Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Joining Transition Systems of Records: Some Congruency and
  Language-Theoretic Results   B\"uchi automaton of records (BAR) has been proposed as a basic operational
semantics for Reo coordination language. It is an extension of B\"uchi
automaton by using a set of records as its alphabet or transition labels.
Records are used to express the synchrony between the externally visible
actions of coordinated components modeled by BARs. The main composition
operator on the set of BARs is called as join which is the semantics of its
counterpart in Reo. In this paper, we define the notion of labeled transition
systems of records as a generalization of the notion of BAR, abstracting away
from acceptance or rejection of strings. Then, we consider four equivalence
relations (semantics) over the set of labeled transition systems of records and
investigate their congruency with respect to the join composition operator. In
fact, we prove that the finite-traces-based, infinite-traces-based, and
nondeterministic finite automata (NFA)-based equivalence relations all are
congruence relations over the set of all labeled transition systems of records
with respect to the join operation. However, the equivalence relation using
B\"uchi acceptance condition is not so. In addition, using these results, we
introduce the language-theoretic definitions of the join operation considering
both finite and infinite strings notions. Also, we show that there is no
language-based and structure-independent definition of the join operation on
B\"uchi automata of records.

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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: physics