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The Australian Square Kilometre Array Pathfinder (ASKAP) will give us an unprecedented opportunity to investigate the transient sky at radio wavelengths. In this paper we present VAST, an ASKAP survey for Variables and Slow Transients. VAST will exploit the wide-field survey capabilities of ASKAP to enable the discovery and investigation of variable and transient phenomena from the local to the cosmological, including flare stars, intermittent pulsars, X-ray binaries, magnetars, extreme scattering events, interstellar scintillation, radio supernovae, and orphan afterglows of gamma-ray bursts. In addition, it will allow us to probe unexplored regions of parameter space where new classes of transient sources may be detected. In this paper we review the known radio transient and variable populations and the current results from blind radio surveys. We outline a comprehensive program based on a multi-tiered survey strategy to characterise the radio transient sky through detection and monitoring of transient and variable sources on the ASKAP imaging timescales of 5 s and greater. We also present an analysis of the expected source populations that we will be able to detect with VAST.
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