TY - GEN

T1 - On Synthesis of Specifications with Arithmetic

AU - Faran, Rachel

AU - Kupferman, Orna

N1 - Publisher Copyright: © 2020, Springer Nature Switzerland AG.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85079100884&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-3-030-38919-2_14

DO - https://doi.org/10.1007/978-3-030-38919-2_14

M3 - Conference contribution

SN - 9783030389185

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

SP - 161

EP - 173

BT - SOFSEM 2020

A2 - Chatzigeorgiou, Alexander

A2 - Dondi, Riccardo

A2 - Herodotou, Herodotos

A2 - Kapoutsis, Christos

A2 - Manolopoulos, Yannis

A2 - Papadopoulos, George A.

A2 - Sikora, Florian

T2 - 46th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2020

Y2 - 20 January 2020 through 24 January 2020

ER -