Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Complexity of ATL and ATL* Module Checking   Module checking has been introduced in late 1990s to verify open systems,
i.e., systems whose behavior depends on the continuous interaction with the
environment. Classically, module checking has been investigated with respect to
specifications given as CTL and CTL* formulas. Recently, it has been shown that
CTL (resp., CTL*) module checking offers a distinctly different perspective
from the better-known problem of ATL (resp., ATL*) model checking. In
particular, ATL (resp., ATL*) module checking strictly enhances the
expressiveness of both CTL (resp., CTL*) module checking and ATL (resp. ATL*)
model checking. In this paper, we provide asymptotically optimal bounds on the
computational cost of module checking against ATL and ATL*, whose upper bounds
are based on an automata-theoretic approach. We show that module-checking for
ATL is EXPTIME-complete, which is the same complexity of module checking
against CTL. On the other hand, ATL* module checking turns out to be
3EXPTIME-complete, hence exponentially harder than CTL* module checking.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas