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ECE Seminar Series: Logical Signal Processing: a Fourier Analysis of Temporal Logic

Speaker Name: 
Houssam Abbas
Speaker Title: 
Assistant Professor of Electrical Engineering and Computer Science
Speaker Organization: 
Oregon State University
Start Time: 
Monday, March 1, 2021 - 10:40am
End Time: 
Monday, March 1, 2021 - 11:45am
Via Zoom Presentation
Asst. Prof. Shiva Abbaszadeh


Temporal logic is a mathematical language for describing the properties of computer and dynamical systems, and has found wide use in the verification and control of cyber-physical systems. It is obtained by adding temporal modalities to classical boolean logic. In this work we seek to re-cast temporal logic and its various uses as "just another signal processing operation", which is essential for the study of Cyber-Physical Systems. Speciically, we ask: What is the frequency content of temporal logic formulas? That is, when we monitor a signal against a formula, which frequency bands of the signal are relevant to the logic, and which can be safely discarded? To answer this question, we focus on monitors that measure the robustness of a signal relative to a specification in Signal Temporal Logic. We prove that robustness monitors can be modeled using Volterra series. We then study the Fourier transforms of these Volterra representations, and provide a method to derive the Fourier transforms of entire formulas. Experiments illustrate these results. Beyond compression, this work enables a common formalism to study both logical and non-logical operations in the frequency domain, which we refer to as Logical Signal Processing.


Houssam Abbas is an Assistant Professor of Electrical Engineering and Computer Science at Oregon State University. His research interests are in the verification of autonomous systems, with particular emphasis on unpiloted ground and aerial vehicles and formal theories of autonomous systems. He was a postdoctoral fellow at the University of Pennsylvania, and a design automation engineer at Intel. Houssam holds a PhD in Electrical Engineering from Arizona State University.

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