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Summary: Modular Strategies for In nite Games on
Recursive Graphs ?
Rajeev Alur 1 , Salvatore La Torre 2 , and P. Madhusudan 1
1 University of Pennsylvania
2 Universita degli Studi di Salerno
Abstract. In this paper, we focus on solving games in recursive game
graphs that can model the control
ow of sequential programs with recur-
sive procedure calls. The winning condition is given as an !-regular speci-
cation over the observable, and, unlike traditional pushdown games, the
strategy is required to be modular : resolution of choices within a com-
ponent should not depend on the context in which the component is
invoked, but only on the history within the current invocation of the
component. We rst consider the case when the speci cation is given
as a deterministic Buchi automaton. We show the problem to be decid-
able, and present a solution based on two-way alternating tree automata
with time complexity that is polynomial in the number of internal nodes,
exponential in the speci cation and exponential in the number of exits
of the components. We show that the problem is Exptime-complete in
general, and Np-complete for xed-size speci cations. Then, we show
that the same complexity bounds apply if the speci cation is given as a
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