Periodic Reporting for period 1 - SyGaST (Synthesising Game Solving Techniques)
Período documentado: 2021-07-01 hasta 2023-06-30
Infinite games can be used as formalisations for the correctness of non-terminating systems and protocols, where winning or losing is determined by long term averages or states that appear infinitely often. Various winning conditions can be defined, and several of them have widespread applications to real-life processes. Infinite games are connected to each other, and so discoveries that advance one game can apply to others. With the support of the Marie Skłodowska-Curie Actions programme, the SyGaST project investigated recent advances for some classes of infinite games to enable insight into connections and differences between the types of infinite-duration games and faster algorithms to solve them.
The research objectives have been organized into three work plans. In a first task, it has been investigated the connection and differences between different types of infinite-duration games and considered the reductions that go back in the standard chain of reductions. The second task aimed at transferring the algorithmic advances between the algorithms that solve parity games to mean payoff games or discounted payoff games. Finally, in the last task, the advances have been implemented and evaluated. The research plan has been ambitious, containing high risk/reward problems and other objectives that naturally extend prior works. As a consequence, not all the objectives have been exhaustively investigated, although many resulted in conference papers.
In particular, the research on the first task, that was the most speculative one, provided many negative results, that do not allow for an immediate publication but requires additional time. The transfer of algorithmic advances led to the development of new progress measures for solving parity games. A general approach has been accepted and will appear on "Computation and Automata" in the work "From Quasi-Dominions to Progress Measures", while a specific succinct approach has been published on "Frontiers in Computer Science" as "Smaller Progress Measures and Separating Automata for Parity Games". The composition of two techniques, one efficient in practice and the other with an efficient complexity bound, has been described in the journal "Priority Promotion with Parysian Flair" that is under submission. The proposed algorithm is the only efficient solver with quasi-polynomial guarantees, since the other known quasi-polynomial approaches tend to realize their worst-case behaviour. Advancements have been obtained also on mean-payoff games and discounted payoff games. For the first class of games, a refinement of the quasi-dominion approach has been submitted to a journal in the work "Solving Mean-Payoff Games via Quasi Dominions". For the second class of games, a novel technique will be presented at "GandALF 2023" in the work "An Objective Improvement Approach to Solving Discounted Payoff Games". To achieve the objectives of the last task, it has been started a collaboration with students to develop a quantitative framework that supports classes of games such as mean payoff in addition to parity games. While the set of parity games solvers will be imported from an older framework, the set of energy games solvers was incomplete, hence, in a first step of this collaboration the set of energy games has been completely implemented. In a second step, it has been started the development of the framework. The release of the first version as a tool paper has been planned within the year. In addition to these objectives, it has been conducted research on automata theory to investigate the good-for-games property. This study has been submitted in the work "Semantic Flowers for Good-for-Games and Deterministic Automata". Both this latter work and "Solving Mean-Payoff Games via Quasi Dominions" have passed the first review stage with positive comments and are waiting for the final comments.
In particular, the research on the first task, that was the most speculative one, provided many negative results, that do not allow for an immediate publication but requires additional time. The transfer of algorithmic advances led to the development of new progress measures for solving parity games. A general approach has been accepted and will appear on "Computation and Automata" in the work "From Quasi-Dominions to Progress Measures", while a specific succinct approach has been published on "Frontiers in Computer Science" as "Smaller Progress Measures and Separating Automata for Parity Games". The composition of two techniques, one efficient in practice and the other with an efficient complexity bound, has been described in the journal "Priority Promotion with Parysian Flair" that is under submission. The proposed algorithm is the only efficient solver with quasi-polynomial guarantees, since the other known quasi-polynomial approaches tend to realize their worst-case behaviour. Advancements have been obtained also on mean-payoff games and discounted payoff games. For the first class of games, a refinement of the quasi-dominion approach has been submitted to a journal in the work "Solving Mean-Payoff Games via Quasi Dominions". For the second class of games, a novel technique will be presented at "GandALF 2023" in the work "An Objective Improvement Approach to Solving Discounted Payoff Games". To achieve the objectives of the last task, it has been started a collaboration with students to develop a quantitative framework that supports classes of games such as mean payoff in addition to parity games. While the set of parity games solvers will be imported from an older framework, the set of energy games solvers was incomplete, hence, in a first step of this collaboration the set of energy games has been completely implemented. In a second step, it has been started the development of the framework. The release of the first version as a tool paper has been planned within the year. In addition to these objectives, it has been conducted research on automata theory to investigate the good-for-games property. This study has been submitted in the work "Semantic Flowers for Good-for-Games and Deterministic Automata". Both this latter work and "Solving Mean-Payoff Games via Quasi Dominions" have passed the first review stage with positive comments and are waiting for the final comments.
As explained above, the research objectives have been organized into three work plans. For the first task, many little negative results have been obtained. Hence, it is too early to disseminate the results that currently would have a minor impact on the state of the art, and it is not possible to predict the impact of future findings. For the second task, contributions have been provided for three classes of games: parity, mean payoff, and discounted payoff. The work "From Quasi-Dominions to Progress Measures" that will appear on "Computation and Automata", provides more insight on the use of efficient progress measure for solving parity games thanks to the integration of quasi dominions and progress measures. The algorithm described in this paper, despite the exponential complexity bound, proved to be the most efficient in practice, since as shown in the experimental section, to scales better than any known algorithm on games with a complex structure. To overcome the exponential worst-case behaviours, it has been developed an integration of the efficient quasi dominion technique called priority promotion and the quasi-polynomial bounded approach proposed by Parys. Such a work submitted to a journal in the work "Priority Promotion with Parysian Flair" describes the most efficient quasi-polynomial algorithm for solving parity games. On the theoretical side, the time complexity bound for parity games has been improved in the journal "Smaller Progress Measures and Separating Automata for Parity Games" that has been published on "Frontiers in Computer Science". In this journal a more succinct progress measure has been proposed, that led to a state space reduction, and then, to a better complexity bound. The journal "Solving Mean-Payoff Games via Quasi Dominions" refined a previous work presented at TACAS 2020, providing a better complexity study and including an experimental section that shows how the proposed approach is very effective and reduces the solution time of several orders of magnitude with respect to other known algorithms. A new approach for solving discounted payoff games has been developed and accepted at GandALF 2023. In "An Objective Improvement Approach to Solving Discounted Payoff Games" the classic strategy improvement approach, that is asymmetric and at every iteration changes the set of constraints, is revisited and turned into a new approach that is symmetric and works on the same set of constraints while changing the objective function. For the last task, the development of the first quantitative framework is still in progress. So far it has been implemented the full set of parity and mean payoff solvers. Once the first version of the framework will be available, it may have significant impact of the development of future algorithms, allowing on one hand to test the solver on worst case families of games and on the other hand to compare it with other solvers. This will provide to the researchers a tool to study the behaviour and to verify the practical efficiency of the different approaches. A side research work on automata theory investigated the good-for-games property of automata. The work "Semantic Flowers for Good-for-Games and Deterministic Automata" proposes alternative proofs of the expressive power of good-for-games automata by means of the application of the notion of "flowers".