Automatic Synthesis of Generalized Winning Strategies of Impartial Combinatorial Games Using SMT Solvers

Wu, Kaisheng; Fang, Liangda; Xiong, Liping; Lai, Zhao-Rong; Qiao, Yong; Chen, Kaidong; Rong, Fei

doi:10.24963/ijcai.2020/236

Cited by 4 publications

(7 citation statements)

References 16 publications

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“…Next, we will further study these new proposed strategic logics under incomplete information [45][46][47], where the strategies of agents maybe memoryless or perfect recall [48]. In this paper, we present formal frameworks and show technical results; in the future, we will also present case studies or practical applications to illustrate these theories, such as information security [49], solving winning strategies [50], and voting protocol [51].…”

Section: Discussionmentioning

confidence: 99%

Representation and Reasoning about Strategic Abilities with ω-Regular Properties

Xiong

Guo

2021

Mathematics

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Specification and verification of coalitional strategic abilities have been an active research area in multi-agent systems, artificial intelligence, and game theory. Recently, many strategic logics, e.g., Strategy Logic (SL) and alternating-time temporal logic (ATL*), have been proposed based on classical temporal logics, e.g., linear-time temporal logic (LTL) and computational tree logic (CTL*), respectively. However, these logics cannot express general ω-regular properties, the need for which are considered compelling from practical applications, especially in industry. To remedy this problem, in this paper, based on linear dynamic logic (LDL), proposed by Moshe Y. Vardi, we propose LDL-based Strategy Logic (LDL-SL). Interpreted on concurrent game structures, LDL-SL extends SL, which contains existential/universal quantification operators about regular expressions. Here we adopt a branching-time version. This logic can express general ω-regular properties and describe more programmed constraints about individual/group strategies. Then we study three types of fragments (i.e., one-goal, ATL-like, star-free) of LDL-SL. Furthermore, we show that prevalent strategic logics based on LTL/CTL*, such as SL/ATL*, are exactly equivalent with those corresponding star-free strategic logics, where only star-free regular expressions are considered. Moreover, results show that reasoning complexity about the model-checking problems for these new logics, including one-goal and ATL-like fragments, is not harder than those of corresponding SL or ATL*.

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Section: Discussionmentioning

confidence: 99%

Representation and Reasoning about Strategic Abilities with ω-Regular Properties

Xiong

Guo

2021

Mathematics

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“…We did experiments with combinatorial games Nim, its variants and Chomp2xN from [Farzan and Kincaid 2018;Wu et al 2020 Coloring: Two players take turns to perform actions. A player paints red and another player does cleaning on a 1xN grid.…”

Section: Experimentationmentioning

confidence: 99%

“…E.&D. Mon. 2-Nim Ch.2xN Ch.NxN Coloring Leader [Wu et al 2020] Our method -Table 2: means that a strategy is synthesized successfully; means that the framework cannot formalize the problem.…”

Section: Experimentationmentioning

confidence: 99%

“…We do not directly compare with the related method presented in [Wu et al 2020], as their problem is defined differently, in that their formalizations of domains do not include initial states but include legal states. Their method generates strategies within 250 seconds for all the tested domains, while for domain Subtraction, our method needs more than 250 seconds.…”

Section: Experimentationmentioning

confidence: 99%

“…The task is to synthesize a strategy that works for all instances of the n-Nim game. Wu et al [2020] consider the automated synthesis of generalized winning strategies for impartial combinatorial games. They first generate a winning formula using given templates by trying to include or exclude states corresponding to counterexamples generated during the verification process.…”

Section: Introductionmentioning

confidence: 99%

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Automated Synthesis of Generalized Invariant Strategies via Counterexample-Guided Strategy Refinement

Luo

Liu

2022

AAAI

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Strategy synthesis for multi-agent systems has proved to be a hard task, even when limited to two-player games with safety objectives. Generalized strategy synthesis, an extension of generalized planning which aims to produce a single solution for multiple (possibly infinitely many) planning instances, is a promising direction to deal with the state-space explosion problem. In this paper, we formalize the problem of generalized strategy synthesis in the situation calculus. The synthesis task involves second-order theorem proving generally. Thus we consider strategies aiming to maintain invariants; such strategies can be verified with first-order theorem proving. We propose a sound but incomplete approach to synthesize invariant strategies by adapting the framework of counterexample-guided refinement. The key idea for refinement is to generate a strategy using a model checker for a game constructed from the counterexample, and use it to refine the candidate general strategy. We implemented our method and did experiments with a number of game problems. Our system can successfully synthesize solutions for most of the domains within a reasonable amount of time.

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Synthesizing Understandable Strategies

Backeman

2023

Engineering of Computer-Based Systems

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Automatic Synthesis of Generalized Winning Strategies of Impartial Combinatorial Games Using SMT Solvers

Cited by 4 publications

References 16 publications

Representation and Reasoning about Strategic Abilities with ω-Regular Properties

Representation and Reasoning about Strategic Abilities with ω-Regular Properties

Automated Synthesis of Generalized Invariant Strategies via Counterexample-Guided Strategy Refinement

Synthesizing Understandable Strategies

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