Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The firing squad synchronization problem for squares with holes   The firing squad synchronization problem (FSSP, for short) is a problem in
automata theory introduced in 1957 by John Myhill. Its goal is to design a
finite automaton A such that, if copies of A are placed in a line and connected
and are started at time 0 with their leftmost copy in a special triggering
state, then at some time (the "firing time") all copies enter a special "firing
state" simultaneously for the first time. FSSP has many variations and for many
of them we know minimal-time solutions (solutions having shortest firing time).
One of such variations is the FSSP for squares (denoted by SQ) in which copies
are placed in a square. In this paper we introduce a variation which we call
the FSSP for squares with k holes and denote by SH[k] by slightly modifying SQ
(k >= 1). In the variation, copies of a finite automaton are placed in a square
but there are k positions ("holes") in the square where no copies are placed.
We show that SH[1] has a minimal-time solution. Moreover, for each problem
instance (a placement of copies in a square) C of SH[2], we determine the
minimum firing time of C (the minimum value of firing times of C by A where A
ranges over all solutions of SH[2]). The variation SQ was introduced and its
minimal-time solutions were found in 1970's. However, to find minimal-time
solutions of SH[k], a very simple modification of SQ, seems to be a very
difficult and challenging problem for k >= 2.

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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph