Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
Formal probabilistic analysis of cyber-physical transportation systems
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part III
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Optical systems are becoming increasingly important as they tend to resolve many bottlenecks in the present age communications and electronics. Some common examples include their usage to meet high capacity link demands in communication systems and to overcome the performance limitations of metal interconnect in silicon chips. Though, the inability to efficiently analyze optical systems using traditional analysis approaches, due to the continuous nature of optics, somewhat limits their application, specially in safety-critical applications. In order to overcome this limitation, we propose to formally analyze optical systems using a higher-order-logic theorem prover (HOL). As a first step in this endeavor, we formally analyze eigenvalues for planar optical waveguides, which are some of the most fundamental components in optical devices. For the formalization, we have utilized the mathematical concepts of differentiation of piecewise functions and one-sided limits of functions. In order to illustrate the practical effectiveness of our results, we present the formal analysis of a planar asymmetric waveguide.