Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequential decision problems, dependent types and generic solutions   We present a computer-checked generic implementation for solving
finite-horizon sequential decision problems. This is a wide class of problems,
including inter-temporal optimizations, knapsack, optimal bracketing,
scheduling, etc. The implementation can handle time-step dependent control and
state spaces, and monadic representations of uncertainty (such as stochastic,
non-deterministic, fuzzy, or combinations thereof). This level of genericity is
achievable in a programming language with dependent types (we have used both
Idris and Agda). Dependent types are also the means that allow us to obtain a
formalization and computer-checked proof of the central component of our
implementation: Bellman's principle of optimality and the associated backwards
induction algorithm. The formalization clarifies certain aspects of backwards
induction and, by making explicit notions such as viability and reachability,
can serve as a starting point for a theory of controllability of monadic
dynamical systems, commonly encountered in, e.g., climate impact research.

27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph