Abstract
During the last four years research on lower level computational complexity has yielded a rich set of interesting results which have revealed deep and unexpected connections between various problems and thus brought new unity to this area of computer science. This work has also yielded new techniques and insights which are likely to have further applications, and it has identified some very central problems in the quantitative theory of computing. The purpose of this paper is to give the reader an overview of these developments, an insight into some of these results and applications, as well as an appreciation of the unity and structure which has emerged in this area of research.
This research has been supported in part by the National Science Foundation Grant GJ-33171X and Grant 70/755 from Fundacao de Amparo a Pesquisa do Estado de Sao Paulo, and by Universidade Estadual de Campinas.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Aho, A., J.E. Hoperoft, and J.D. Ullman: The design and analysis of computer algorithms. Addison-Wesley, Reading, Mass. 1974
Baker, T., J. Gill and R. Solovay: Relativization of the P =? NP question. To be published in SICOMP.
Büchi, J.R.: Weak second order arithmetic and finite automata. Zeit. f. Math. Log. und Grund. der Math., 6 (1960) 66–92.
Büchi, J.R. and C.C. Elgot: Decision problems of weak second order arithmetics and finite automata, Part I. AMS Notices, 5 (1959) Abstract 834.
Cook, S.: Linear time simulation of deterministic two-way pushdown automata. Information Processing 71. North Holland, Amsterdam 1972. 75–80.
Cook, S.: The complexity of theorem-proving procedures. Proc. 3rd Ann. ACM Symp. Th. Comp. 1971 151–158.
Fisher, M.J. and M.O. Rabin: Super-exponential complexity of Pressburger arithmetic. Project MAC TM 43 (1974)
Greibach, S.: The hardest context-free language. SIAM J. Como. v. 2, (1973) 304–310.
Hartmanis, J. and H.B. Hunt III: The lba problem and its importance in the theory of computing. TR-171 Dept. Comp. Sci. Cornell University (1973). To be published by the AMS.
Hartmanis, J. and H. Shank: Two memory bounds for the recognition of primes by automata. MST v. 3 (1969) 125–129.
Hartmanis, J. and H. Shank: On the recognition of primes by automata. JACM v. 15 (1968) 382–389.
Hartmanis, J. and J. Simon: On the power of multiplication in random access machines. Conf. Rec. IEEE 15th SWAT (1974).
Hoperoft, J.E. and J.D. Ullman: Formal languages and their relation to automata. Addison-Wesley, Reading, Mass. 1969.
Hunt, H.B. III: On time and tape complexity of languages. Ph.D. Dissertation, 1973, Cornell University, Ithaca, N.Y.
Hunt, H.B. III: On time and tape complexity of languages. 5th Ann. ACM Symp. Th. Comp. (1973) 10–19.
Karp, R.: Reducibilities among combinatorial problems. R. Miller and J. Thatcher (eds), Complexity of Computer Computations. Plenum Press (1972) 85–104.
Kuroda, S.Y.: Classes of languages and linear bounded automata. Information and Control v. 3 (1964) 207–223.
Landweber, P.S.: Three theorems on phrase structure grammars of type 1. Information and Control v. 2 (1963) 131–136.
McNaughton, R. and H. Yamada: Regular expressions and state graphs. E.F. Moore (ed) Sequential Machines: Selected Papers. Addison-Wesley, Reading, Mass. 1964.
Meyer, A.: Weak monadic second order theory of successor is not elementary recursive. M.I.T. Project MAC TM 38(1973).
Meyer, A. and L. Stockmeyer: The equivalence problem for regular expressions with squaring requires exponential space, Conf. Rec. IEEE 13th SWAT (1972) 125–129.
Meyer, A. and L. Stockmeyer: Word problems requiring exponential tape. Proc. 5th Ann. ACM Symp. Th. Comp. (1973) 1–9.
Minsky, M.: Form and content in computer science. JACM v. 17 n. 2 (1970) 197–215.
Myhill, J.: Linearly bounded automata. WADD Technical Note 60–165 (June 1960).
Oppen, D.C.: Elementary bounds for Pressburger arithmetic. Proc. 5th Ann. ACM Symp. Th. Comp. (1973) 34–37.
Pratt, V.R.: Every prime has a succinct certification. Unpublished manuscript (January 1974).
Pratt, V., L. Stockmeyer and M.O. Rabin: A characterization of the power of vector machines. Proc. 6th Ann. ACM Symp. Th. Comp. (1974) 122–134.
Pressburger, M.: Über die Vollstandigkeit eines gewissen System der Arithmetik ganzen Zahlen, in welchen die Addition als einzige Operation hervortritt. Comptes-Rendus du I Congres des Mathematiciens des Pays Slays. Warsaw, 1929.
Rangel, J.L.: The equivalence problem for regular expressions over one letter alphabet is elementary. Conf. Rec. IEEE 15th SWAT (1974)
Rogers, H. Jr.: Theory of recursive functions and effective computability. McGraw-Hill, New York. 1967.
Savitch, W.J.: Relations between nondeterministic and deterministic tape complexities. JCSS v. 4 (1970) 177–192.
Simon, J.: On the power of multiplication in random access ma-chines. TR 74–205 Dept. of Comp. Sci. Cornell University (1974).
Stearns, R.E., J. Hartmanis and P.M. Lewis: Hierarchies of memory limited computations. Conf. Rec. IEEE 6th SWAT (1965) 179–190.
Stockmeyer, L.J.: The complexity of decision problems in automata theory and logic. Project MAC TR 133 (July 1974).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hartmanis, J., Simon, J. (1975). On the Structure of Feasible Computations. In: Siefkes, D. (eds) GI-4.Jahrestagung. Lecture Notes in Computer Science, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-40087-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-40087-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-39104-4
Online ISBN: 978-3-662-40087-6
eBook Packages: Springer Book Archive