Folk Theorems on the Determinization and Minimization of Timed Automata

Timed automata are known not to be complementable or determinizable. Natural questions are, then, could we check whether a given TA enjoys these properties? These problems are not algorithmically solvable, if we require not just a yes/no answer, but also a witness. Minimizing the “resources” of a TA (number of clocks or size of constants) are also unsolvable problems. Proofs are provided as simple reductions from the universality problem. These proofs are not applicable to the corresponding decision problems, the decidability of which remains open.

[1]  Rajeev Alur,et al.  Minimization of Timed Transition Systems , 1992, CONCUR.

[2]  Stavros Tripakis,et al.  Fault Diagnosis for Timed Automata , 2002, FTRTFT.

[3]  Frits W. Vaandrager,et al.  Minimizable Timed Automata , 1996, FTRTFT.

[4]  Patricia Bouyer,et al.  Expressiveness of Updatable Timed Automata , 2000, MFCS.

[5]  Deepak D'Souza,et al.  Timed Control with Partial Observability , 2003, CAV.

[6]  Stavros Tripakis,et al.  Analysis of Timed Systems Using Time-Abstracting Bisimulations , 2001, Formal Methods Syst. Des..

[7]  David Lee,et al.  An Efficient Algorithm for Minimizing Real-Time Transition Systems , 1997, Formal Methods Syst. Des..

[8]  Frits W. Vaandrager,et al.  Testing timed automata , 1997, Theor. Comput. Sci..

[9]  Thomas Wilke.  Automaten und Logiken zur Beschreibung zeitabhängiger Systeme , 1994 .

[10]  Thomas A. Henzinger,et al.  A Determinizable Class of Timed Automata , 1994, CAV.

[11]  Mihalis Yannakakis,et al.  Minimum and maximum delay problems in real-time systems , 1991, Formal Methods Syst. Des..

[12]  P. Madhusudan,et al.  Timed Control Synthesis for External Specifications , 2002, STACS.

[13]  Brian Nielsen,et al.  Automated test generation from timed automata , 2001, International Journal on Software Tools for Technology Transfer.

[14]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[15]  Conrado Daws,et al.  Reducing the number of clock variables of timed automata , 1996, RTSS.

[16]  Olivier Finkel.  On Decision Problems for Timed Automata , 2005, Bull. EATCS.

[17]  Patricia Bouyer,et al.  Are Timed Automata Updatable? , 2000, CAV.

[18]  Paul Gastin,et al.  Characterization of the Expressive Power of Silent Transitions in Timed Automata , 1998, Fundam. Informaticae.