On simple programs with primitive conditional statements

Q4 Mathematics
Oscar H. Ibarra , Louis E. Rosier
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引用次数: 1

Abstract

This paper is concerned with the expressive power (or computational power) of loop programs over different sets of primitive instructions. In particular, we show that an {x ← 0, xy, xx + 1, do xend, if x = 0 then yz}-program which contains no nested loops can be transformed into an equivalent {x ← 0, xy, xx + 1, do xend}-program (also without nested loops) in exponential time and space. This translation was earlier claimed, in the literature, to be obtainable in polynomial time, but then this was subsequently shown to imply that PSPACE = PTIME. Consequently, the question of translatability was left unanswered. Also, we show that the class of functions computable by {x ← 0, xy, xx + 1, x − 1, do xend, if x = 0 then xc}-programs is exactly the class of Presburger functions.

用原始条件语句的简单程序
本文关注的是循环程序在不同原始指令集上的表达能力(或计算能力)。特别地,我们证明了不包含嵌套循环的{x←0,x←y, x←x + 1, do x…end,如果x = 0,则y←z}程序可以在指数时间和空间中转换为等价的{x←0,x←y, x←x + 1, do x…end}程序(也不包含嵌套循环)。在文献中,这种转换早先声称在多项式时间内可获得,但随后证明这意味着PSPACE = PTIME。因此,可译性问题没有得到答复。同时,我们证明了可由{x←0,x←y, x←x + 1, x−1,do x…end计算的函数类,如果x = 0则x←c}-程序正是Presburger函数类。
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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