We study properties of normal, superconducting (SC) and CDW states for an attractive Hubbard model on the square lattice, using a variational Monte Carlo method. In trial wave functions, we introduce an interspinon binding factor, indispensable to induce a spin-gap transition in the normal state, in addition to the onsite attractive and intersite repulsive factors. It is found that, in the normal state, as the interaction strength $|U|/t$ increases, a first-order spin-gap transition arises at $|U_{rm c}|sim W$ ($W$: band width) from a Fermi liquid to a spin-gapped state, which is conductive through hopping of doublons. In the SC state, we confirm by analysis of various quantities that the mechanism of superconductivity undergoes a smooth crossover at around $|U_{ma{co}}|sim |U_{rm c}|$ from a BCS type to a Bose-Einstein condensation (BEC) type, as $|U|/t$ increases. For $|U|<|U_{ma{co}}|$, quantities such as the condensation energy, a SC correlation function and the condensate fraction of onsite pairs exhibit behavior of $sim exp(-t/|U|)$, as expected from the BCS theory. For $|U|>|U_{ma{co}}|$, quantities such as the energy gain in the SC transition and superfluid stiffness, which is related to the cost of phase coherence, behave as $sim t^2/|U|propto T_{rm c}$, as expected in a bosonic scheme. In this regime, the SC transition is induced by a gain in kinetic energy, in contrast with the BCS theory. We refer to the relevance to the pseudogap in cuprate superconductors.
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