These examples provide proofs which are both illustrative and applicable to genuine symbolic computation problems.
Lecture Notes in Computer Science, 2004
We introduce control engineering as a new domain of application for formal methods. We discuss de... more We introduce control engineering as a new domain of application for formal methods. We discuss design verification, drawing attention to the role played by diagrammatic evaluation criteria involving numeric plots of a design, such as Nichols and Bode plots. We show that symbolic computation and computational logic can be used to discharge these criteria and provide symbolic, automated, and very general alternatives to these standard numeric tests. We illustrate our work with reference to a standard reference model drawn from military avionics.
We introduce control engineering as a new domain of ap- plication for formal methods. We discuss ... more We introduce control engineering as a new domain of ap- plication for formal methods. We discuss design verification, drawing attention to the role played by diagrammatic evaluation criteria involv- ing numeric plots of a design, such as Nichols and Bode plots. We show that symbolic computation and computational logic can be used to dis- charge these criteria and provide symbolic, automated, and very general alternatives to these standard numeric tests. We illustrate our work with reference to a standard reference model drawn from military avionics.
Journal of Symbolic Computation, 2005
We present hidden verification as a means to make the power of computational logic available to u... more We present hidden verification as a means to make the power of computational logic available to users of computer algebra systems while shielding them from its complexity. We have implemented in PVS a library of facts about elementary and transcendental functions, and automatic procedures to attempt proofs of continuity, convergence and differentiability for functions in this class. These are called directly from Maple by a simple pipe-lined interface. Hence we are able to support the analysis of differential equations in Maple by direct calls to PVS for: result refinement and verification, discharge of verification conditions, harnesses to ensure more reliable differential equation solvers, and verifiable look-up tables.
Citeseer
... Towards a Hoare Logic for Continuous Systems 27 Erik Mathiesen, Queen Mary University of ... more ... Towards a Hoare Logic for Continuous Systems 27 Erik Mathiesen, Queen Mary University of London Invited talk: Incorporating Formal Methods in the Design Flow of DSP Systems . 31 Sofiène Tahar, Concordia University ...
We present early work on a PVS implementation of a model of simple control as signal flow graphs ... more We present early work on a PVS implementation of a model of simple control as signal flow graphs to enable formal verification of input/output behaviour of the control system. As has been shown by Rutten, Signal flow graphs can be described using Escardo's coinductive stream calculus, which includes a definition of differentiation for streams over the real numbers and the use of differential equations. The basics of coinductive stream calculus has been implemented in PVS.
Formal Aspects of Computing, 2013
Real number theorem proving has many uses, particularly for verification of safety critical syste... more Real number theorem proving has many uses, particularly for verification of safety critical systems and systems for which design errors may be costly. We discuss a chain of developments building on real number theorem proving in PVS. This leads from the verification of aspects of an air traffic control system, through work on the integration of computer algebra and automated theorem proving to a new tool, NRV, first presented here that builds on the capabilities of Maple and PVS to provide a verified and automatic analysis of Nichols plots. This automates a standard technique used by control engineers and greatly improves assurance compared with the traditional method of visual inspection of the Nichols plots.
New concepts for automating air traffic management functions at small non-towered airports raise ... more New concepts for automating air traffic management functions at small non-towered airports raise serious safety issues associated with the software implementations and their underlying key algorithms. The criticality of such software systems necessitates that strong guarantees of the safety be developed for them. In this paper we present a formal method for modeling and verifying such systems using the PVS theorem proving system. The method is demonstrated on a preliminary concept of operation for the Small Aircraft Transportation System (SATS) project at NASA Langley.
New concepts for automating air traffic management functions at small non-towered airports raise ... more New concepts for automating air traffic management functions at small non-towered airports raise serious safety issues associated with the software implementations and their underlying key algorithms. The criticality of such software systems necessitates that strong guarantees of the safety be developed for them. In this paper we present a formal method for modeling and verifying such systems using the PVS theorem proving system. The method is demonstrated on a preliminary concept of operation for the Small Aircraft Transportation System (SATS) project at NASA Langley.
