research-article

Open access

Non-polynomial Worst-Case Analysis of Recursive Programs

Authors:

Krishnendu Chatterjee,

Amir Kafshdar GoharshadyAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 41, Issue 4

Article No.: 20, Pages 1 - 52

https://doi.org/10.1145/3339984

Published: 12 October 2019 Publication History

All formats PDF

Abstract

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of non-recursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in non-polynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas Lemma, and Handelman’s Theorem using linear programming. While previous methods obtain polynomial worst-case bounds, our approach can synthesize bounds of various forms including O(n log n) and O(n^r), where r is not an integer. We present experimental results to demonstrate that our approach can efficiently obtain worst-case bounds of classical recursive algorithms such as (i) Merge sort, Heap sort, and the divide-and-conquer algorithm for the Closest Pair problem, where we obtain O(n log n) worst-case bound, and (ii) Karatsuba’s algorithm for polynomial multiplication and Strassen’s algorithm for matrix multiplication, for which we obtain O(n^r) bounds such that r is not an integer and is close to the best-known bound for the respective algorithm. Besides the ability to synthesize non-polynomial bounds, we also show that our approach is equally capable of obtaining polynomial worst-case bounds for classical programs such as Quick sort and the dynamic programming algorithm for computing Fibonacci numbers.

References

[1]

Elvira Albert, Puri Arenas, Samir Genaim, Miguel Gómez-Zamalloa, German Puebla, Diana V. Ramírez-Deantes, Guillermo Román-Díez, and Damiano Zanardini. 2009. Termination and cost analysis with COSTA and its user interfaces. Electr. Notes Theor. Comput. Sci. 258, 1 (2009), 109–121.

Digital Library

[2]

Elvira Albert, Puri Arenas, Samir Genaim, and Germán Puebla. 2008. Automatic inference of upper bounds for recurrence relations in cost analysis. In Proceedings of the 15th International Symposium on Static Analysis (SAS’08), (Lecture Notes in Computer Science), María Alpuente and Germán Vidal (Eds.). Vol. 5079, Springer, 221--237.

Digital Library

[3]

Elvira Albert, Puri Arenas, Samir Genaim, Germán Puebla, and Damiano Zanardini. 2007. Cost analysis of Java bytecode. In Programming Languages and Systems, 16th European Symposium on Programming (ESOP’07), held as part of the Proceedings of the Joint European Conferences on Theory and Practics of Software (ETAPS’07), (Lecture Notes in Computer Science), Rocco De Nicola (Ed.), Vol. 4421. Springer, 157--172.

[4]

Christophe Alias, Alain Darte, Paul Feautrier, and Laure Gonnord. 2010. Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs. In Proceedings of the Static Analysis Symposium (SAS’10), (LNCS), Radhia Cousot and Matthieu Martel (Eds.). Vol. 6337, Springer, 117--133.

[5]

Rajeev Alur and Swarat Chaudhuri. 2010. Temporal reasoning for procedural programs. In Proceedings of the 11th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI’10), (Lecture Notes in Computer Science), Gilles Barthe and Manuel V. Hermenegildo (Eds.), Vol. 5944. Springer, 45--60.

Digital Library

[6]

Roberto Bagnara, Patricia M Hill, Elisa Ricci, and Enea Zaffanella. 2003. Precise widening operators for convex polyhedra. In Proceedings of the International Static Analysis Symposium. Springer, 337--354.

[7]

Robert G. Bartle and Donald R. Sherbert. 2011. Introduction to Real Analysis (4th ed.). John Wiley 8 Sons, Inc.

[8]

Rastislav Bodík and Rupak Majumdar (Eds.). 2016. Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL’16). ACM.

Digital Library

[9]

Olivier Bournez and Florent Garnier. 2005. Proving positive almost-sure termination. In 16th International Conference on Term Rewriting and Applications (RTA'05). Lecture Notes in Computer Science, Vol. 3467. Springer, 323--337.

