Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment
Journal of the ACM (JACM)
Introduction to the Theory of Computation
Introduction to the Theory of Computation
Preemptive Job-Shop Scheduling Using Stopwatch Automata
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Computing simulations on finite and infinite graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Priority-Driven Scheduling of Periodic Task Systems on Multiprocessors
Real-Time Systems
Covering sharing trees: a compact data structure for parameterized verification
International Journal on Software Tools for Technology Transfer (STTT)
Task automata: Schedulability, decidability and undecidability
Information and Computation
ISORC '08 Proceedings of the 2008 11th IEEE Symposium on Object Oriented Real-Time Distributed Computing
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
An Antichain Algorithm for LTL Realizability
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
SEUS'07 Proceedings of the 5th IFIP WG 10.2 international conference on Software technologies for embedded and ubiquitous systems
Brute-force determination of multiprocessor schedulability for sets of sporadic hard-deadline tasks
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Global deadline-monotonic scheduling of arbitrary-deadline sporadic task systems
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Feasibility analysis of sporadic real-time multiprocessor task systems
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Tests for global EDF schedulability analysis
Journal of Systems Architecture: the EUROMICRO Journal
Timed Games for Computing WCET for Pipelined Processors with Caches
ACSD '11 Proceedings of the 2011 Eleventh International Conference on Application of Concurrency to System Design
Antichains: a new algorithm for checking universality of finite automata
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Antichain algorithms for finite automata
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Feasibility intervals for homogeneous multicores, asynchronous periodic tasks, and FJP schedulers
Proceedings of the 21st International conference on Real-Time Networks and Systems
Power-aware fixed priority scheduling for sporadic tasks in hard real-time systems
Journal of Systems and Software
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Baker and Cirinei (Lecture Notes in Computer Science, vol. 4878, Springer, pp. 62---75, 2007) have introduced an exact but naive algorithm, that consists in solving a state reachability problem in a finite automaton, to check whether a set of sporadic hard real-time tasks is schedulable on an identical multiprocessor platform. However, this algorithm suffers from poor performance due to the exponential size of the automaton relative to the size of the task set. In this paper, we build on the work of Baker and Cirinei, and rely on their formalism to characterise the complexity of this problem. We prove that it is PSpace-complete. In order to obtain an algorithm that is applicable in practice to systems of realistic sizes, we successfully apply techniques developed by the formal verification community, specifically antichain techniques (Doyen and Raskin in Lecture Notes in Computer Science, vol. 6015, Springer, pp. 2---22, 2010) to this scheduling problem. For that purpose, we define and prove the correctness of a simulation relation on Baker and Cirinei's automaton. We show that our improved algorithm yields dramatically improved performance for the schedulability test and opens for many further improvements. This work is an extended and revised version of a previous conference paper by the same authors (Lindström et al., Proceedings of the 19th International Conference on Real-Time and Network Systems (RTNS 2011), pp. 25---34, 2011).