Abstract
The basic notion of encoding is one of the most important present in computer science. So far, they have not been per se the subject of serious research, because of their apparent simplicity. In this paper we show how the realm of encodings, instead, deserves big attention. In particular, we address the fundamental question of optimality of encodings: data need a certain storage cost, so it seems natural to investigate whether some encodings are better than others, in the sense they waste less space. We give a precise formalization of this analysis, within the context of extendable families of encodings, and show that the structure is so rich that no optimal encoding can be found, viz. one can arbitrarily improve the data packing. Secondly, we raise the subtle point of the effect of encodings on the computational power of the device: although so far this problem has been passed over, it is not obvious at all whether or not an encoding affects the computational power of a machine. The subtlety of the point. is formally shown, by proving that for almost all the machines encodings behave nicely. However, things become deeply involved just in the most basic case of the 2-register machine, where only particular encodings are safe. The analysis then reveals than in this context not only there are optimal elements, but even a best one, which rather intriguingly is shown to be the first encoding system ever developed.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
R. Balzer. Evolution as a new basis for reusability. In Reusability in Programming, pages 80–82. Newport, RI, 1983.
H.P. Barendregt. The Lambda Calculus: its Syntax and Semantics. North-Holland, 1981.
V.R. Basili and A.J. Turner. Iterative enhancement: A practical technique for software development. IEEE Transactions on Software Engineering, 4:390–396, December 1975.
M. Bezem, J.W. Klop, and R.C de Vrijer. Term Rewriting Systems, volume 25 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1997. To appear.
K. Clark and D. Cowell. Programs, machines, and computation. McGraw-Hill, 1976.
B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 1990.
K. Gödel. On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Oliver&Boyd, Edinburgh and London, 1962.
J.E. Hopcroft and I. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.
I.V. Horebeek and J. Lewi. Algebraic Specifications in Software Engineering. Springer-Verlag, 1989.
M. Kanovich. Petri nets, horn programs, linear logic, and vector games. In M. Hagiya and J.C. Mitchell, editors, International Symposium on Theoretical Aspects of Computer Software, volume 789 of LNCS, pages 642–666. Springer-Verlag, 1994.
A.J. Kfoury, R.N. Moll, and M.A. Arbib. A programming approach to computability. Springer-Verlag, New York, 1982.
A.J. Kfoury, R.N. Moll, and M.A. Arbib. A programming approach to computability. Springer-Verlag, New York, 1982.
S.S. Lam and A.U. Shankar. A composition theorem for layered systems. In B. Jonsson, J. Parrow, and B. Perhson, editors, 11th International Symposium on Protocol Specification, pages 93–108. North-Holland, 1991.
M. Machtey and P. Young. An Introduction to the General Theory of Algorithms. North-Holland, 1978.
Yu.I. Manin. A Course in Mathematical Logic. Springer-Verlag, 1977.
I.C.C. Phillips. Recursion theory. In S. Abramsky, Dov M. Gabbay, and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, volume 1, chapter 1, pages 79–188. Clarendon Press, Oxford, 1992.
D. Scott. Some definitional suggestions for automata theory. Journal of Computer and System Sciences, 1:187–212, 1967.
J.D Warnier. Logical Constructions of Programs. H.E. Stenfert Kroese, 1974.
P. Wegner. Varietes of reusability. In Reusability in Programming, pages 30–44. Newport, RI, 1983.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Marchiori, M. (1997). Optimal encodings. In: Plášil, F., Jeffery, K.G. (eds) SOFSEM'97: Theory and Practice of Informatics. SOFSEM 1997. Lecture Notes in Computer Science, vol 1338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63774-5_131
Download citation
DOI: https://doi.org/10.1007/3-540-63774-5_131
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63774-5
Online ISBN: 978-3-540-69645-2
eBook Packages: Springer Book Archive