Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal Proof Search for Modal Logic K Model Checking   Most modal logics such as S5, LTL, or ATL are extensions of Modal Logic K.
While the model checking problems for LTL and to a lesser extent ATL have been
very active research areas for the past decades, the model checking problem for
the more basic Multi-agent Modal Logic K (MMLK) has important applications as a
formal framework for perfect information multi-player games on its own.
  We present Minimal Proof Search (MPS), an effort number based algorithm
solving the model checking problem for MMLK. We prove two important properties
for MPS beyond its correctness. The (dis)proof exhibited by MPS is of minimal
cost for a general definition of cost, and MPS is an optimal algorithm for
finding (dis)proofs of minimal cost. Optimality means that any comparable
algorithm either needs to explore a bigger or equal state space than MPS, or is
not guaranteed to find a (dis)proof of minimal cost on every input.
  As such, our work relates to A* and AO* in heuristic search, to Proof Number
Search and DFPN+ in two-player games, and to counterexample minimization in
software model checking.

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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph