Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Alternating Turing machines for inductive languages   We show that alternating Turing machines, with a novel and natural definition
of acceptance, accept precisely the inductive (Pi-1-1) languages. Total
alternating machines, that either accept or reject each input, accept precisely
the hyper-elementary (Delta-1-1) languages. Moreover, bounding the permissible
number of alternations yields a characterization of the levels of the
arithmetical hierarchy. Notably, these results use simple finite computing
devices, with finitary and discrete operational semantics, and neither the
results nor their proofs make any use of transfinite ordinals. Our
characterizations elucidate the analogy between the polynomial-time hierarchy
and the arithmetical hierarchy, as well as between their respective limits,
namely polynomial-space and Pi-1-1.

23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an