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Küster, G. (1991) On the Hurwitz Product of Formal Power Series and Automata. Theoretical Computer Science, 83, 261-273.
http://dx.doi.org/10.1016/0304-3975(91)90278-A

has been cited by the following article:

  • TITLE: A Generic Graph Model for WCET Analysis of Multi-Core Concurrent Applications

    AUTHORS: Robert Mittermayr, Johann Blieberger

    KEYWORDS: Worst-Case Execution Time Analysis, Program Analysis; Concurrency, Multi-Threaded Programs, Kronecker Algebra

    JOURNAL NAME: Journal of Software Engineering and Applications, Vol.9 No.5, May 23, 2016

    ABSTRACT: Worst-case execution time (WCET) analysis of multi-threaded software is still a challenge. This comes mainly from the fact that synchronization has to be taken into account. In this paper, we focus on this issue and on automatically calculating and incorporating stalling times (e.g. caused by lock contention) in a generic graph model. The idea that thread interleavings can be studied with a matrix calculus is novel in this research area. Our sparse matrix representations of the program are manipulated using an extended Kronecker algebra. The resulting graph represents multi-threaded programs similar as CFGs do for sequential programs. With this graph model, we are able to calculate the WCET of multi-threaded concurrent programs including stalling times which are due to synchronization. We employ a generating function-based approach for setting up data flow equations which are solved by well-known elimination-based dataflow analysis methods or an off-the-shelf equation solver. The WCET of multi-threaded programs can finally be calculated with a non-linear function solver.