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  • 1.
    Fersman, Elena
    et al.
    Uppsala University, Sweden.
    Mokrushin, Leonid
    Uppsala University, Sweden.
    Pettersson, Paul
    Uppsala University, Sweden.
    Yi, Wang
    Uppsala University, Sweden.
    Schedulability Analysis of Fixed Priority Systems using Timed Automata2006In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 354, no 2, p. 301-317Article in journal (Refereed)
    Abstract [en]

    In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which is in many cases huge. In this paper, we show that for fixed-priority scheduling strategy, the schedulability checking problem can be solved using standard timed automata with two extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Analysis (RMA). The result is further extended to systems with data-dependent control, in which the release time of a task may depend on the time-point at which other tasks finish their execution. For the case when the execution times of tasks are constants, we show that the schedulability problem can be solved using n+1 extra clocks, where n is the number of tasks. The presented analysis techniques have been implemented in the Times tool. For systems with only periodic tasks, the performance of the tool is comparable with tools implementing the classic RMA technique based on equation-solving, without suffering from the exponential explosion in the number of tasks.

  • 2.
    Freivalds, R.
    et al.
    Latvian State Univ.
    Bonner, Richard
    Mälardalen University, Department of Mathematics and Physics.
    Quantum inductive inference by finite automata2008In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 397, no 1-3, p. 70-76Article in journal (Refereed)
    Abstract [en]

    Freivalds and Smith [R. Freivalds, C.H. Smith Memory limited inductive inference machines, Springer Lecture Notes in Computer Science 621 (1992) 19-29] proved that probabilistic limited memory inductive inference machines can learn with probability 1 certain classes of total recursive functions, which cannot be learned by deterministic limited memory inductive inference machines. We introduce quantum limited memory inductive inference machines as quantum finite automata acting as inductive inference machines. These machines, we show, can learn classes of total recursive functions not learnable by any deterministic, nor even by probabilistic, limited memory inductive inference machines.

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