2000 character limit reached
The Church Synthesis Problem over Continuous Time (2404.04782v2)
Published 7 Apr 2024 in cs.LO
Abstract: The Church Problem asks for the construction of a procedure which, given a logical specification A(I,O) between input omega-strings I and output omega-strings O, determines whether there exists an operator F that implements the specification in the sense that A(I, F(I)) holds for all inputs I. Buchi and Landweber provided a procedure to solve the Church problem for MSO specifications and operators computable by finite-state automata. We investigate a generalization of the Church synthesis problem to the continuous time domain of the non-negative reals. We show that in the continuous time domain there are phenomena which are very different from the canonical discrete time domain of the natural numbers.
- A theory of timed automata. Theoretical Computer Science, 126(2):183–235, 1994.
- The benefits of relaxing punctuality. J. ACM, 43(1):116-–146, 1996.
- Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society, 138:295–311, 1969.
- J. Richard Buchi. On a decision method in restricted second order arithmetic. In E. Nagel, P. Suppes, and A. Tarski (Eds.), Logic, methodology and philosophy of science. Stanford: Stanford University Press, 1–11, 1962.
- Timed parity games: Complexity and robustness. Logical Methods in Computer Science, 7, 12 2011.
- Dense real-time games. In Proceedings 17th Annual IEEE Symposium on Logic in Computer Science, pages 167–176, 2002.
- Daniel Fattal. Selection and uniformization over continuous time. Master’s thesis, Tel-Aviv university, 1923.
- The church synthesis problem with metric. In Marc Bezem, editor, Computer Science Logic, 25th International Workshop / 20th Annual Conference of the EACSL, CSL 2011, September 12-15, 2011, Bergen, Norway, Proceedings, volume 12 of LIPIcs, pages 307–321. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2011.
- A. Rabinovich. Finite variability interpretation of monadic logic of order. Theoretic]al Computer Science, 275:111–125, 2002.
- S. Shelah. The monadic theory of order. The Annals of Mathematics, 102(3):379–419, 1975.
- B. Trakhtenbrot and Y. M. Barzdin. Finite automate: behaviour and synthesis. 1973.
- B. Trakhtenbrot. Origins and metamorphoses of the trinity: logic, nets, automata. In Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science, pages 506–507, 1995.