This paper addresses the problem of loop iteration number estimation, applied to linear loops. This is important to statically
put an upper bound on the execution time of real-time systems and implement timing constraint verification. In our approach,
matrix calculation is applied to derive the analytical equation that holds the number of iterations as a solution, and it
is proved that such solution is related to a zero of an exponential function of the eigenvalues. So, the number of iterations
turns out to be an implicit variable of the equation, which can be easily exactly calculated for loops depending on few free
variables.
Keywords high-level specification - system synthesis - real-time concurrent systems - loop analysis - iterations' number's prediction - execution time evaluation - timing verification - difference equations
Francesco Curatelli received the degree in Electronic Engineering and the Ph.D. degree in Microelectronics from the University of Genova, Italy.
During the years 1980-85 he worked as a design engineer at Elsag Inc., Genova. Since 1985 he has been working at the Microelectronics
group of the Department of Biophysical and Electronic Engineering (DIBE) at the University of Genova, initially as Research
assistant and, since 1992, as Professor in Electronics. His research activities concern the study and development of algorithms
and design tools for real-time systems, HCI and assistive technology. He is the author of more than 80 papers published in
journals, conference proceedings, and books.
Leonardo Mangeruca received his master and PhD degrees in Electrical Engineering and Computer Science from the University of Genoa, Italy, between
1995 and 1998. In 1999 he joined PARADES, Roma, Italy, directed by Prof. A.L. Sangiovanni-Vincentelli, where he focused on
research activities in System Level Design and Advanced Architectures for Embedded Systems. His interests include formal models
and methods for system design, distributed systems, fault-tolerant architectures, embedded software, real-time scheduling.
He is involved in numerous cooperations with international research institutions and represents PARADES in several European
Projects.