Article

Adventures in time and space

Authors:

James S. RoyerAuthors Info & Claims

POPL '06: Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 168 - 179

https://doi.org/10.1145/1111037.1111053

Published: 11 January 2006 Publication History

Abstract

This paper investigates what is essentially a call-by-value version of PCF under a complexity-theoretically motivated type system. The programming formalism, ATR1, has its first-order programs characterize the poly-time computable functions, and its second-order programs characterize the type-2 basic feasible functionals of Mehlhorn and of Cook and Urquhart. (The ATR1-types are confined to levels 0, 1, and 2.) The type system comes in two parts, one that primarily restricts the sizes of values of expressions and a second that primarily restricts the time required to evaluate expressions. The size-restricted part is motivated by Bellantoni and Cook's and Leivant's implicit characterizations of poly-time. The time-restricting part is an affine version of Barber and Plotkin's DILL. Two semantics are constructed for ATR₁. The first is a pruning of the naïve denotational semantics for ATR₁. This pruning removes certain functions that cause otherwise feasible forms of recursion to go wrong. The second semantics is a model for ATR₁'s time complexity relative to a certain abstract machine. This model provides a setting for complexity recurrences arising from ATR1 recursions, the solutions of which yield second-order polynomial time bounds. The time-complexity semantics is also shown to be sound relative to the costs of interpretation on the abstract machine.

References

[1]

A. Barber and G. Plotkin, Dual intuitionistic linear logic, Tech. report, LFCS, Univ of Edinburgh, 1997.

[2]

S. Bellantoni and S. Cook, A new recursion-theoretic characterization of the polytime functions, Computational Complexity 2 (1992), 97--110.

Digital Library

[3]

S. Bellantoni, K.-H. Niggl, and H. Schwichtenberg, Characterising polytime through higher type recursion, Annals of Pure and Applied Logic (2000), 17--30.

[4]

A. Cobham, The intrinsic computational difficulty of functions, Proceedings of the International Conference on Logic, Methodology and Philosophy (Y. Bar Hillel, ed.), North-Holland, 1965, pp. 24--30.

[5]

S. Cook and A. Urquhart, Functional interpretations of feasibly constructive arithmetic, Annals of Pure and Applied Logic 63 (1993), 103--200.

[6]

M. Felleisen and D. Friedman, Control operators, the SECD-machine, and the lambda calculus, Formal Descriptions of Programming Concepts III, 1987, pp. 193--217.

[7]

C. Frederiksen and N. Jones, Recognition of polynomial-time programs, Tech. Report TOPPS/D-501, DIKU, University of Copenhagen, 2004.

[8]

O. Goldreich, Foundations of cryptography, Vol. I: Basic tools, Cambridge University Press, 2001.

Digital Library

[9]

D. J. Gurr, Semantic frameworks for complexity, Ph.D. thesis, University of Edinburgh, 1990.

[10]

M. Hofmann, Programming languages capturing complexity classes, SIGACT News 31 (2000), 31--42.

Digital Library

[11]

-----, Linear types and non-size increasing polynomial time computation, Information and Computation 183 (2003), 57--85.

Digital Library

[12]

R. Irwin, B. Kapron, and J. Royer, On characterizations of the basic feasible functional, Part I, Journal of Functional Programming 11 (2001), 117--153.

Digital Library

[13]

-----, On characterizations of the basic feasible functional, Part II, unpublished manuscript, 2002.

[14]

B. Kapron, Feasible computation in higher types, Ph.D. thesis, Department of Computer Science, University of Toronto, 1991.

Digital Library

[15]

B. Kapron and S. Cook, A new characterization of type 2 feasibility, SIAM Journal on Computing 25 (1996), 117--132.

Digital Library

[16]

D. Leivant, A foundational delineation of poly-time, Information and Computation 110 (1994), 391--420.

Digital Library

[17]

-----, Ramified recurrence and computational complexity I: Word recurrence and poly-time, Feasible Mathematics II (P. Clote and J. Remmel, eds.), Birkhäuser, 1995, pp. 320--343.

[18]

D. Leivant and J.-Y. Marion, Lambda calculus characterizations of polytime, FundamentæInformaticæ19 (1993), 167--184.

Digital Library

[19]

J. Longley, On the ubiquity of certain total type structures (Extended abstract), Proceedings of the Workshop on Domains VI (M. Escardó and A. Jung, eds.), Electronic Notes in Theoretical Computer Science, vol. 73, Elsevier Science Publishers, 2004, pp. 87--109.

Digital Library

[20]

-----, Notions of computability at higher types, I, Logic Colloquium 2000 (R. Cori, A. Razborov, S. Torcevic, and C. Wood, eds.), Lecture Notes in Logic, vol. 19, A. K. Peters, 2005.

[21]

K. Mehlhorn, Polynomial and abstract subrecursive classes, Journal of Computer and System Science 12 (1976), 147--178.

Digital Library

[22]

B. Pierce, Types and programming languages, MIT Press, 2002.

Digital Library

[23]

G. Plotkin, Call-by-name, call-by-value and the γ-calculus, Theoretical Computer Science 1 (1975), 125--159.

[24]

-----, LCF considered as a programming language, Theoretical Computer Science 5 (1977), 223--255.