Digital Library

[10]

Aaron R. Bradley, Zohar Manna, and Henny B. Sipma. 2005. Linear ranking with reachability. In Proceedings of the 17th International Conference on Computer Aided Verification (CAV’05), (Lecture Notes in Computer Science), Kousha Etessami and Sriram K. Rajamani (Eds.), Vol. 3576. Springer, 491--504.

Digital Library

[11]

Marc Brockschmidt, Fabian Emmes, Stephan Falke, Carsten Fuhs, and Jürgen Giesl. 2016. Analyzing runtime and size complexity of integer programs. ACM Trans. Program. Lang. Syst. 38, 4 (2016), 13:1--13:50. http://dl.acm.org/citation.cfm?id=2866575.

Digital Library

[12]

Giuseppe Castagna and Andrew D. Gordon (Eds.). 2017. Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL’17). ACM.

Digital Library

[13]

Aleksandar Chakarov and Sriram Sankaranarayanan. 2013. Probabilistic program analysis with martingales. In Proceedings of the 25th International Conference on Computer Aided Verification (CAV’13), (Lecture Notes in Computer Science), Natasha Sharygina and Helmut Veith (Eds.). Vol. 8044, Springer, 511--526.

[14]

Krishnendu Chatterjee, Hongfei Fu, and Amir Kafshdar Goharshady. 2016. Termination analysis of probabilistic programs through Positivstellensatz’s. In Proceedings of the 28th International Conference on Computer Aided Verification (CAV’16), Part I Lecture Notes in Computer Science, Swarat Chaudhuri and Azadeh Farzan (Eds.). Vol. 9779, Springer, 3--22.

[15]

Krishnendu Chatterjee, Hongfei Fu, and Amir Kafshdar Goharshady. 2017. Non-polynomial worst-case analysis of recursive programs. In Proceedings of the 29th International Conference on Computer Aided Verification (CAV’17), Part II, Lecture Notes in Computer Science, Rupak Majumdar and Viktor Kuncak (Eds.). Vol. 10427, Springer, 41--63.

[16]

Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady, and Ehsan Kafshdar Goharshady. 2019. Polynomial invariant generation for non-deterministic recursive programs. CoRR abs/1902.04373 (2019). arxiv:1902.04373 http://arxiv.org/abs/1902.04373.

[17]

Krishnendu Chatterjee, Hongfei Fu, Petr Novotný, and Rouzbeh Hasheminezhad. 2016. Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs, See Reference Bodík and Majumdar [8], 327--342.

Digital Library

[18]

Krishnendu Chatterjee, Petr Novotný, and Đorđe Žikelić. 2017. Stochastic invariants for probabilistic termination, See Reference Castagna and Gordon [12], 145--160.

Digital Library

[19]

Wei-Ngan Chin and Siau-Cheng Khoo. 2001. Calculating sized types. Higher-Order. Comput. 14, 2--3 (2001), 261--300.

Digital Library

[20]

Michael Colón, Sriram Sankaranarayanan, and Henny Sipma. 2003. Linear invariant generation using non-linear constraint solving. In Proceedings of the 15th International Conference on Computer Aided Verification (CAV’03), Lecture Notes in Computer Science, Warren A. Hunt Jr. and Fabio Somenzi (Eds.). Vol. 2725, Springer, 420--432.

[21]

Michael Colón and Henny Sipma. 2001. Synthesis of linear ranking functions. In Proceedings of the 7th International ConferenceTools and Algorithms for the Construction and Analysis of Systems (TACAS’01), held as part of the Joint European Conferences on Theory and Practice of Software (ETAPS’01), Lecture Notes in Computer Science, Tiziana Margaria and Wang Yi (Eds.). Vol. 2031, Springer, 67--81.

