What a difference three months makes. Nuance Communications has halved its all-cash takeover bid for mobile ad and search firm Zi Corp. from $40.5 million to $20 million. Nuance, which makes speech-based technology for customer service, directory assistance and voice-activated commands on wireless devices, has been dogged in its pursuit of Zi for months. Less than two weeks after Zi rejected Nuance’s offer of 80 cents per share (or $40.5 million total). Last August, Nuance accused Zi of patent infringement and filed suit over SMS technology used by the company. The Burlington, Mass.-based company says its new 40-cent a share offer is good through the end of the year. Nuance points out that the new offer still represents a 25 percent premium over the Calgary-based company’s closing price of shares before the original offer was made, and a 38 percent premium over the closing price on Nov. 25. This week, Nuance announced fourth-quarter earnings, saying it recorded a profit, and its mobile division in particular achieved record revenues, however, cautioned that going forward the softening economy may impact the company’s results in the new year. Release.