Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Syntactic Regions for Concurrent Programs   In order to gain a better understanding of the state space of programs, with
the aim of making their verification more tractable, models based on directed
topological spaces have been introduced, allowing to take in account
equivalence between execution traces, as well as translate features of the
execution (such as the presence of deadlocks) into geometrical situations. In
this context, many algorithms were introduced, based on a description of the
geometrical models as regions consisting of unions of rectangles. We explain
here that these constructions can actually be performed directly on the syntax
of programs, thus resulting in representations which are more natural and
easier to implement. In order to do so, we start from the observation that
positions in a program can be described as partial explorations of the program.
The operational semantics induces a partial order on positions, and regions can
be defined as formal unions of intervals in the resulting poset. We then study
the structure of such regions and show that, under reasonable conditions, they
form a boolean algebra and admit a representation in normal form (which
corresponds to covering a space by maximal intervals), thus supporting the
constructions needed for the purpose of studying programs. All the operations
involved here are given explicit algorithmic descriptions.

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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: cond-mat