For 17 years, Terrill Swift and three other men convicted in the 1994 rape and strangulation of a prostitute here have insisted on their innocence. And last May, a powerful new piece of evidence emerged that appeared to back their claim: a DNA profile, constructed from semen found in the victim’s body, matched a man who was convicted of raping and strangling another prostitute a few years later.

“It’s over,” Mr. Swift remembers thinking when the DNA match surfaced. But six months later, the exoneration of the four men, who as teenagers confessed during questioning by the police, is still uncertain.

The Cook County state’s attorney has opposed vacating the men’s convictions, arguing that the DNA match alone is not sufficient to cast significant doubt on their guilt. Johnny Douglas, whose DNA matched the profile, was known to frequent prostitutes and could have had consensual sex with the victim before the murder occurred, the prosecutors have argued.