[25]

J. Royer and J. Case, Subrecursive programming systems: Complexity & succinctness, Birkhääuser, 1994.

Digital Library

[26]

D. Sands, Calculi for time analysis of functional programs, Ph.D. thesis, University of London, 1990.

[27]

A. Schönhage, Storage modification machines, SIAM Journal on Computing 8 (1980), 490--508.

[28]

J. Shultis, On the complexity of higher-order programs, Tech. Report CU-CS-288-85, University of Colorado, Boulder, 1985.

[29]

K. Van Stone, A denotational approach to measuring complexity in functional programs, Ph.D. thesis, School of Computer Science, Carnegie Mellon University, 2003.

Digital Library

[30]

G. Winskel, Formal semantics, MIT Press, 1993.

Cited By

Hainry EKapron BMarion JPéchoux RSobocinski PLago UEsparza J(2024)Declassification Policy for Program Complexity AnalysisProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662100(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662100
Baillot PDal Lago UKop CVale D(2024)On Basic Feasible Functionals and the Interpretation MethodFoundations of Software Science and Computation Structures10.1007/978-3-031-57231-9_4(70-91)Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/978-3-031-57231-9_4
Fre H(2017)Game semantics approach to higher-order complexityJournal of Computer and System Sciences10.1016/j.jcss.2017.02.00387:C(1-15)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1016/j.jcss.2017.02.003
Show More Cited By

Index Terms

Adventures in time and space
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Recursion
2. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Semantics and reasoning
    1. Program constructs
      1. Program schemes
      2. Type structures
    2. Program semantics

Recommendations

Adventures in time and space
Proceedings of the 2006 POPL Conference

This paper investigates what is essentially a call-by-value version of PCF under a complexity-theoretically motivated type system. The programming formalism, ATR1, has its first-order programs characterize the poly-time computable functions, and its ...
Adventures in monitorability: from branching to linear time and back again

This paper establishes a comprehensive theory of runtime monitorability for Hennessy-Milner logic with recursion, a very expressive variant of the modal µ-calculus. It investigates the monitorability of that logic with a linear-time semantics and then ...
Constructive linear-time temporal logic: Proof systems and Kripke semantics

In this paper we study a version of constructive linear-time temporal logic (LTL) with the ''next'' temporal operator. The logic is originally due to Davies, who has shown that the proof system of the logic corresponds to a type system for binding-time ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

POPL '06: Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages

January 2006

432 pages

ISBN:1595930272

DOI:10.1145/1111037

General Chair:
Greg Morrisett
Harvard University, USA
,
Program Chair:
Simon Peyton Jones
Microsoft Research, UK

ACM SIGPLAN Notices Volume 41, Issue 1
Proceedings of the 2006 POPL Conference
January 2006
421 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/1111320
Issue’s Table of Contents

Copyright © 2006 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 11 January 2006

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

POPL06

Sponsor:

POPL06: The 33rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages 2006

January 11 - 13, 2006

South Carolina, Charleston, USA

Acceptance Rates

Overall Acceptance Rate 824 of 4,130 submissions, 20%

Upcoming Conference

POPL '25

Sponsor:
sigplan

The 52nd Annual ACM SIGPLAN Symposium on Principles of Programming Languages

January 19 - 25, 2025

Denver , CO , USA

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
424
Total Downloads

Downloads (Last 12 months)3
Downloads (Last 6 weeks)0

Reflects downloads up to 13 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Hainry EKapron BMarion JPéchoux RSobocinski PLago UEsparza J(2024)Declassification Policy for Program Complexity AnalysisProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662100(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662100
Baillot PDal Lago UKop CVale D(2024)On Basic Feasible Functionals and the Interpretation MethodFoundations of Software Science and Computation Structures10.1007/978-3-031-57231-9_4(70-91)Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/978-3-031-57231-9_4
Fre H(2017)Game semantics approach to higher-order complexityJournal of Computer and System Sciences10.1016/j.jcss.2017.02.00387:C(1-15)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1016/j.jcss.2017.02.003
Gaboardi MMarion JRonchi Della Rocca S(2012)An Implicit Characterization of PSPACEACM Transactions on Computational Logic10.1145/2159531.215954013:2(1-36)Online publication date: 1-Apr-2012
https://dl.acm.org/doi/10.1145/2159531.2159540
Danner NRoyer J(2009)Two Algorithms in Search of a Type-SystemTheory of Computing Systems10.1007/s00224-009-9181-y45:4(787-821)Online publication date: 31-Jul-2009
https://dl.acm.org/doi/10.1007/s00224-009-9181-y
Danner NRoyer J(2007)Time-Complexity Semantics for Feasible Affine RecursionsProceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World10.1007/978-3-540-73001-9_22(205-217)Online publication date: 18-Jun-2007
https://dl.acm.org/doi/10.1007/978-3-540-73001-9_22

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents