具有有限存储策略的交替时序逻辑
Alternating-time temporal logic with finite-memory strategies
摘要：
不完全信息的交替时序逻辑ATL和ATL* 的模型检查对于完美召回语义是不可判定的。然而，当限制到无记忆策略的模型检查问题变得可判定。在本文中，我们考虑其他两种类型的语义有限记忆策略的基础上。一种是允许的内存大小有界，另一种是内存大小无界（但必须是有限的）。这是由具有完美召回语义的模型检查的高复杂性和无记忆策略的严重限制所激发的。我们表明，这两种类型的语义介绍是不同的完美召回和无记忆语义和下一个重点的可判定性和复杂性的模型检查在完整和不完整的信息游戏ATL/ATL*。特别是，我们证明了模型检测的复杂性与有界记忆语义是Delta_2 p-完全的ATL和PSPACE-完全的ATL* 在不完全信息的游戏，就像在无记忆的情况下。我们还提出了一个证明，ATL和ATL* 模型检查是不可判定的n >= 3的球员与有限记忆语义的不完全信息游戏。
英文摘要：
Model-checking the alternating-time temporal logics ATL and ATL* with incomplete information is undecidable for perfect recall semantics. However, when restricting to memoryless strategies the model-checking problem becomes decidable. In this paper we consider two other types of semantics based on finite-memory strategies. One where the memory size allowed is bounded and one where the memory size is unbounded (but must be finite). This is motivated by the high complexity of model-checking with perfect recall semantics and the severe limitations of memoryless strategies. We show that both types of semantics introduced are different from perfect recall and memoryless semantics and next focus on the decidability and complexity of model-checking in both complete and incomplete information games for ATL/ATL*. In particular, we show that the complexity of model-checking with bounded-memory semantics is Delta_2p-complete for ATL and PSPACE-complete for ATL* in incomplete information games just as in the memoryless case. We also present a proof that ATL and ATL* model-checking is undecidable for n >= 3 players with finite-memory semantics in incomplete information games.
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