On Expressive Powers of Timed Logics: Comparing Boundedness, Non-punctuality, and Deterministic Freezing
On Expressive Powers of Timed Logics: Comparing Boundedness, Non-punctuality, and Deterministic Freezing
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论定时逻辑的表达能力：比较有界性、非守时性和确定性冻结
DOI：
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发表时间：
2011
期刊：
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通讯作者：
Simoni S. Shah
中科院分区：
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作者：
P. Pandya;Simoni S. Shah
临时逻辑表现出令人困惑的运营商的多样性，而由此产生的决策性和表达性能也有所不同LTL EF Games of Etessami和Wilke，我们使用相关的EF定理来定义MTL Ehrenfeucht-Fraisse游戏。定时逻辑有限的逻辑[UI，SI]，MTL [FI，PI]和MITL [UI，SI]（分别纳入有界的限制，单位模态和非正常性），都是我们的第一个主要结果。证明MTL [UI，SI]严格包含在弱和严格单调的定时单词中的冻结逻辑TPTL [U，S]中，从而扩展了Bouyer等人的结果并完成了原始的证明从1990年开始的Alur和Henziger的猜想也将最近提出的确定性冻结逻辑TTL [Xθ，Yθ]（具有NP完整满意度）与MTL联系起来。 [xθ，yθ]严格位于一元，非正式逻辑Mitl [FI，pi]中。 mitl [fi，pi]。
Timed temporal logics exhibit a bewildering diversity of operators and the resulting decidability and expressiveness properties also vary considerably. We study the expressive power of timed logics TPTL[U,S] and MTL[UI, SI] as well as of their several fragments. Extending the LTL EF games of Etessami and Wilke, we define MTL Ehrenfeucht-Fraisse games on a pair of timed words. Using the associated EF theorem, we show that, expressively, the timed logics BoundedMTL[UI, SI], MTL[FI, PI] and MITL[UI, SI] (respectively incorporating the restrictions of boundedness, unary modalities and non-punctuality), are all pairwise incomparable. As our first main result, we show that MTL[UI, SI] is strictly contained within the freeze logic TPTL[U,S] for both weakly and strictly monotonic timed words, thereby extending the result of Bouyer et al and completing the proof of the original conjecture of Alur and Henziger from 1990. We also relate the expressiveness of a recently proposed deterministic freeze logic TTL[Xθ, Yθ] (with NP-complete satisfiability) to MTL. As our second main result, we show by an explicit reduction that TTL[Xθ, Yθ] lies strictly within the unary, non-punctual logic MITL[FI, PI]. This shows that deterministic freezing with punctuality is expressible in the non-punctual MITL[FI, PI].