From Parity and Payoff Games to Linear Programming

This paper establishes a surprising reduction from parity and mean pay-off games to linear programming problems. While Such a connection is trivial for solitary games, it is Surprising for two player games, because the players have opposing objectives, whose natural translations into ail optimisation problem are minimisation and maximisation, respectively. Our reduction to linear programming circumvents the need for concurrent minimisation and maximisation by replacing one of them, the maximisation, by approximation. The resulting optimisation problem call be translated to a linear programme by a simple space transformation, which is inexpensive in the unit cost model, but results ill ail exponential growth of the coefficients. The discovered connection opens up unexpected applications like mu-calculus model checking-of linear programming ill the unit Cost model, and thus turns the intriguing academic problem of finding a polynomial time algorithm for linear programming in this model of computation (and subsequently a strongly polynomial algorithm) into a problem of paramount practical importance: All advancements ill this area call immediately be applied to accelerate solving parity and payoff games, or to improve their complexity analysis.