Propositional dynamic logic of flowcharts

Q4 Mathematics
D. Harel, R. Sherman
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引用次数: 33

Abstract

Following a suggestion of Pratt, we consider propositional dynamic logic in which programs are nondeterministic finite automata over atomic programs and tests (i.e., flowcharts), rather than regular expressions. While the resulting version of PDL, call it APDL, is clearly equivalent in expressive power to PDL, it is also (in the worst case) exponentially more succinct. In particular, deciding its validity problem by reducing it to that of PDL leads to a double exponential time procedure, although PDL itself is decidable in exponential time. We present an elementary combined proof of the completeness of a simple axiom system for APDL and decidability of the validity problem in exponential time. The results are thus stronger than those for PDL, since PDL can be encoded in APDL with no additional cost, and the proofs simpler, since induction on the structure of programs is virtually eliminated. Our axiom system for APDL relates to the PDL system just as Floyd's proof method for partial correctness relates to Hoare's.

流程图的命题动态逻辑
根据Pratt的建议,我们考虑命题动态逻辑,其中程序是原子程序和测试(即流程图)上的非确定性有限自动机,而不是正则表达式。虽然PDL的最终版本(称为APDL)在表达能力上明显等同于PDL,但它也(在最坏的情况下)更加简洁。特别是,通过将其简化为PDL的有效性问题来确定其有效性问题导致了一个双指数时间过程,尽管PDL本身在指数时间内是可确定的。给出了一个简单的APDL公理系统的完备性的初等组合证明和指数时间下有效性问题的可判定性。因此,结果比PDL的结果更强,因为PDL可以在APDL中编码而不需要额外的成本,而且证明更简单,因为实际上消除了对程序结构的归纳。我们的APDL公理系统与PDL系统的关系就像Floyd的部分正确性证明方法与Hoare的证明方法的关系一样。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
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