Context: Gamma-ray bursts are cosmological sources emitting radiation from the gamma-rays to the radio band. Substantial observational efforts have been devoted to the study of gamma-ray bursts during the prompt phase, i.e. the initial burst of high-energy radiation, and during the long-lasting afterglows. In spite of many successes in interpreting these phenomena, there are still several open key questions about the fundamental emission processes, their energetics and the environment. Aim: Independently of specific gamma-ray burst theoretical recipes, spectra in the GeV/TeV range are predicted to be remarkably simple, being satisfactorily modeled with power-laws, and therefore offer a very valuable tool to probe the extragalactic background light distribution. Furthermore, the simple detection of a component at very-high energies, i.e. at $sim 100$,GeV, would solve the ambiguity about the importance of various possible emission processes, which provide barely distinguishable scenarios at lower energies. Methods: We used the results of the MAGIC telescope observation of the moderate resdhift ($zsim0.76$) object{GRB,080430} at energies above about 80,GeV, to evaluate the perspective for late-afterglow observations with ground based GeV/TeV telescopes. Results: We obtained an upper limit of $F_{rm 95%,CL} = 5.5 times 10^{-11}$,erg,cm$^{-2}$,s$^{-1}$ for the very-high energy emission of object{GRB,080430}, which cannot set further constraints on the theoretical scenarios proposed for this object also due to the difficulties in modeling the low-energy afterglow. Nonetheless, our observations show that Cherenkov telescopes have already reached the required sensitivity to detect the GeV/TeV emission of GRBs at moderate redshift ($z lesssim 0.8$), provided the observations are carried out at early times, close to the onset of their afterglow phase.
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