Reducing Clocks in Timed Automata while Preserving Bisimulation

Model checking timed automata becomes increasingly complex with the increase in the number of clocks. Hence it is desirable that one constructs an automaton with the minimum number of clocks possible. The problem of checking whether there exists a timed automaton with a smaller number of clocks such that the timed language accepted by the original automaton is preserved is known to be undecidable. In this paper, we give a construction, which for any given timed automaton produces a timed bisimilar automaton with the least number of clocks. Further, we show that such an automaton with the minimum possible number of clocks can be constructed in time that is doubly exponential in the number of clocks of the original automaton.

Energy-Dependent Timing of Thermal Emission in Solar Flares

We report solar flare plasma to be multi-thermal in nature based on the theoretical model and study of the energy-dependent timing of thermal emission in ten M-class flares. We employ high-resolution X-ray spectra observed by the Si detector of the Solar X-ray Spectrometer (SOXS). The SOXS onboard the Indian GSAT-2 spacecraft was launched by the GSLV-D2 rocket on 8 May 2003. Firstly we model the spectral evolution of the X-ray line and continuum emission flux F(epsilon) from the flare by integrating a series of isothermal plasma flux. We find that multi-temperature integrated flux F(epsilon) is a power-law function of epsilon with a spectral index (gamma) approx -4.65. Next, based on spectral-temporal evolution of the flares we find that the emission in the energy range E= 4 - 15 keV is dominated by temperatures of T= 12 - 50 MK, while the multi-thermal power-law DEM index (gamma) varies in the range of -4.4 and -5.7. The temporal evolution of the X-ray flux F(epsilon,t) assuming a multi-temperature plasma governed by thermal conduction cooling reveals that the temperature-dependent cooling time varies between 296 and 4640 s and the electron density (n_e) varies in the range of n_e= (1.77-29.3)*10^10 cm-3. Employing temporal evolution technique in the current study as an alternative method for separating thermal from non-thermal components in the energy spectra, we measure the break-energy point ranging between 14 and 21pm1.0 keV.