[22]

Byron Cook, Andreas Podelski, and Andrey Rybalchenko. 2006. Termination proofs for systems code. In Proceedings of the Programming Language Design and Implementation Conference (PLDI’06), Michael I. Schwartzbach and Thomas Ball (Eds.). ACM, 415--426.

Digital Library

[23]

Byron Cook, Andreas Podelski, and Andrey Rybalchenko. 2009. Summarization for termination: No return&excl; Formal Methods Syst. Des. 35, 3 (2009), 369--387.

Digital Library

[24]

Byron Cook, Abigail See, and Florian Zuleger. 2013. Ramsey vs. Lexicographic termination proving. In Proceedings of the International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’13), Lecture Notes in Computer Science, Nir Piterman and Scott A. Smolka (Eds.). Vol. 7795, Springer, 47--61.

Digital Library

[25]

Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2009. Introduction to Algorithms (3rd ed.). MIT Press.

Digital Library

[26]

Patrick Cousot. 2005. Proving program invariance and termination by parametric abstraction, Lagrangian relaxation and semidefinite programming. In Proceedings of the 6th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI’05), Lecture Notes in Computer Science, Radhia Cousot (Ed.). Vol. 3385, Springer, 1--24.

Digital Library

[27]

Patrick Cousot and Radhia Cousot. 1977. Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In Conference Record of the 4th ACM Symposium on Principles of Programming Languages, Robert M. Graham, Michael A. Harrison, and Ravi Sethi (Eds.). ACM, 238--252.

Digital Library

[28]

Patrick Cousot and Radhia Cousot. 2012. An abstract interpretation framework for termination. In Proceedings of the ACM SIGPLAN Symposium on Principles of Programming Languages (POPL’12), John Field and Michael Hicks (Eds.). ACM, 245--258.

Digital Library

[29]

J. Farkas. 1894. A Fourier-féle mechanikai elv alkalmazásai (Hungarian). Math. Term. Értesitö 12 (1894), 457--472.

[30]

Luis María Ferrer Fioriti and Holger Hermanns. 2015. Probabilistic termination: Soundness, completeness, and compositionality. In Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL’15), Sriram K. Rajamani and David Walker (Eds.). ACM, 489--501.

Digital Library

[31]

Philippe Flajolet, Bruno Salvy, and Paul Zimmermann. 1991. Automatic average-case analysis of algorithm. Theor. Comput. Sci. 79, 1 (1991), 37--109.

Digital Library

[32]

Robert W. Floyd. 1967. Assigning meanings to programs. Mathematical Aspects of Computer Science (Proceedings of a Symposium in Applied Mathematics), J. T. Schwarz (Ed.) 19 (1967), 19--32.

[33]

Hongfei Fu and Krishnendu Chatterjee. 2019. Termination of nondeterministic probabilistic programs. In Proceedings of the 20th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI’19), Lecture Notes in Computer Science, Constantin Enea and Ruzica Piskac (Eds.). Vol. 11388, Springer, 468--490.

[34]

Stéphane Gimenez and Georg Moser. 2016. The complexity of interaction, See Reference Bodík and Majumdar [8], 243--255.

Digital Library

[35]

Kurt Gödel. On undecidable propositions of formal mathematical systems. 1934. A reprint of XXXI 484. The Journal of Symbolic Logic 55, 1 (1934), 347. https://doi.org/10.2307/2274987

[36]

Bernd Grobauer. 2001. Cost recurrences for DML programs. In Proceedings of the 6th ACM SIGPLAN International Conference on Functional Programming (ICFP’01), Benjamin C. Pierce (Ed.). ACM, 253--264.

Digital Library

[37]

Bhargav S. Gulavani and Sumit Gulwani. 2008. A numerical abstract domain based on expression abstraction and max operator with application in timing analysis. In Proceedings of the 20th International Conference on Computer Aided Verification (CAV’08), Lecture Notes in Computer Science, Aarti Gupta and Sharad Malik (Eds.). Vol. 5123, Springer, 370--384.

