# Efficient Normalization of Linear Temporal Logic

arXiv: https://arxiv.org/abs/2310.12613 · HTML: https://mlsanity.com/paper/2310.12613/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2023.

## Built on by (most cited first, 1 of 1)

- [LTLf+ and PPLTL+: Extending LTLf and PPLTL to Infinite Traces](https://mlsanity.com/paper/2411.09366/) (2024)

## Abstract (arXiv)

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 bigwedgei=1n GF, varphii vee FG, psii , where varphii and psii 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.