Bibliographic Details
| Title: |
Efficient Normalization of Linear Temporal Logic. |
| Authors: |
Esparza, Javier1 esparza@in.tum.de, Rubio, Rubén2 rubenrub@ucm.es, Sickert, Salomon3 salomon.sickert@mail.huji.ac.il |
| Superior Title: |
Journal of the ACM. Apr2024, Vol. 71 Issue 2, p1-42. 42p. |
| Subject Terms: |
*LOGIC, *ROBOTS |
| Geographic Terms: |
LIECHTENSTEIN |
| Abstract: |
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 \(\bigwedge _{i=1}^n {\mathbf {G}}{\mathbf {F}}\varphi _i \vee {\mathbf {F}}{\mathbf {G}}\psi _i\) , where φi and ψi 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Business Source Premier |