Digital Library

[38]

Sumit Gulwani. 2009. SPEED: Symbolic complexity bound analysis. In Proceedings of the 21st International Conference on Computer Aided Verification, (CAV’09), Lecture Notes in Computer Science, Ahmed Bouajjani and Oded Maler (Eds.). Vol. 5643, Springer, 51--62.

Digital Library

[39]

Sumit Gulwani, Krishna K. Mehra, and Trishul M. Chilimbi. 2009. SPEED: Precise and efficient static estimation of program computational complexity. In Proceedings of the 36th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL’09), Zhong Shao and Benjamin C. Pierce (Eds.). ACM, 127--139.

Digital Library

[40]

D. Handelman. 1988. Representing polynomials by positive linear functions on compact convex polyhedra. Pac. J. Math. 132 (1988), 35--62.

[41]

Wim H. Hesselink. 1993. Proof rules for recursive procedures. Form. Asp. Comput. 5, 6 (1993), 554--570.

Digital Library

[42]

Jan Hoffmann, Klaus Aehlig, and Martin Hofmann. 2012. Multivariate amortized resource analysis. ACM Trans. Program. Lang. Syst. 34, 3 (2012), 14.

Digital Library

[43]

Jan Hoffmann, Klaus Aehlig, and Martin Hofmann. 2012. Resource aware ML. In Proceedings of the 24th International Conference on Computer Aided Verification (CAV’12), Lecture Notes in Computer Science, P. Madhusudan and Sanjit A. Seshia (Eds.). Vol. 7358, Springer, 781--786.

Digital Library

[44]

Jan Hoffmann and Martin Hofmann. 2010. Amortized resource analysis with polymorphic recursion and partial big-step operational semantics. In Proceedings of the 8th Asian Symposium on Programming Languages and Systems (APLAS’10), Lecture Notes in Computer Science, Kazunori Ueda (Ed.). Vol. 6461, Springer, 172--187.

[45]

Jan Hoffmann and Martin Hofmann. 2010. Amortized resource analysis with polynomial potential. In Proceedings of the 19th European Symposium on Programming Languages and Systems (ESOP’10), held as part of the Joint European Conferences on Theory and Practice of Software (ETAPS’10), Lecture Notes in Computer Science, Andrew D. Gordon (Ed.). Vol. 6012, Springer, 287--306.

Digital Library

[46]

Martin Hofmann and Steffen Jost. 2003. Static prediction of heap space usage for first-order functional programs. In Conference Record of POPL 2003: Proceedings of the 30th SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Alex Aiken and Greg Morrisett (Eds.). ACM, 185--197.

Digital Library

[47]

Martin Hofmann and Steffen Jost. 2006. Type-based amortised heap-space analysis. In Proceedings of the 15th European Symposium on Programming Languages and Systems (ESOP’06) held as part of the Joint European Conferences on Theory and Practice of Software (ETAPS’06), Lecture Notes in Computer Science, Peter Sestoft (Ed.). Vol. 3924, Springer, 22--37.

Digital Library

[48]

Martin Hofmann and Dulma Rodriguez. 2009. Efficient type-checking for amortised heap-space analysis. In Proceedings of the 23rd International Workshop on the Conference on Computer Science Logic (CSL’09), Lecture Notes in Computer Science, Erich Grädel and Reinhard Kahle (Eds.). Vol. 5771, Springer, 317--331.

[49]

John Hughes and Lars Pareto. 1999. Recursion and dynamic data-structures in bounded space: Towards embedded ML programming. In Proceedings of the 4th ACM SIGPLAN International Conference on Functional Programming (ICFP’99), Didier Rémi and Peter Lee (Eds.). ACM, 70--81.

Digital Library

[50]

John Hughes, Lars Pareto, and Amr Sabry. 1996. Proving the correctness of reactive systems using sized types. In Conference Record of POPL’96: Proceedings of the 23rd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Hans-Juergen Boehm and Guy L. Steele Jr. (Eds.). ACM Press, 410--423.

