Periodic Reporting for period 1 - ADVANSYNT (Theoretical Foundations of Advanced Synthesis)
Berichtszeitraum: 2022-09-01 bis 2025-02-28
We develop the theoretical foundations of synthesis problems and algorithms that take into account the complex settings in which synthesis is needed and the many considerations that are abstracted in current definition of the problem. We formalize and study the following three topics in advanced synthesis: (1) Quality and complexity measures, (2) Game-theoretic considerations, and (3) Evolving and unpredictable environments. The contribution involves advances in the theory and applications of automata on infinite objects, specifically on different levels of nondeterminism that automata can exhibit.
Our main contributions in each of the topics above are as follows
(1) Quality: Our contributions include advances in reasoning about multi-valued formalisms, developing a framework for reasoning about systems that maintain privacy, and continuing our study of synthesis of systems with optimized sensing.
(2) Game-theoretic considerations: We introduced and studied the notion of trading of control in multi-agent games. We continued our study on rational synthesis in various settings, in particular ones with incomplete information. These days we are studying multi-agent games with coalitions as well as a new model of games in which players may experience a reset of their memory.
(3) Evolving and unpredictable environments: We introduced the notion of guided environments, which are hostile, in the sense they may exhibit unpredictable inputs, yet are collaborative, in the sense they want the specification to be satisfied. We study new forms of incomplete information, in particular one in which the exact costs of actions are revealed only after their application.
(4) Theoretical foundations: we studied different levels of determinism in nondeterministic automata, focusing on nondeterministic automata that are useful for the synthesis problem. We studied variants of problems in classic theoretical computer science that correspond to challenges in formal methods (labelled flow networks and their game variant). We also suggested a characterization of regular languages by the way the length of a word affects its probability to be in the language. The characterization is useful in sorting of vacuity results.
(1) Quality: Our contributions include advances in reasoning about multi-valued formalisms, developing a framework for reasoning about systems that maintain privacy, and continuing our study of synthesis of systems with optimized sensing.
(2) Game-theoretic considerations: We introduced and studied the notion of trading of control in multi-agent games. We continued our study on rational synthesis in various settings, in particular ones with incomplete information. These days we are studying multi-agent games with coalitions as well as a new model of games in which players may experience a reset of their memory.
(3) Evolving and unpredictable environments: We introduced the notion of guided environments, which are hostile, in the sense they may exhibit unpredictable inputs, yet are collaborative, in the sense they want the specification to be satisfied. We study new forms of incomplete information, in particular one in which the exact costs of actions are revealed only after their application.
(4) Theoretical foundations: we studied different levels of determinism in nondeterministic automata, focusing on nondeterministic automata that are useful for the synthesis problem. We studied variants of problems in classic theoretical computer science that correspond to challenges in formal methods (labelled flow networks and their game variant). We also suggested a characterization of regular languages by the way the length of a word affects its probability to be in the language. The characterization is useful in sorting of vacuity results.
I am mostly happy about conceptual contributions: the framework of formalizing and reasoning about privacy in reactive systems, the introduction of guided environments, and of games with trading of control.
In the context of privacy, we introduce a framework for synthesis that addresses privacy of the system and its environment. In addition to a specification, the user provides a secret (both in terms of LTL formulas). We distinguish between two settings. In the first, values of some input and output signals are hidden from an observer in a way that respects budget constraints on the set of signals that may be hidden. In all environments, the specification should be satisfied and the value of the secret should be hidden from the observer. In the second setting, the system and the environment hide values of some signals from each other (technically, the generated transducer instructs the environment which input signals to assign in each round, and provides a partial assignment to the output signals). Here, in all environments, the specification should be satisfied with the incomplete information, and the satisfaction value of the secret should be hidden.
In synthesis with guided environments (SGE, for short), the system may harness the knowledge and computational power of the environment during the interaction. The underlying idea in SGE is that in many settings, in particular when the system serves or directs the environment, it is of the environment's interest that the specification is satisfied, and it would follow the guidance of the system. Thus, while the environment is still hostile, in the sense that the system should satisfy the specification no matter how the environment assigns values to the input signals, in SGE the system assigns values to some output signals and guides the environment via programs how to assign values to other output signals.
In the game-theoretic approach to reasoning about multi-agent systems, the interaction among components in a system is traditionally modeled by a game. In the turned-based setting, the players in the game jointly move a token along the game graph, with each player deciding where to move the token in vertices she controls. The objectives of the players are modeled by ω-regular winning conditions, and players whose objectives are satisfied get rewards. Thus, the game is non-zero-sum, and we are interested in its stable outcomes. In particular, in the rational-synthesis problem, we seek a strategy for the system player that guarantees the satisfaction of the system's objective in all rational environments. We studied an extension of the traditional setting by trading of control. In our game, the players may pay each other in exchange for directing the token also in vertices they do not control. The utility of each player then combines the reward for the satisfaction of her objective and the profit from the trading. The setting combines challenges from ω-regular graph games with challenges in pricing, bidding, and auctions in classical game theory.
In the context of privacy, we introduce a framework for synthesis that addresses privacy of the system and its environment. In addition to a specification, the user provides a secret (both in terms of LTL formulas). We distinguish between two settings. In the first, values of some input and output signals are hidden from an observer in a way that respects budget constraints on the set of signals that may be hidden. In all environments, the specification should be satisfied and the value of the secret should be hidden from the observer. In the second setting, the system and the environment hide values of some signals from each other (technically, the generated transducer instructs the environment which input signals to assign in each round, and provides a partial assignment to the output signals). Here, in all environments, the specification should be satisfied with the incomplete information, and the satisfaction value of the secret should be hidden.
In synthesis with guided environments (SGE, for short), the system may harness the knowledge and computational power of the environment during the interaction. The underlying idea in SGE is that in many settings, in particular when the system serves or directs the environment, it is of the environment's interest that the specification is satisfied, and it would follow the guidance of the system. Thus, while the environment is still hostile, in the sense that the system should satisfy the specification no matter how the environment assigns values to the input signals, in SGE the system assigns values to some output signals and guides the environment via programs how to assign values to other output signals.
In the game-theoretic approach to reasoning about multi-agent systems, the interaction among components in a system is traditionally modeled by a game. In the turned-based setting, the players in the game jointly move a token along the game graph, with each player deciding where to move the token in vertices she controls. The objectives of the players are modeled by ω-regular winning conditions, and players whose objectives are satisfied get rewards. Thus, the game is non-zero-sum, and we are interested in its stable outcomes. In particular, in the rational-synthesis problem, we seek a strategy for the system player that guarantees the satisfaction of the system's objective in all rational environments. We studied an extension of the traditional setting by trading of control. In our game, the players may pay each other in exchange for directing the token also in vertices they do not control. The utility of each player then combines the reward for the satisfaction of her objective and the profit from the trading. The setting combines challenges from ω-regular graph games with challenges in pricing, bidding, and auctions in classical game theory.