DocumentCode :
3112489
Title :
Game Relations and Metrics
Author :
de Alfaro, L. ; Majumdar, Rupak ; Raman, Vishwanath ; Stoelinga, Mariëlle
Author_Institution :
Univ. of California, Santa Cruz
fYear :
2007
fDate :
10-14 July 2007
Firstpage :
99
Lastpage :
108
Abstract :
We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal (e.g., "reach a target state"), the question of winning is thus a probabilistic one: "what is the maximal probability of winning from a given state?". On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two states are equivalent if the players can win the same games with the same probability from both states. Metrics provide a bound on the difference in the probabilities of winning across states, capturing a quantitative notion of state "similarity". We introduce equivalences and metrics for two-player game structures, and we show that they characterize the difference in probability of winning games whose goals are expressed in the quantitative mu-calculus. The quantitative mu- calculus can express a large set of goals, including reachability, safety, and omega-regular properties. Thus, we claim that our relations and metrics provide the canonical extensions to games, of the classical notion of bisimulation for transition systems. We develop our results both for equivalences and metrics, which generalize bisimulation, and for asymmetrical versions, which generalize simulation.
Keywords :
calculus; finite state machines; game theory; probability; equivalences; finite state spaces; metrics; probability; quantitative mu-calculus; two-player games; Computer science; Cost accounting; Heart; Kernel; Logic; Minimax techniques; Probability distribution; Safety; State-space methods; Stochastic systems;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Logic in Computer Science, 2007. LICS 2007. 22nd Annual IEEE Symposium on
Conference_Location :
Wroclaw
ISSN :
1043-6871
Print_ISBN :
0-7695-2908-9
Type :
conf
DOI :
10.1109/LICS.2007.22
Filename :
4276555
Link To Document :
بازگشت