Lecture Notes in Computer Science, 2000
In this paper we present a library of transcendental functions such as exp, log, cos, sin and tan... more In this paper we present a library of transcendental functions such as exp, log, cos, sin and tan and also an automated continuity checker for real valued functions, both done using PVS. Our aim is to develop theorem proving support for computer algebra systems, and other applications which rely on mathematical analysis. The focus of the paper is on the
We present early work on a PVS implementation of a model of simple control as signal flow graphs ... more We present early work on a PVS implementation of a model of simple control as signal flow graphs to enable formal verification of input/output behaviour of the control system. As has been shown by Rutten, Signal flow graphs can be described using Escardo's coinductive stream calculus, which includes a definition of differentiation for streams over the real numbers and the use of differential equations. The basics of coinductive stream calculus has been implemented in PVS.
Maple is a popular and powerful computer algebra system, but it could not guarantee the correctne... more Maple is a popular and powerful computer algebra system, but it could not guarantee the correctness of all answers. PVS provides formal proofs to guarantee the correctness of answers, but it cannot be used efficiently without specific knowl edge of the system. To combine the advantages of PVS and Maple, an interface is built between the systems so that
Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99, 1999
We assess the current state of research in the application of computer aided formal reasoning to ... more We assess the current state of research in the application of computer aided formal reasoning to computer algebra, and argue that embedded verification support allows users to enjoy its benefits without wrestling with technicalities. We illustrate this claim by considering symbolic definite integration, and present a verifiable symbolic definite integral table look up: a system which matches a query comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of lemmas about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. We present the full model of such a system as well as a description of our prototype implementation showing the efficacy of such a system: for example, the prototype is able to obtain correct answers in cases where computer algebra systems [CAS] do not. We extend upon Fateman's web-based table by including parametric limits of integration and queries with side conditions.
Lecture Notes in Computer Science, 1999
We present a veri ed symbolic de nite integral table lookup: a system which matches a query, comp... more We present a veri ed symbolic de nite integral table lookup: a system which matches a query, comprising a de nite integral with parameters and side conditions, against an entry in a veri ed table and uses a call to a library of facts about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. Our system is able to obtain correct answers in cases where standard techniques implemented in computer algebra systems fail.
Lecture Notes in Computer Science, 2001
We describe an interface between version 6 of the Maple computer algebra system with the PVS auto... more We describe an interface between version 6 of the Maple computer algebra system with the PVS automated theorem prover. The interface is designed to allow Maple users access to the robust and checkable proof environment of PVS. We also extend this environment by the provision of a library of proof strategies for use in real analysis. We demonstrate examples using the interface and the real analysis library. These examples provide proofs which are both illustrative and applicable to genuine symbolic computation problems.
Lecture Notes in Computer Science, 2004
We introduce control engineering as a new domain of application for formal methods. We discuss de... more We introduce control engineering as a new domain of application for formal methods. We discuss design verification, drawing attention to the role played by diagrammatic evaluation criteria involving numeric plots of a design, such as Nichols and Bode plots. We show that symbolic computation and computational logic can be used to discharge these criteria and provide symbolic, automated, and very general alternatives to these standard numeric tests. We illustrate our work with reference to a standard reference model drawn from military avionics.
We introduce control engineering as a new domain of ap- plication for formal methods. We discuss ... more We introduce control engineering as a new domain of ap- plication for formal methods. We discuss design verification, drawing attention to the role played by diagrammatic evaluation criteria involv- ing numeric plots of a design, such as Nichols and Bode plots. We show that symbolic computation and computational logic can be used to dis- charge these criteria and provide symbolic, automated, and very general alternatives to these standard numeric tests. We illustrate our work with reference to a standard reference model drawn from military avionics.
Journal of Symbolic Computation, 2005
We present hidden verification as a means to make the power of computational logic available to u... more We present hidden verification as a means to make the power of computational logic available to users of computer algebra systems while shielding them from its complexity. We have implemented in PVS a library of facts about elementary and transcendental functions, and automatic procedures to attempt proofs of continuity, convergence and differentiability for functions in this class. These are called directly from Maple by a simple pipe-lined interface. Hence we are able to support the analysis of differential equations in Maple by direct calls to PVS for: result refinement and verification, discharge of verification conditions, harnesses to ensure more reliable differential equation solvers, and verifiable look-up tables.
Citeseer
... Towards a Hoare Logic for Continuous Systems 27 Erik Mathiesen, Queen Mary University of ... more ... Towards a Hoare Logic for Continuous Systems 27 Erik Mathiesen, Queen Mary University of London Invited talk: Incorporating Formal Methods in the Design Flow of DSP Systems . 31 Sofiène Tahar, Concordia University ...