TY - GEN
T1 - Approximative methods for monotone systems of min-max-polynomial equations
AU - Esparza, Javier
AU - Gawlitza, Thomas
AU - Kiefer, Stefan
AU - Seidl, Helmut
N1 - Funding Information:
This work was in part supported by the DFG project Algorithms for Software Model Checking.
PY - 2008
Y1 - 2008
N2 - A monotone system of min-max-polynomial equations (min-max-MSPE) over the variables X1,...,Xn has for every i exactly one equation of the form Xi = fi (X1,...,Xn) where each fi (X1,...,Xn ) is an expression built up from polynomials with non-negative coefficients, minimum- and maximum-operators. The question of computing least solutions of min-max-MSPEs arises naturally in the analysis of recursive stochastic games [5,6,14]. Min-max-MSPEs generalize MSPEs for which convergence speed results of Newton's method are established in [11,3]. We present the first methods for approximatively computing least solutions of min-max-MSPEs which converge at least linearly. Whereas the first one converges faster, a single step of the second method is cheaper. Furthermore, we compute ε-optimal positional strategies for the player who wants to maximize the outcome in a recursive stochastic game.
AB - A monotone system of min-max-polynomial equations (min-max-MSPE) over the variables X1,...,Xn has for every i exactly one equation of the form Xi = fi (X1,...,Xn) where each fi (X1,...,Xn ) is an expression built up from polynomials with non-negative coefficients, minimum- and maximum-operators. The question of computing least solutions of min-max-MSPEs arises naturally in the analysis of recursive stochastic games [5,6,14]. Min-max-MSPEs generalize MSPEs for which convergence speed results of Newton's method are established in [11,3]. We present the first methods for approximatively computing least solutions of min-max-MSPEs which converge at least linearly. Whereas the first one converges faster, a single step of the second method is cheaper. Furthermore, we compute ε-optimal positional strategies for the player who wants to maximize the outcome in a recursive stochastic game.
UR - https://www.scopus.com/pages/publications/49049100919
U2 - 10.1007/978-3-540-70575-8_57
DO - 10.1007/978-3-540-70575-8_57
M3 - Conference contribution
AN - SCOPUS:49049100919
SN - 3540705740
SN - 9783540705741
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 698
EP - 710
BT - Automata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings
T2 - 35th International Colloquium on Automata, Languages and Programming, ICALP 2008
Y2 - 7 July 2008 through 11 July 2008
ER -