一类简单程序的等价问题及其正确性公式

Q4 Mathematics
Oscar H. Ibarra , Louis E. Rosier
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引用次数: 3

摘要

本文关注的是不同原始指令集上非常简单的循环程序的语义(或计算能力)。摘要给出了不含嵌套循环的{x←0,x←y, x←x + 1, x←x±1,do x…end}类程序的一个完备的、一致的Hoare公理,其中允许的断言是Presburger算术逻辑中的那些公式。这类程序可计算的函数类就是普雷斯伯格函数类。因此,所得到的一类正确性公式具有一个可确定的有效性问题。在本文中,我们提出了简单的循环编程语言,它们在计算上严格来说更强大,也就是说,它可以计算比Presburger函数类更多的函数。此外,使用一种比Presburger算法的逻辑更强大的逻辑断言语言,我们给出了一类同样具有可确定有效性问题的程序的正确性公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The equivalence problem and correctness formulas for a simple class of programs

This paper is concerned with the semantics (or computational power) of very simple loop programs over different sets of primitive instructions. Recently, a complete and consistent Hoare axiomatics for the class of {x ← 0, xy, xx + 1, xx ∸ 1, do xend} programs which contain no nested loops, was given, where the allowable assertions were those formulas in the logic of Presburger arithmetic. The class of functions computable by such programs is exactly the class of Presburger functions. Thus, the resulting class of correctness formulas has a decidable validity problem. In this paper, we present simple loop programming languages which are, computationally, strictly more powerful, i.e., which can compute more than the class of Presburger functions. Furthermore, using a logical assertion language that is also more powerful than the logic of Presburger arithmetic, we present a class of correctness formulas over such programs that also has a decidable validity problem.

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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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