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Home > Archive>Volume 30, Issue 7, 2019 >2033-2051. DOI:10.13328/j.cnki.jos.005757
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Computational Complexity of Several Problems for Resetting Timed Automata
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TP301

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National Natural Science Foundation of China (61472146, 61640221, 61872272); Natural Science Foundation of Guangdong Province of China (2015A030313413).

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    Abstract:

    The reset sequences of finite automata, also known as the synchronizing sequences, have a characteristic:a finite automaton can reach a certain state qw by running a reset sequence from any unknown or unobservable state q0. This is dependent only on the reset sequence w itself, not on the state q0 of the finite automaton at the beginning of running the sequence w. It can be used to restore the running partially observable and complex systems automatically that needs no resetting, and sometimes even that cannot reset. Therefore, the reset problem has been paid attention to since it emerged and has been studied continuously. Recently, it has extended to infinite state models that can describe the complex systems, including distributed and embedded real-time systems, such as timed automata, register automata, etc. In this work, the computational complexity of several problems for the resetting timed automata is studied, and the strong connection between resettability problem and reachability problem for timed automata is found. The main contribution includes:(1) the complexity of the problem for resetting the complete and deterministic timed automata is updated more precisely with the recent achievements in reachability problem for timed automata; (2) the complexity of the problem for resetting the partially specified timed automata is studied. Even if the size of input alphabet is decreased to 2, it is still PSPACE-complete, and in the case of single clock, it is NLOGSPACE-complete; (3) for the complete and nondeterministic timed automata, Di-resetting problems (i=1,2,3) are all undecidable. The resetting problem for nondeterministic register automata and nondeterministic timed automata can be inter-reduced in exponential time, and the reduction in exponential time is closed for relatively high computational complexity classes. Therefore, it concludes that the problem for resetting it in single clock case is Ackermann-complete, and that bounded version is NEXPTIME-complete from the results on corresponding nondeterministic register automata. These conclusions show that most of resetting problems for timed automata are intractable. On the one hand, they make a solid theoretical foundation for checking and solving the resettability of the timed systems, on the other hand, they guide to seek for some subclasses of real time system which have particular structure and effective algorithms for solving it.

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朱凯,毋国庆,吴理华,袁梦霆.有关时间自动机重置的若干问题的计算复杂性.软件学报,2019,30(7):2033-2051

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History
  • Received:July 15,2018
  • Revised:October 14,2018
  • Online: April 03,2019
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