### Abstract

In this paper, we investigate formalisms for specifying periodic signals using time and frequency domain specifications along with algorithms for the signal recognition and generation problems for such specifications. The time domain specifications are in the form of hybrid automata whose continuous state variables generate the desired signals. The frequency domain specifications take the form of an "envelope" that constrains the possible power spectra of the periodic signals with a given frequency cutoff. The combination of time and frequency domain specifications yields mixed-domain specifications that constrain a signal to belong to the intersection of the both specifications. We show that the signal recognition problem for periodic signals specified by hybrid automata is NP-complete, while the corresponding problem for frequency domain specifications can be approximated to any desired degree by linear programs, which can be solved in polynomial time. The signal generation problem for time and frequency domain specifications can be encoded into linear arithmetic constraints that can be solved using existing SMT solvers. We present some preliminary results based on an implementation that uses the SMT solver Z3 to tackle the signal generation problems.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 294-309 |

Number of pages | 16 |

Volume | 7186 LNCS |

DOIs | |

State | Published - 2012 |

Event | 2nd International Conference on Runtime Verification, RV 2011 - San Francisco, CA, United States Duration: Sep 27 2011 → Sep 30 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 7186 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 2nd International Conference on Runtime Verification, RV 2011 |
---|---|

Country | United States |

City | San Francisco, CA |

Period | 9/27/11 → 9/30/11 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 7186 LNCS, pp. 294-309). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7186 LNCS). https://doi.org/10.1007/978-3-642-29860-8_22

**Combining time and frequency domain specifications for periodic signals.** / Chakarov, Aleksandar; Sankaranarayanan, Sriram; Fainekos, Georgios.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 7186 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7186 LNCS, pp. 294-309, 2nd International Conference on Runtime Verification, RV 2011, San Francisco, CA, United States, 9/27/11. https://doi.org/10.1007/978-3-642-29860-8_22

}

TY - GEN

T1 - Combining time and frequency domain specifications for periodic signals

AU - Chakarov, Aleksandar

AU - Sankaranarayanan, Sriram

AU - Fainekos, Georgios

PY - 2012

Y1 - 2012

N2 - In this paper, we investigate formalisms for specifying periodic signals using time and frequency domain specifications along with algorithms for the signal recognition and generation problems for such specifications. The time domain specifications are in the form of hybrid automata whose continuous state variables generate the desired signals. The frequency domain specifications take the form of an "envelope" that constrains the possible power spectra of the periodic signals with a given frequency cutoff. The combination of time and frequency domain specifications yields mixed-domain specifications that constrain a signal to belong to the intersection of the both specifications. We show that the signal recognition problem for periodic signals specified by hybrid automata is NP-complete, while the corresponding problem for frequency domain specifications can be approximated to any desired degree by linear programs, which can be solved in polynomial time. The signal generation problem for time and frequency domain specifications can be encoded into linear arithmetic constraints that can be solved using existing SMT solvers. We present some preliminary results based on an implementation that uses the SMT solver Z3 to tackle the signal generation problems.

AB - In this paper, we investigate formalisms for specifying periodic signals using time and frequency domain specifications along with algorithms for the signal recognition and generation problems for such specifications. The time domain specifications are in the form of hybrid automata whose continuous state variables generate the desired signals. The frequency domain specifications take the form of an "envelope" that constrains the possible power spectra of the periodic signals with a given frequency cutoff. The combination of time and frequency domain specifications yields mixed-domain specifications that constrain a signal to belong to the intersection of the both specifications. We show that the signal recognition problem for periodic signals specified by hybrid automata is NP-complete, while the corresponding problem for frequency domain specifications can be approximated to any desired degree by linear programs, which can be solved in polynomial time. The signal generation problem for time and frequency domain specifications can be encoded into linear arithmetic constraints that can be solved using existing SMT solvers. We present some preliminary results based on an implementation that uses the SMT solver Z3 to tackle the signal generation problems.

UR - http://www.scopus.com/inward/record.url?scp=84861208330&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861208330&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-29860-8_22

DO - 10.1007/978-3-642-29860-8_22

M3 - Conference contribution

AN - SCOPUS:84861208330

SN - 9783642298592

VL - 7186 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 294

EP - 309

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -