"No Smoking" signs began going up in offices, restaurants and other public places Wednesday as a new city ordinance that strictly limits where smokers can puff went into effect.

The ordinance bans or restricts smoking in workplaces, restaurants, hotels, theaters, large stores and taxicabs.

Restaurants with more than 50 seats must ban smoking at more than half their tables. Businesses with more than 15 employees must provide non-smoking work areas one at least 8 feet from a smoker.Some companies, calling that arrangement too difficult to arrange or enforce, have banned smoking except in private offices.

"If everyone is understanding, the month of April will be a time for experimentation," said Cynthia R. Darrison, head of the Restaurant League of New York. "But this is New York. You could have fistfights in restaurants."

Officials conceded that it will take months to sort out how exactly the law will be enforced. The city said it will allow a two-month grace period before issuing fines of up to $500.

"You're talking about a complex social change in a city of 8 million people," said Dr. Stephen Joseph, the city health commissioner.