Author

# Natarajan Shankar

Other affiliations: University of California, Los Angeles, Business International Corporation, Fujitsu

Bio: Natarajan Shankar is an academic researcher from SRI International. The author has contributed to research in topics: Formal verification & Model checking. The author has an hindex of 38, co-authored 134 publications receiving 7327 citations. Previous affiliations of Natarajan Shankar include University of California, Los Angeles & Business International Corporation.

##### Papers published on a yearly basis

##### Papers

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TL;DR: The verifications performed, the lessons learned, and some of the design decisions taken in PVS are described to better support these large, difficult, iterative, and collaborative verifications.

Abstract: PVS is the most recent in a series of verification systems developed at SRI. Its design was strongly influenced, and later refined, by our experiences in developing formal specifications and mechanically checked verifications for the fault-tolerant architecture, algorithms, and implementations of a model "reliable computing platform" (RCP) for life-critical digital flight-control applications, and by a collaborative project to formally verify the design of a commercial avionics processor called AAMP5. Several of the formal specifications and verifications performed in support of RCP and AAMP5 are individually of considerable complexity and difficulty. But in order to contribute to the overall goal, it has often been necessary to modify completed verifications to accommodate changed assumptions or requirements, and people other than the original developer have often needed to understand, review, build on, modify, or extract part of an intricate verification. We outline the verifications performed, present the lessons learned, and describe some of the design decisions taken in PVS to better support these large, difficult, iterative, and collaborative verifications. >

560 citations

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03 Aug 1996TL;DR: PVS (Prototype Verification System) is an environment for constructing clear and precise specifications and for developing readable proofs that have been mechanically verified to exploit the synergies between language and deduction, automation and interaction, and theorem proving and model checking.

Abstract: PVS (Prototype Verification System) is an environment for constructing clear and precise specifications and for developing readable proofs that have been mechanically verified. It is designed to exploit the synergies between language and deduction, automation and interaction, and theorem proving and model checking. For example, the type system of PVS requires the use of theorem proving to establish type correctness, and conversely, type information is used extensively during a proof. Similarly, decision procedures are heavily used in order to simplify the tedious and obvious steps in a proof leaving the user to interactively supply the high-level steps in a verification. Model checking is one such decision procedure that is used to discharge temporal properties of specific finite-state systems. A variety of examples from functional programming, fault tolerance, and real time computing have been verified using PVS [7]. The most substantial use of PVS has been in the verification of the microcode for selected instructions of a commercial-scale microprocessor called AAMP5 designed by Rockwell-Collins and containing about 500,000 transistors [5]. Most recently, PVS has been applied to the verification of the design of an SRT divider [9]. The key elements of the PVS design are described below in greater detail below.

521 citations

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TL;DR: It is shown that unlike most other propositional (quantifier-free) logics, full propositional linear logic is undecidable, and it is proved that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes PSPACE-complete.

280 citations

01 Jan 1998

TL;DR: This document provides an introductory example, a tutorial, and a compact reference to the PVS veri cation system to get you started using PVS and to help appreciate the capabilities of the system and the purposes for which it is suitable.

Abstract: This document provides an introductory example, a tutorial, and a compact reference to the PVS veri cation system. It is intended to provide enough information to get you started using PVS, and to help you appreciate the capabilities of the system and the purposes for which it is suitable. Dave Stringer-Calvert provided valuable comments on earlier versions of this tutorial, and also checked the speci cations and proofs appearing here. Preparation of this tutorial was partially funded by NASA Langley Research Center under Contract NAS1-18969, and by the Advanced Research Projects Agency through NASA Ames Research Center NASA-NAG-2-891 (Arpa order A721) to Stanford Unversity.

253 citations

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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Microsoft

^{1}TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

10,141 citations

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TL;DR: Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of the authors' brain’s wiring.

Abstract: In 1974 an article appeared in Science magazine with the dry-sounding title “Judgment Under Uncertainty: Heuristics and Biases” by a pair of psychologists who were not well known outside their discipline of decision theory. In it Amos Tversky and Daniel Kahneman introduced the world to Prospect Theory, which mapped out how humans actually behave when faced with decisions about gains and losses, in contrast to how economists assumed that people behave. Prospect Theory turned Economics on its head by demonstrating through a series of ingenious experiments that people are much more concerned with losses than they are with gains, and that framing a choice from one perspective or the other will result in decisions that are exactly the opposite of each other, even if the outcomes are monetarily the same. Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of our brain’s wiring.

4,351 citations

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[...]

TL;DR: A detailed user guide is given which describes how to use the various tools of Uppaal version 2.02 to construct abstract models of a real-time system, to simulate its dynamical behavior, to specify and verify its safety and bounded liveness properties in terms of its model.

Abstract: This paper presents the overal structure, the design criteria, and the main features of the tool box Uppaal. It gives a detailed user guide which describes how to use the various tools of Uppaal version 2.02 to construct abstract models of a real-time system, to simulate its dynamical behavior, to specify and verify its safety and bounded liveness properties in terms of its model. In addition, the paper also provides a short review on case-studies where Uppaal is applied, as well as references to its theoretical foundation.

2,358 citations

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[...]

TL;DR: This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.

Abstract: Linear logic was introduced by Girard in 1987 [11] . Since then many results have supported Girard' s statement, \"Linear logic is a resource conscious logic,\" and related slogans . Increasingly, computer scientists have come to recognize linear logic as an expressive and powerful logic with connection s to a variety of topics in computer science . This column presents a.n intuitive overview of linear logic, some recent theoretical results, an d summarizes several applications of linear logic to computer science . Other introductions to linear logic may be found in [12, 361 .

2,304 citations