Digital Library

[51]

Claire Jones. 1989. Probabilistic Non-Determinism. Ph.D. Dissertation. The University of Edinburgh.

[52]

Steffen Jost, Kevin Hammond, Hans-Wolfgang Loidl, and Martin Hofmann. 2010. Static determination of quantitative resource usage for higher-order programs. In Proceedings of the 37th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL’10), Manuel V. Hermenegildo and Jens Palsberg (Eds.). ACM, 223--236.

Digital Library

[53]

Steffen Jost, Hans-Wolfgang Loidl, Kevin Hammond, Norman Scaife, and Martin Hofmann. 2009. “Carbon credits” for resource-bounded computations using amortised analysis. In Proceedings of the Internaional Conference on Formal Methods (FM’09), Lecture Notes in Computer Science, Ana Cavalcanti and Dennis Dams (Eds.). Vol. 5850, Springer, 354--369.

Digital Library

[54]

Donald E. Knuth. 1973. The Art of Computer Programming, Volume I--III. Addison-Wesley.

Digital Library

[55]

Takuya Kuwahara, Tachio Terauchi, Hiroshi Unno, and Naoki Kobayashi. 2014. Automatic termination verification for higher-order functional programs. In Proceedings of the 23rd European Symposium on Programming Languages and Systems (ESOP'14). Lecture Notes in Computer Science, Vol. 8410, Zhong Shao (Ed.). Springer, 392--411.

Digital Library

[56]

Chin Soon Lee. 2009. Ranking functions for size-change termination. ACM Trans. Program. Lang. Syst. 31, 3 (2009), 10:1--10:42.

Digital Library

[57]

Chin Soon Lee, Neil D. Jones, and Amir M. Ben-Amram. 2001. The size-change principle for program termination. In Proceedings of the Principles of Programming Languages Symposium (POPL’01), Chris Hankin and Dave Schmidt (Eds.). ACM, 81--92.

Digital Library

[58]

lpsolve 2016. lp_solve 5.5.2.3. Retrieved from http://lpsolve.sourceforge.net/5.5/.

[59]

Martin Lukasiewycz. 2008. Java ILP—Java Interface to ILP Solvers. Retrieved from http://javailp.sourceforge.net/.

[60]

Federico Olmedo, Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Christoph Matheja. 2016. Reasoning about recursive probabilistic programs. In Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS’16), Martin Grohe, Eric Koskinen, and Natarajan Shankar (Eds.). ACM, 672--681.

Digital Library

[61]

Andreas Podelski and Andrey Rybalchenko. 2004. A complete method for the synthesis of linear ranking functions. In Proceedings of the 5th International Conference on Verification, Model Checking, and Abstract Interpretation, (VMCAI’04), Lecture Notes in Computer Science, Bernhard Steffen and Giorgio Levi (Eds.). Vol. 2937, Springer, 239--251.

[62]

Sriram Sankaranarayanan, Henny B. Sipma, and Zohar Manna. 2004. Constraint-based linear-relations analysis. In International Static Analysis Symposium. Springer, 53--68.

[63]

Alexander Schrijver. 1999. Theory of Linear and Integer Programming. Wiley.

Digital Library

[64]

Alexander Schrijver. 2003. Combinatorial Optimization—Polyhedra and Efficiency. Springer.

[65]

Liyong Shen, Min Wu, Zhengfeng Yang, and Zhenbing Zeng. 2013. Generating exact nonlinear ranking functions by symbolic-numeric hybrid method. J. Syst. Sci. 8 Complexity 26, 2 (2013), 291--301.

[66]

Olha Shkaravska, Ron van Kesteren, and Marko C. J. D. van Eekelen. 2007. Polynomial size analysis of first-order functions. In Proceedings of the 8th International Conference on Typed Lambda Calculi and Applications (TLCA’07), Lecture Notes in Computer Science, Simona Ronchi Della Rocca (Ed.). Vol. 4583, Springer, 351--365.

