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Time polynomial in input or output

  • Yuri Gurevich (a1) (a2) and Saharon Shelah (a3)


We introduce the class PIO of functions computable in time that is polynomial in max {the length of input, the length of output}, observe that there is no notation system for total PIO functions but there are notation systems for partial PIO functions, and give an algebra of partial PIO functions from binary strings to binary strings.



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[CP]Cai, Jiazhen and Paige, Robert, Binding performance at language design time, Conference record of the fourteenth annual ACM symposium on principles of programming languages, 1987, pp. 8087.
[GS]Gurevich, Yuri and Shelah, Saharon, Nearly linear time, Lecture Notes in Computer Science, Springer-Verlag (to appear).
[Pa]Paige, Robert, Private communication, Fall 1985.


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