Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Generative Power of Omega-Grammars and Omega-Automata   An \omega-grammar is a formal grammar used to generate \omega-words (i.e.
infinite length words), while an \omega-automaton is an automaton used to
recognize \omega-words. This paper gives clean and uniform definitions for
\omega-grammars and \omega-automata, provides a systematic study of the
generative power of \omega-grammars with respect to \omega-automata, and
presents a complete set of results for various types of \omega-grammars and
acceptance modes. We use the tuple (\sigma,\rho,\pi) to denote various
acceptance modes, where \sigma denotes that some designated elements should
appear at least once or infinitely often, \rho denotes some binary relation
between two sets, and \pi denotes normal or leftmost derivations. Technically,
we propose (\sigma,\rho,\pi)-accepting \omega-grammars, and systematically
study their relative generative power with respect to (\sigma,\rho)-accepting
\omega-automata. We show how to construct some special forms of
\omega-grammars, such as \epsilon-production-free \omega-grammars. We study the
equivalence or inclusion relations between \omega$-grammars and \omega-automata
by establishing the translation techniques. In particular, we show that, for
some acceptance modes, the generative power of \omega-CFG is strictly weaker
than \omega-PDA, and the generative power of \omega-CSG is equal to \omega-TM
(rather than linear-bounded \omega-automata-like devices). Furthermore, we
raise some remaining open problems for two of the acceptance modes.

32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin