Abstract
A problem is feasible if it can be computed in a practically acceptable amount of time for large input. This is vague, and we will have to make the notion of “feasibility” more precise. Instead of measuring real time we will introduce some abstract notion of time. This chapter defines runtime measures for the languages considered so far and discusses fairness of those definitions. A programming language with a runtime measure is called a timed programming language. This concept admits comparisons between the runtime of programs of different languages via compilation from one (timed) programming language into another one.
How do we measure runtime of programs? How do we measure runtime of WHILE-programs independently of any assumptions on the hardware they run on?
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Notes
- 1.
Juris Hartmanis was born July 5, 1928 in Latvia and was a professor at Cornell University.
- 2.
Richard Edwin Stearns was born July 5, 1936 and was a professor at University at Albany (State University of New York).
- 3.
They both received the 1993 ACM Turing Award “in recognition of their seminal paper which established the foundations for the field of computational complexity theory”.
- 4.
Whether it is one or two does not make a difference anyway which we will see later.
- 5.
They are however usable for space complexity considerations.
- 6.
See Exercise 7 in Chap. 5.
- 7.
In cases where the data types are different one can still apply the same techniques but the translations get more complicated as one needs to encode data values and this is somewhat distracting. For details see e.g. [3].
References
Cook, S.A., Reckhow, R.A.: Time-bounded random access machines. J. Comput. Syst. Sci. 7, 354–375 (1973)
Hartmanis, J., Stearns, R.E.: On the computational complexity of algorithms. Trans. Am. Math. Soc. 117, 285–306 (1965)
Jones, N.D.: Computability and Complexity: From a Programming Perspective. MIT Press, Cambridge (1997) (Also available online at http://www.diku.dk/neil/Comp2book.html.)
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Reus, B. (2016). Measuring Time Usage. In: Limits of Computation. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-27889-6_12
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