Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonicity in GFG and Transition-Based Automata   Minimization of deterministic automata on finite words results in a {\em
canonical\/} automaton. For deterministic automata on infinite words, no
canonical minimal automaton exists, and a language may have different minimal
deterministic B\"uchi (DBW) or co-B\"uchi (DCW) automata. In recent years,
researchers have studied {\em good-for-games\/} (GFG) automata --
nondeterministic automata that can resolve their nondeterministic choices in a
way that only depends on the past. Several applications of automata in formal
methods, most notably synthesis, that are traditionally based on deterministic
automata, can instead be based on GFG automata. The {\em minimization\/}
problem for DBW and DCW is NP-complete, and it stays NP-complete for GFG
B\"uchi and co-B\"uchi automata. On the other hand, minimization of GFG
co-B\"uchi automata with {\em transition-based\/} acceptance (GFG-tNCWs) can be
solved in polynomial time. In these automata, acceptance is defined by a set
$\alpha$ of transitions, and a run is accepting if it traverses transitions in
$\alpha$ only finitely often. This raises the question of canonicity of minimal
deterministic and GFG automata with transition-based acceptance. In this paper
we study this problem. We start with GFG-tNCWs and show that the safe
components (that is, these obtained by restricting the transitions to these not
in $\alpha$) of all minimal GFG-tNCWs are isomorphic, and that by saturating
the automaton with transitions in $\alpha$ we get isomorphism among all minimal
GFG-tNCWs. Thus, a canonical form for minimal GFG-tNCWs can be obtained in
polynomial time. We continue to DCWs with transition-based acceptance (tDCWs),
and their dual tDBWs. We show that here, while no canonical form for minimal
automata exists, restricting attention to the safe components is useful, and
implies that the only minimal tDCWs that have no canonical form are these for
which the transition to the GFG model results in strictly smaller automaton,
which do have a canonical minimal form.

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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess