## Abstract

Variable automata with arithmetic enable the specification of reactive systems with variables over an infinite domain of numeric values and whose operation involves arithmetic manipulation of these values [9]. We study the synthesis problem for such specifications. While the problem is in general undecidable, we define a fragment, namely semantically deterministic variable automata with arithmetic, for which the problem is decidable. Essentially, an automaton is semantically deterministic if the restrictions on the possible assignments to the variables that are accumulated along its runs resolve its nondeterministic choices. We show that semantically deterministic automata can specify many interesting behaviors – many more than deterministic ones, and that the synthesis problem for them can be reduced to a solution of a two-player game. For automata with simple guards, the game has a finite state space, and the synthesis problem can be solved in time polynomial in the automaton and exponential in the number of its variables.

Original language | American English |
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Title of host publication | SOFSEM 2020 |

Subtitle of host publication | Theory and Practice of Computer Science - 46th International Conference on Current Trends in Theory and Practice of Informatics, SOFSEM 2020, Proceedings |

Editors | Alexander Chatzigeorgiou, Riccardo Dondi, Herodotos Herodotou, Christos Kapoutsis, Yannis Manolopoulos, George A. Papadopoulos, Florian Sikora |

Publisher | Springer |

Pages | 161-173 |

Number of pages | 13 |

ISBN (Print) | 9783030389185 |

DOIs | |

State | Published - 2020 |

Event | 46th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2020 - Limassol, Cyprus Duration: 20 Jan 2020 → 24 Jan 2020 |

### 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 | 12011 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 46th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2020 |
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Country/Territory | Cyprus |

City | Limassol |

Period | 20/01/20 → 24/01/20 |

### Bibliographical note

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