[67]

Moritz Sinn, Florian Zuleger, and Helmut Veith. 2014. A simple and scalable static analysis for bound analysis and amortized complexity analysis. In Proceedings of the International Conference on Computer-aided Verification (CAV’14), Lecture Notes in Computer Science, Armin Biere and Roderick Bloem (Eds.). Vol. 8559, Springer, 745--761.

Digital Library

[68]

Kirack Sohn and Allen Van Gelder. 1991. Termination detection in logic programs using argument sizes. In Proceedings of the 10th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Daniel J. Rosenkrantz (Ed.). ACM Press, 216--226.

Digital Library

[69]

Akhilesh Srikanth, Burak Sahin, and William R. Harris. 2017. Complexity verification using guided theorem enumeration, See Reference Castagna and Gordon [12], 639--652.

Digital Library

[70]

Caterina Urban. 2013. The abstract domain of segmented ranking functions. In Proceedings of the Static Analysis Symposium (SAS’13), Lecture Notes in Computer Science, Francesco Logozzo and Manuel Fähndrich (Eds.). Vol. 7935, Springer, 43--62.

[71]

Reinhard Wilhelm, Jakob Engblom, Andreas Ermedahl, Niklas Holsti, Stephan Thesing, David B. Whalley, Guillem Bernat, Christian Ferdinand, Reinhold Heckmann, Tulika Mitra, Frank Mueller, Isabelle Puaut, Peter P. Puschner, Jan Staschulat, and Per Stenström. 2008. The worst-case execution-time problem—Overview of methods and survey of tools. ACM Trans. Embedded Comput. Syst. 7, 3 (2008), 36:1--36:53.

Digital Library

[72]

Lu Yang, Chaochen Zhou, Naijun Zhan, and Bican Xia. 2010. Recent advances in program verification through computer algebra. Front. Comput. Sci. Chin. 4, 1 (2010), 1--16.

Cited By

Pham LSaad FHoffmann J(2024)Robust Resource Bounds with Static Analysis and Bayesian InferenceProceedings of the ACM on Programming Languages10.1145/36563808:PLDI(76-101)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656380
Zhang EWu FLu X(2024)An Intelligent Scheduling System for Large-Scale Online JudgingComputer Science and Education. Computer Science and Technology10.1007/978-981-97-0730-0_24(265-279)Online publication date: 26-Feb-2024
https://doi.org/10.1007/978-981-97-0730-0_24
Liu HLi G(2024)Empirically Scalable Invariant Generation Leveraging Divide-and-Conquer with PruningTheoretical Aspects of Software Engineering10.1007/978-3-031-64626-3_19(324-342)Online publication date: 29-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-64626-3_19
Show More Cited By

Index Terms

Non-polynomial Worst-Case Analysis of Recursive Programs
1. Theory of computation
  1. Semantics and reasoning
    1. Program reasoning
      1. Program verification

Recommendations

A MILP approach to DRAM access worst-case analysis
Abstract
The Dynamic Random Access Memory (DRAM) is among the major points of contention in multi-core systems. We consider a challenging optimization problem arising in worst-case performance analysis of systems architectures: computing the ...
Highlights
- Exact worst-case delay in COTS DRAM can be computed as a MILP optimum.
- Worst-...
Elementary Yet Precise Worst-Case Analysis of Floyd's Heap-Construction Program

The worst-case behavior of the heap-construction phase of Heapsort escaped mathematically precise characterization by a closed-form formula for almost five decades. This paper offers a proof that the exact number of comparisons of keys performed in the ...
Type-guided worst-case input generation

This paper presents a novel technique for type-guided worst-case input generation for functional programs. The technique builds on automatic amortized resource analysis (AARA), a type-based technique for deriving symbolic bounds on the resource usage of ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Programming Languages and Systems

