%0 Journal Article
%A Esparza, Javier
%A Rubio Cuéllar, Rubén Rafael
%A Salomon Sickert
%T Efficient Normalization of Linear Temporal Logic
%D 2024
%@ 0004-5411
%@ 1557-735X
%U https://hdl.handle.net/20.500.14352/103063
%X In the mid 1980s, Lichtenstein, Pnueli, and Zuck proved a classical theorem stating that every formula of Past LTL (the extension of Linear Temporal Logic (LTL) with past operators) is equivalent to a formula of the form ⋀<sup>n</sup><sub>i=1</sub>GF φ<sub>i</sub> ∨ FG ψ<sub>i</sub> where φ<sub>i</sub> and ψ<sub>i</sub> contain only past operators. Some years later, Chang, Manna, and Pnueli built on this result to derive a similar normal form for LTL. Both normalization 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 direct and purely syntactic normalization procedures for LTL, yielding a normal form very similar to the one by Chang, Manna, and Pnueli, that exhibit only a single exponential blow-up. As an application, we derive a simple algorithm to translate LTL into deterministic Rabin automata. The algorithm normalizes the formula, translates it into a special very weak alternating automaton, and applies a simple determinization procedure, valid only for these special automata.
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