STL⁎: Extending signal temporal logic with signal-value freezing operator

To express temporal properties of dense-time real-valued signals, the Signal Temporal Logic (STL) has been defined by Maler et al. The work presented a monitoring algorithm deciding the satisfiability of STL formulae on finite discrete samples of continuous signals. The logic is not expressive enough to sufficiently distinguish oscillatory properties important in biology. In this paper we introduce the extended logic STL⁎ in which STL is augmented with a signal-value freezing operator allowing to express (and distinguish) various dynamic aspects of oscillations. This operator may be nested for further increase of expressiveness. The logic is supported by a monitoring algorithm prototyped in Matlab for the fragment that avoids nesting of the freezing operator. The monitoring procedure for STL⁎ is evaluated on a sample oscillatory signal with varied parameters. Application of the extended logic is demonstrated on a case study of a biological oscillator. We also discuss expressive power of STL with respect to STL⁎.