ACM Transactions on Programming Languages and Systems Volume 41, Issue 4

December 2019

186 pages

ISSN:0164-0925

EISSN:1558-4593

DOI:10.1145/3366632

Editor:
Andrew Myers
Cornell University, USA

Issue’s Table of Contents

Copyright © 2019 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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 October 2019

Accepted: 01 May 2019

Revised: 01 February 2019

Received: 01 August 2017

Published in TOPLAS Volume 41, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed

Funding Sources

Vienna Science and Technology Fund (WWTF)
ERC
DOC Fellowship of the Austrian Academy of Sciences
Austrian Science Fund (FWF) NFN
Natural Science Foundation of China (NSFC)
CDZ project CAP (GZ 1023)
IBM Ph.D.Fellowship program

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

16
Total Citations
View Citations
535
Total Downloads

Downloads (Last 12 months)149
Downloads (Last 6 weeks)12

Reflects downloads up to 18 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

Pham LSaad FHoffmann J(2024)Robust Resource Bounds with Static Analysis and Bayesian InferenceProceedings of the ACM on Programming Languages10.1145/36563808:PLDI(76-101)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656380
Zhang EWu FLu X(2024)An Intelligent Scheduling System for Large-Scale Online JudgingComputer Science and Education. Computer Science and Technology10.1007/978-981-97-0730-0_24(265-279)Online publication date: 26-Feb-2024
https://doi.org/10.1007/978-981-97-0730-0_24
Liu HLi G(2024)Empirically Scalable Invariant Generation Leveraging Divide-and-Conquer with PruningTheoretical Aspects of Software Engineering10.1007/978-3-031-64626-3_19(324-342)Online publication date: 29-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-64626-3_19
Cai ZFarokhnia SGoharshady AHitarth S(2023)Asparagus: Automated Synthesis of Parametric Gas Upper-Bounds for Smart ContractsProceedings of the ACM on Programming Languages10.1145/36228297:OOPSLA2(882-911)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1145/3622829
Ishimwe DChandra SBlincoe KTonella P(2023)Inferring Complexity Bounds from Recurrence RelationsProceedings of the 31st ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering10.1145/3611643.3617853(2198-2200)Online publication date: 30-Nov-2023
https://doi.org/10.1145/3611643.3617853
Goharshady AHitarth SMohammadi FMotwani H(2023)Algebro-geometric Algorithms for Template-Based Synthesis of Polynomial ProgramsProceedings of the ACM on Programming Languages10.1145/35860527:OOPSLA1(727-756)Online publication date: 6-Apr-2023
https://dl.acm.org/doi/10.1145/3586052
Grosen JKahn DHoffmann J(2023)Automatic Amortized Resource Analysis with Regular Recursive Types2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175720(1-14)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175720
Liu HFu HYu ZSong JLi G(2022)Scalable linear invariant generation with Farkas’ lemmaProceedings of the ACM on Programming Languages10.1145/35632956:OOPSLA2(204-232)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563295
Ishimwe DNguyen TNguyen KDwyer M(2022)DynaplexProceedings of the ACM/IEEE 44th International Conference on Software Engineering: Companion Proceedings10.1145/3510454.3516853(61-64)Online publication date: 19-Oct-2022
https://doi.org/10.1145/3510454.3516853
Ishimwe DNguyen TNguyen K(2022)Dynaplex: Inferring Asymptotic Runtime Complexity of Recursive Programs2022 IEEE/ACM 44th International Conference on Software Engineering: Companion Proceedings (ICSE-Companion)10.1109/ICSE-Companion55297.2022.9793811(61-64)Online publication date: May-2022
https://doi.org/10.1109/ICSE-Companion55297.2022.9793811
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

HTML Format

View this article in HTML Format.

Get Access

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 Article

Media

Figures

Other

Tables

View Issue’s Table of Contents