Time-dependent, multidimensional, reactive Navier-Stokes fluid-dynamics simulations are used to examine the effects of bifurcated shock structures on shock-flame interactions and deflagration-to-detonation transition (DDT) in shock-tube experiments. The computations are performed for low-pressure (100 torr) ethylene-air mixtures using a dynamically adapting computational mesh to resolve flames, shocks, boundary layers, and vortices in flow. Results of the simulations show a complex sequence of events, starting from the interactions of an incident shock with an initially laminar flame, formation of a flame brush, DDT, and finally the emergence of a self-sustained detonation with the type of transverse-wave structure that forms detonations cells. An important process, studied here in detail, is the interaction of the reflected shock with the boundary layer formed by the incident shock. This interaction leads to bifurcation of the reflected shock and the formation of a complex structure containing a leading oblique shock followed by a recirculation region. If the flame is close enough to the bifurcated structure, it becomes entrained in the recirculation region and attached to the bifurcated shock. This changes the nature of the shock-flame interaction both qualitatively and quantitatively. The reactive bifurcated structure, containing an attached flame, appears as a shock-flame complex propagating at approximately one half of the CJ velocity. The presence of a bifurcated structure leads to an increase in the energy-release rate, the formation of Mach stems in the middle of the shock tube, and creation of multiple hot spots behind the Mach stem, thus facilitating DDT.