Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Efficient Normalisation Procedure for Linear Temporal Logic and Very
  Weak Alternating Automata   In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem
stating that every formula of Past LTL (the extension of LTL with past
operators) is equivalent to a formula of the form $\bigwedge_{i=1}^n
\mathbf{G}\mathbf{F} \varphi_i \vee \mathbf{F}\mathbf{G} \psi_i$, where
$\varphi_i$ and $\psi_i$ contain only past operators. Some years later, Chang,
Manna, and Pnueli built on this result to derive a similar normal form for LTL.
Both normalisation procedures have a non-elementary worst-case blow-up, and
follow an involved path from formulas to counter-free automata to star-free
regular expressions and back to formulas. We improve on both points. We present
a direct and purely syntactic normalisation procedure for LTL yielding a normal
form, comparable to the one by Chang, Manna, and Pnueli, that has only a single
exponential blow-up. As an application, we derive a simple algorithm to
translate LTL into deterministic Rabin automata. The algorithm normalises the
formula, translates it into a special very weak alternating automaton, and
applies a simple determinisation procedure, valid only for these special
automata.

3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph