Theoretical Computer Science ( IF 1.1 ) Pub Date : 2020-02-13 , DOI: 10.1016/j.tcs.2020.02.015 Alexander Bolotov , Montserrat Hermo , Paqui Lucio
Temporal logic has become essential for various areas in computer science, most notably for the specification and verification of hardware and software systems. For the specification purposes rich temporal languages are required that, in particular, can express fairness constraints. For linear-time logics which deal with fairness in the linear-time setting, one-pass and two-pass tableau methods have been developed. In the repository of the CTL-type branching-time setting, the well-known logics and were developed to explicitly deal with fairness. However, due to the syntactical restrictions, these logics can only express restricted versions of fairness. The logic , often considered as ‘the full branching-time logic’ overcomes these restrictions on expressing fairness. However, is extremely challenging for the application of verification techniques, and the tableau technique, in particular. For example, there is no one-pass tableau construction for , while one-pass tableau has an additional benefit enabling the formulation of dual sequent calculi that are often treated as more ‘natural’ being more friendly for human understanding. These two considerations lead to the following problem - are there logics that have richer expressiveness than , allowing the formulation of a new range of fairness constraints with ‘until’ operator, yet ‘simpler’ than , and for which a one-pass tableau can be developed? Here we give a positive answer to this question, introducing a sub-logic of called , its tree-style one-pass tableau, and an algorithm for obtaining a systematic tableau, for any given admissible branching-time formulae. We prove the termination, soundness and completeness of the method. As tree-shaped one-pass tableaux are well suited for the automation and are amenable for the implementation and for the formulation of sequent calculi. Our results also open a prospect of relevant developments of the automation and implementation of the tableau method for , and of a dual sequent calculi.
中文翻译:
分支时间逻辑 及其树型一遍画面:扩展了商品的公平性
时间逻辑对于计算机科学的各个领域都至关重要,尤其是对于硬件和软件系统的规范和验证。为了说明的目的,需要丰富的时间语言,特别是可以表达公平性约束的语言。对于处理线性时间设置中的公平性的线性时间逻辑,已经开发了一种通过和两次通过的表格方法。在CTL类型分支时间设置的存储库中,众所周知的逻辑 和 旨在明确处理公平问题。但是,由于语法上的限制,这些逻辑只能表达公平性的受限制版本。逻辑,通常被视为“完整的分支时间逻辑”,克服了表达公平性方面的这些限制。然而,对于验证技术尤其是表格技术的应用而言,这是极具挑战性的。例如,没有用于,而一次通过的画面还有一个额外的好处,那就是可以制定双重继发性结石,这些结石通常被视为更“自然”,对人类的理解更为友好。这两个考虑因素导致了以下问题-是否存在比表达更丰富的逻辑?,允许使用“直到”运算符来制定一系列新的公平性约束,但比“更简单” ,并且可以为此开发一张通行证?在这里,我们对这个问题给出肯定的答案,并介绍了 叫 ,其树型单次通过画面,以及针对任何给定的允许分支时间公式获取系统画面的算法。我们证明了该方法的终止,正确性和完整性。由于树形的单次工作流程非常适合于自动化,并且易于实施和计算后续的结石。我们的结果也为自动化和实现Tableau方法的相关开发开辟了前景。,以及双重继发性结石。