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­sing Mathematics to Hunt For Computer Errors

Improving the security of computer software and hardware requires mathematical analytic methods.

Thanks to research by a team of computer scientists in a project funded by the Austrian Science Fund FWF, mathmatical analytical methods for enhancing hardware and software will work significantly faster in the future.

Credit: agsandrew/Shutterstock

The Austrian Science Fund FWF is funding the development of methods devised by researchers led by Institute for Science and Technology Austria professor Krishnendu Chatterjee to apply mathematical analysis to enhancing software and hardware security.

Chatterjee notes scientists use graph theory for the mathematical analysis of computer systems for verification, and the speed of these verification algorithms is what particularly interests him.

"Some algorithmic problems in verification development have been stagnating since the 1990s," he says. "A new aspect of this project was to use cutting-edge approaches from graph theory to improve the algorithms."

In collaboration with project partner Monika Henzinger at the University of Vienna, Chatterjee successfully exceeded several speed limits for certain verification algorithms, including those involving Markov decision processes. Chatterjee says these processes are models containing multiple options and an element of randomness, such as the development of robots.

"The most efficient algorithm for addressing that problem available till now dated back to 1995 and had quadratic complexity," he notes. "In our project, we were able to overcome this limit by using graph algorithm techniques."

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