### Abstract

We identify a new class of decidable hybrid automata: namely, parallel compositions of semi-algebraic o-minimal automata. The class we consider is fundamental to hierarchical modeling in many exemplar systems, both natural and engineered. Unfortunately, parallel composition, which is an atomic operator in such constructions, does not preserve the decidability of reachability. Luckily, this paper is able to show that when one focuses on the composition of semi-algebraic o-minimal automata, it is possible to translate the decidability problem into a satisfiability problem over formulæinvolving both real and integer variables. While in the general case such formulæ would be undecidable, the particular format of the formulæ obtained in our translation allows combining decidability results stemming from both algebraic number theory and first-order logic over (ℝ, 0, 1, +,*, <) to yield a novel decidability algorithm. From a more general perspective, this paper exposes many new open questions about decidable combinations of real/integer logics.

Original language | English (US) |
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Title of host publication | Automated Technology for Verification and Analysis - 6th International Symposium, ATVA 2008, Proceedings |

Pages | 274-288 |

Number of pages | 15 |

Volume | 5311 LNCS |

DOIs | |

State | Published - 2008 |

Event | 6th International Symposium on Automated Technology for Verification and Analysis, ATVA 2008 - Seoul, Korea, Republic of Duration: Oct 20 2008 → Oct 23 2008 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5311 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 6th International Symposium on Automated Technology for Verification and Analysis, ATVA 2008 |
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Country | Korea, Republic of |

City | Seoul |

Period | 10/20/08 → 10/23/08 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Automated Technology for Verification and Analysis - 6th International Symposium, ATVA 2008, Proceedings*(Vol. 5311 LNCS, pp. 274-288). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5311 LNCS). https://doi.org/10.1007/978-3-540-88387-6-25

**Decidable compositions of O-minimal automata.** / Casagrande, Alberto; Corvaja, Pietro; Piazza, Carla; Mishra, Bhubaneswar.

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

*Automated Technology for Verification and Analysis - 6th International Symposium, ATVA 2008, Proceedings.*vol. 5311 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5311 LNCS, pp. 274-288, 6th International Symposium on Automated Technology for Verification and Analysis, ATVA 2008, Seoul, Korea, Republic of, 10/20/08. https://doi.org/10.1007/978-3-540-88387-6-25

}

TY - GEN

T1 - Decidable compositions of O-minimal automata

AU - Casagrande, Alberto

AU - Corvaja, Pietro

AU - Piazza, Carla

AU - Mishra, Bhubaneswar

PY - 2008

Y1 - 2008

N2 - We identify a new class of decidable hybrid automata: namely, parallel compositions of semi-algebraic o-minimal automata. The class we consider is fundamental to hierarchical modeling in many exemplar systems, both natural and engineered. Unfortunately, parallel composition, which is an atomic operator in such constructions, does not preserve the decidability of reachability. Luckily, this paper is able to show that when one focuses on the composition of semi-algebraic o-minimal automata, it is possible to translate the decidability problem into a satisfiability problem over formulæinvolving both real and integer variables. While in the general case such formulæ would be undecidable, the particular format of the formulæ obtained in our translation allows combining decidability results stemming from both algebraic number theory and first-order logic over (ℝ, 0, 1, +,*, <) to yield a novel decidability algorithm. From a more general perspective, this paper exposes many new open questions about decidable combinations of real/integer logics.

AB - We identify a new class of decidable hybrid automata: namely, parallel compositions of semi-algebraic o-minimal automata. The class we consider is fundamental to hierarchical modeling in many exemplar systems, both natural and engineered. Unfortunately, parallel composition, which is an atomic operator in such constructions, does not preserve the decidability of reachability. Luckily, this paper is able to show that when one focuses on the composition of semi-algebraic o-minimal automata, it is possible to translate the decidability problem into a satisfiability problem over formulæinvolving both real and integer variables. While in the general case such formulæ would be undecidable, the particular format of the formulæ obtained in our translation allows combining decidability results stemming from both algebraic number theory and first-order logic over (ℝ, 0, 1, +,*, <) to yield a novel decidability algorithm. From a more general perspective, this paper exposes many new open questions about decidable combinations of real/integer logics.

UR - http://www.scopus.com/inward/record.url?scp=56749155690&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56749155690&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-88387-6-25

DO - 10.1007/978-3-540-88387-6-25

M3 - Conference contribution

AN - SCOPUS:56749155690

SN - 354088386X

SN - 9783540883869

VL - 5311 LNCS

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

SP - 274

EP - 288

BT - Automated Technology for Verification and Analysis - 6th International Symposium, ATVA 2008, Proceedings

ER -