Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Coinductive Reformulation of Milner's Proof System for Regular
  Expressions Modulo Bisimilarity   Milner (1984) defined an operational semantics for regular expressions as
finite-state processes. In order to axiomatize bisimilarity of regular
expressions under this process semantics, he adapted Salomaa's proof system
that is complete for equality of regular expressions under the language
semantics. Apart from most equational axioms, Milner's system Mil inherits from
Salomaa's system a non-algebraic rule for solving single fixed-point equations.
Recognizing distinctive properties of the process semantics that render
Salomaa's proof strategy inapplicable, Milner posed completeness of the system
Mil as an open question.
  As a proof-theoretic approach to this problem we characterize the
derivational power that the fixed-point rule adds to the purely equational part
Mil$^-$ of Mil. We do so by means of a coinductive rule that permits cyclic
derivations that consist of a finite process graph with empty steps that
satisfies the layered loop existence and elimination property LLEE, and two of
its Mil$^{-}$-provable solutions. With this rule as replacement for the
fixed-point rule in Mil, we define the coinductive reformulation cMil as an
extension of Mil$^{-}$. In order to show that cMil and Mil are theorem
equivalent we develop effective proof transformations from Mil to cMil, and
vice versa. Since it is located half-way in between bisimulations and proofs in
Milner's system Mil, cMil may become a beachhead for a completeness proof of
Mil.
  This article extends our contribution to the CALCO 2022 proceedings. Here we
refine the proof transformations by framing them as eliminations of derivable
and admissible rules, and we link coinductive proofs to a coalgebraic
formulation of solutions of process graphs.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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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: econ
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The categories of this paper are: hep-lat
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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: gr-qc