A formula game is an artificial game represented by a fully quantified Boolean formula. Players' turns alternate and the space of possible moves is denoted by bound variables. If a variable is universally quantified, the formula following it has the same truth value as the formula beginning with the universal quantifier regardless of the move taken. If a variable is existentially quantified, the formula following it has the same truth value as the formula beginning with the existential quantifier for at least one move available at the turn. Turns alternate, and a player loses if he cannot move at his turn. In computational complexity theory, the language FORMULA-GAME is defined as all formulas such that Player 1 has a winning strategy in the game represented by . FORMULA-GAME is PSPACE-complete.
Famous quotes containing the words formula and/or game:
“Hidden away amongst Aschenbach’s writing was a passage directly asserting that nearly all the great things that exist owe their existence to a defiant despite: it is despite grief and anguish, despite poverty, loneliness, bodily weakness, vice and passion and a thousand inhibitions, that they have come into being at all. But this was more than an observation, it was an experience, it was positively the formula of his life and his fame, the key to his work.”
—Thomas Mann (18751955)
“Vanessa wanted to be a ballerina. Dad had such hopes for her.... Corin was the academically brilliant one, and a fencer of Olympic standard. Everything was expected of them, and they fulfilled all expectations. But I was the one of whom nothing was expected. I remember a game the three of us played. Vanessa was the President of the United States, Corin was the British Prime Minister—and I was the royal dog.”
—Lynn Redgrave (b. 1943)