Synthesis of Infinite State Systems
Ohad Drucker, Alexander Rabinovich
TL;DR
The paper tackles the problem of synthesizing infinite-state systems using Monadic Second Order logic, extending the classical Church synthesis problem to the omega-domain and beyond. It develops a cohesive framework based on MSO-definable parity games and uniform memoryless strategies, leveraging the selection property and the copying technique to handle bounded and unbounded degree graphs, as well as expansions by parameters. A key achievement is showing decidability and definability results for both finite- and infinite-alphabet settings, via regular-expression representations and MSO-translation, enabling the construction of transducers implementing the specified relations. This work provides a principled, systematic approach that unifies logic, automata, and game-theoretic methods for infinite-state synthesis and lays groundwork for applications to hardware/software synthesis in more expressive models.
Abstract
The classical Church synthesis problem, solved by Buchi and Landweber, treats the synthesis of finite state systems. The synthesis of infinite state systems, on the other hand, has only been investigated few times since then, with no complete or systematic solution. We present a systematic study of the synthesis of infinite state systems. The main step involves the synthesis of MSO-definable parity games, which is, finding MSO-definable uniform memoryless winning strategies for these games.