Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Processes with Expected Stopping Time   Markov chains are the de facto finite-state model for stochastic dynamical
systems, and Markov decision processes (MDPs) extend Markov chains by
incorporating non-deterministic behaviors. Given an MDP and rewards on states,
a classical optimization criterion is the maximal expected total reward where
the MDP stops after $T$ steps, which can be computed by a simple dynamic
programming algorithm. We consider a natural generalization of the problem
where the stopping times can be chosen according to a probability distribution,
such that the expected stopping time is $T$, to optimize the expected total
reward. Quite surprisingly we establish inter-reducibility of the expected
stopping-time problem for Markov chains with the Positivity problem (which is
related to the well-known Skolem problem), for which establishing either
decidability or undecidability would be a major breakthrough. Given the
hardness of the exact problem, we consider the approximate version of the
problem: we show that it can be solved in exponential time for Markov chains
and in exponential space for MDPs.

17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph