In this paper, we study the extension of 1-clock Alternating Timed Automata (1-ATA) with the ability to read in both forward and backward direction, the 2-Way 1-clock Alternating Timed Automata (2-Way 1-ATA). We show that subclass of 2-Way 1-ATA with reset free loops (2-Way 1-ATA-rfl) is expressively equivalent to MSO[<] extended with Guarded Metric Quantifiers (GQMSO). Emptiness Checking problem for 2-Way 1-ATA-rfl (and hence GQMSO) is undecidable, in general. We propose a "non-punctuality" like restriction, called non-adjacency, for 2-Way 1-ATA-rfl, and also for GQMSO, for which the emptiness (respectively, satisfiability) checking becomes decidable. Non-Adjacent 2-Way 1-ATA is the first such class of Timed Automata with alternations and 2-wayness for which the emptiness checking is decidable (and that too with elementary complexity). We also show that 2-Way 1-ATA-rfl, even with the non-adjacent restrictions, can express properties is not recognizable using 1-ATA.

中文翻译：

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逻辑满足 2 路 1 时钟交替定时自动机

在本文中，我们研究了具有正向和反向读取能力的 1-clock 交替定时自动机 (1-ATA) 的扩展，即 2-Way 1-clock 交替定时自动机 (2-Way 1-ATA) . 我们展示了具有复位自由循环的 2-Way 1-ATA 的子类 (2-Way 1-ATA-rfl) 在表达上等效于使用 Guarded Metric Quantifiers (GQMSO) 扩展的 MSO[<]。通常，2-Way 1-ATA-rfl（以及 GQMSO）的空性检查问题是不可判定的。我们为 2-Way 1-ATA-rfl 和 GQMSO 提出了一种类似“非守时性”的限制，称为非邻接，也适用于 GQMSO，其空性（分别是可满足性）检查变得可判定。Non-Adjacent 2-Way 1-ATA 是第一类具有交替和 2-wayness 的定时自动机，其空性检查是可判定的（并且也具有基本复杂性）。我们还表明，即使具有非相邻限制，2-Way 1-ATA-rfl 也可以表达使用 1-ATA 无法识别的属性。