An extract on #taengshispace

The New York Stock Exchange is closed on New Years Day, Martin Luther King, Jr. Day, Washington's Birthday, Good Friday, Memorial Day, Fourth of July, Labor Day, Thanksgiving and Christmas. When those holidays occur on a weekend, the holiday is observed on the closest weekday. In addition, the Stock Exchange closes early on the day before Independence Day, the day after Thanksgiving, and the day before Christmas.

Many of the people who ring the bell are business executives whose companies trade on the exchange. However, there have also been many famous people from outside the world of business that have rung the bell. Athletes such as Joe DiMaggio of the New York Yankees and Olympic swimming champion Michael Phelps, entertainers such as rapper Snoop Dogg, singer and actress Liza Minnelli and members of the band Kiss, and politicians such as Mayor of New York City Rudy Giuliani and President of South Africa Nelson Mandela have all had the honor of ringing the bell. Two United Nations Secretaries General have also rung the bell. On April 27, 2006, Secretary-General Kofi Annan rang the opening bell to launch the United Nations Principles for Responsible Investment. On July 24, 2013, Secretary-General Ban Ki-moon rang the closing bell to celebrate the NYSE joining the United Nations Sustainable Stock Exchanges Initiative. In addition there have been many bell-ringers who are famous for heroic deeds, such as members of the New York police and fire departments following the events of 9/11, members of the United States Armed Forces serving overseas, and participants in various charitable organizations. There have also been several fictional characters that have rung the bell, including Mickey Mouse, the Pink Panther, Mr. Potato Head, the Aflac Duck, and Darth Vader.

The two definitions of NP as the class of problems solvable by a nondeterministic Turing machine (TM) in polynomial time and the class of problems verifiable by a deterministic Turing machine in polynomial time are equivalent. The proof is described by many textbooks, for example Sipser's Introduction to the Theory of Computation, section 7.3. To show this, first suppose we have a deterministic verifier. A nondeterministic machine can simply nondeterministically run the verifier on all possible proof strings (this requires only polynomially many steps because it can nondeterministically choose the next character in the proof string in each step, and the length of the proof string must be polynomially bounded). If any proof is valid, some path will accept; if no proof is valid, the string is not in the language and it will reject. Conversely, suppose we have a nondeterministic TM called A accepting a given language L. At each of its polynomially many steps, the machine's computation tree branches in at most a finite number of directions. There must be at least one accepting path, and the string describing this path is the proof supplied to the verifier. The verifier can then deterministically simulate A, following only the accepting path, and verifying that it accepts at the end. If A rejects the input, there is no accepting path, and the verifier will always reject.