Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak Singular Hybrid Automata   The framework of Hybrid automata, introduced by Alur, Courcourbetis,
Henzinger, and Ho, provides a formal modeling and analysis environment to
analyze the interaction between the discrete and the continuous parts of
cyber-physical systems. Hybrid automata can be considered as generalizations of
finite state automata augmented with a finite set of real-valued variables
whose dynamics in each state is governed by a system of ordinary differential
equations. Moreover, the discrete transitions of hybrid automata are guarded by
constraints over the values of these real-valued variables, and enable
discontinuous jumps in the evolution of these variables. Singular hybrid
automata are a subclass of hybrid automata where dynamics is specified by
state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed
that for even very restricted subclasses of singular hybrid automata, the
fundamental verification questions, like reachability and schedulability, are
undecidable. In this paper we present \emph{weak singular hybrid automata}
(WSHA), a previously unexplored subclass of singular hybrid automata, and show
the decidability (and the exact complexity) of various verification questions
for this class including reachability (NP-Complete) and LTL model-checking
(PSPACE-Complete). We further show that extending WSHA with a single
unrestricted clock or extending WSHA with unrestricted variable updates lead to
undecidability of reachability problem.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin