Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deciding Conditional Termination   We address the problem of conditional termination, which is that of defining
the set of initial configurations from which a given program always terminates.
First we define the dual set, of initial configurations from which a
non-terminating execution exists, as the greatest fixpoint of the function that
maps a set of states into its pre-image with respect to the transition
relation. This definition allows to compute the weakest non-termination
precondition if at least one of the following holds: (i) the transition
relation is deterministic, (ii) the descending Kleene sequence
overapproximating the greatest fixpoint converges in finitely many steps, or
(iii) the transition relation is well founded. We show that this is the case
for two classes of relations, namely octagonal and finite monoid affine
relations. Moreover, since the closed forms of these relations can be defined
in Presburger arithmetic, we obtain the decidability of the termination problem
for such loops.

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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom