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:
“I feel like a white granular mass of amorphous crystals—my formula appears to be isomeric with Spasmotoxin. My aurochloride precipitates into beautiful prismatic needles. My Platinochloride develops octohedron crystals,—with a fine blue florescence. My physiological action is not indifferent. One millionth of a grain injected under the skin of a frog produced instantaneous death accompanied by an orange blossom odor.”
—Lafcadio Hearn (1850–1904)
“Life is a game in which the rules are constantly changing; nothing spoils a game more than those who take it seriously. Adultery? Phooey! You should never subjugate yourself to another nor seek the subjugation of someone else to yourself. If you follow that Crispian principle you will be able to say “Phooey,” too, instead of reaching for your gun when you fancy yourself betrayed.”
—Quentin Crisp (b. 1908)