Timed pushdown automata (TPDA) are an expressive formalism combining recursion with a rich logic of timing constraints. We prove that reachability relations of TPDA are expressible in linear arithmetic, a rich logic generalising Presburger arithmetic and rational arithmetic. The main technical ingredients are a novel quantifier elimination result for clock constraints (used to simplify the syntax of TPDA transitions), the use of clock difference relations to express reachability relations of the fractional clock values, and an application of Parikh's theorem to reconstruct the integral clock values.

中文翻译：

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定时下推自动机的可达性关系

定时下推自动机（TPDA）是一种表现形式，结合了递归和丰富的时序约束逻辑。我们证明了TPDA的可达性关系在线性算术中是可表达的，这是广义的Presburger算术和有理算术的逻辑。主要技术成分是针对时钟约束的新颖量词消除结果（用于简化TPDA转换的语法），使用时钟差关系来表达分数时钟值的可达性关系以及应用帕里克定理来重构积分时钟值。