# Deciding Persistence or Recurrence Membership in Spot

### From LRDE

- Authors
- Alexandre Gbaguidi Aïsse
- Type
- techreport
- Year
- 2018
- Number
- 1801

## Abstract

There is a hierarchy of temporal properties, defined by Manna and Pnueli (1990). This hierarchy contains, amongst others, the recurrence and persistence classes. Knowing that a formula of linear time temporal logic (LTL) **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f}**
is recurrent (respectively persistent) is interesting because it ensures that **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f}**
can be translated into a deterministic Büchi automaton (respectively into a co-Büchi automaton). Originally, Spot, a library for **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega}**
-automata manipulation, had a single way to decide if a linear temporal logic formula belongs to the recurrence or to the persistence class. Thanks to our previous work introduced in emphA co-Büching Toolbox