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Selectively-Amortized Resource Bounding (Extended Version) [article]

Tianhan Lu, Bor-Yuh Evan Chang, Ashutosh Trivedi
2021 arXiv   pre-print
We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression.  ...  We present a framework for selectively-amortized analysis that mixes worst-case and amortized reasoning via a property decomposition and a program transformation.  ...  We also thank the anonymous reviewers and members of the CUPLV lab for their helpful reviews and suggestions.  ... 
arXiv:2108.08263v2 fatcat:j7phf6uigbf3rcyxa6gkmvvxge

A tight lower bound for top-down skew heaps

Berry Schoenmakers
1997 Information Processing Letters  
Previously, it was shown in a paper by Kaldewaij and Schoenmakers that for topdown skew heaps the amortized number of comparisons required for meld and delmin is upper bounded by log φ n, where n is the  ...  As the remaining heap operations require no comparisons, it then follows that the set of bounds is tight.  ...  The upper bound (Theorem 1) for the amortized cost of this operation is log φ |G n | = log φ (n + 1), which is bounded by approximately k − 0.67, using that F k+1 ≈ φ k+1 / √ 5.  ... 
doi:10.1016/s0020-0190(97)00028-8 fatcat:vrglt5pfeva5ndwrmbv7ehmxqy

A cost-aware logical framework [article]

Yue Niu
2021 arXiv   pre-print
We evaluate calf as a general framework for cost analysis by implementing two fundamental techniques for algorithm analysis: the method of recurrence relations and physicist's method for amortized analysis  ...  We deploy these techniques on a variety of case studies: we prove a tight, closed bound for Euclid's algorithm, verify the amortized complexity of batched queues, and derive tight, closed bounds for the  ...  Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the AFOSR, NSF, or AFRL.  ... 
arXiv:2107.04663v2 fatcat:3bit6tz77ff65drvkyiid5zgne

Monadic refinements for relational cost analysis

Ivan Radiček, Gilles Barthe, Marco Gaboardi, Deepak Garg, Florian Zuleger
2017 Proceedings of the ACM on Programming Languages  
We also develop a corresponding unary system, U C , that establishes upper and lower bounds on the cost of a single program.  ...  Hence, n is an upper bound on the difference of the costs of m 1 and m 2 . We call this proof system R C .  ...  INTRODUCTION Cost analysis aims to statically establish upper and lower bounds on the cost of evaluating a program.  ... 
doi:10.1145/3158124 dblp:journals/pacmpl/RadicekBG0Z18 fatcat:txbpyql76raxvjkjm2biiiy5ti

Page 1260 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
99b:68044 commonly used programming data structures can be recast as spe- cial cases of wp-graphs and, thus, that these data-structures may be expressed in a common framework, which partially explains  ...  Summary: “We present lower and upper bounds on adaptive heuristics for maintaining binary search trees using a constant number of link or pointer changes for each operation (constant linkage cost (CLC)  ... 

A unifying type-theory for higher-order (amortized) cost analysis

Vineet Rajani, Marco Gaboardi, Deepak Garg, Jan Hoffmann
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
This paper presents 𝜆-amor, a new type-theoretic framework for amortized cost analysis of higher-order functional programs and shows that existing type systems for cost analysis can be embedded in it.  ...  One of the embeddings also implies that 𝜆-amor is relatively complete for all terminating PCF programs.  ...  Some prior work such as the unary fragment of Çiçek et al. [2017] uses effect-based type systems for non-amortized cost analysis.  ... 
doi:10.1145/3434308 fatcat:wdzunsacrvgr5hwvo35e3c4u4m

Verifying and Synthesizing Constant-Resource Implementations with Types

Van Chan Ngo, Mario Dehesa-Azuara, Matthew Fredrikson, Jan Hoffmann
2017 2017 IEEE Symposium on Security and Privacy (SP)  
Our type system extends recent work on automatic amortized resource analysis (AARA), a set of techniques that automatically derive provable upper bounds on the resource consumption of programs.  ...  We also show how a second novel AARA system that computes lower bounds on resource usage can be used to derive quantitative bounds on the amount of information that a program leaks through its resource  ...  Any opinions, findings, and conclusions contained in this document are those of the authors and do not necessarily reflect the views of the sponsoring organizations.  ... 
doi:10.1109/sp.2017.53 dblp:conf/sp/NgoDFH17 fatcat:j2e6usxfefcwje5pvg26iiu2zy

Differential Cost Analysis with Simultaneous Potentials and Anti-potentials [article]

Đorđe Žikelić, Bor-Yuh Evan Chang, Pauline Bolignano, Franco Raimondi
2022 arXiv   pre-print
evaluates to an upper bound for the cost incurred in the first program and an anti-potential function that evaluates to a lower bound for the cost incurred in the second.  ...  In this paper, our key insight is that we can avoid the need for and the limitations of program alignment if, instead, we bound the difference of two cost-bound summaries rather than directly bounding  ...  Acknowledgements We thank Shaun Willows, Thomas Lugnet, and the Living Room Application Vending team for suggesting threshold bounds as a developer-friendly way to interact with a differential cost analyzer  ... 
arXiv:2204.00870v2 fatcat:obzl7tdamreovnqajfaqkqzmf4

Resource Bound Analysis (Dagstuhl Seminar 17291)

Marco Gaboardi, Jan Hoffman, Reinhard Wilhelm, Florian Zuleger, Marc Herbstritt
2018 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 17291 "Resource Bound Analysis".  ...  Resource-bound analysis is studied in formal methods and programming languages at different levels of abstraction.  ...  Based on the characteristics of the problem and the demands of these applications, we motivate the objective of obtaining upper and lower bounds, the requirement that these bounds be functions of program  ... 
doi:10.4230/dagrep.7.7.72 dblp:journals/dagstuhl-reports/GaboardiHWZ17 fatcat:iptaivhumfa6ra7wnzliupfkgm

A Note on Amortized Branching Program Complexity [article]

Aaron Potechin
2017 arXiv   pre-print
This result disproves a conjecture about non-uniform catalytic computation, rules out a certain type of bottleneck argument for proving non-monotone space lower bounds, and can be thought of as a constructive  ...  In this paper, we show that while almost all functions require exponential size branching programs to compute, for all functions f there is a branching program computing a doubly exponential number of  ...  In particular, any lower bound technique which would prove a lower bound on amortized branching program complexity as well as branching program size cannot prove non-trivial lower bounds.  ... 
arXiv:1611.06632v2 fatcat:gw5vnomjmnauxn3zvedevl367a

Automatic Static Cost Analysis for Parallel Programs [chapter]

Jan Hoffmann, Zhong Shao
2015 Lecture Notes in Computer Science  
The experiments show that the analysis infers bounds for realistic example programs such as quick sort for lists of lists, matrix multiplication, and an implementation of sets with lists.  ...  The cost semantics of parallel programs is based on call-by-value evaluation and the standard cost measures work and depth.  ...  Amortized Resource Analysis Amortized resource analysis is a type-based technique for deriving upper bounds on the resource cost of programs [23] .  ... 
doi:10.1007/978-3-662-46669-8_6 fatcat:l4ieqjjnzrf4bdp7mwbzidguwu

Page 3750 of Mathematical Reviews Vol. , Issue 86h [page]

1986 Mathematical Reviews  
We find lower and upper bounds for the mean number of binary comparisons necessary for determining the kth smallest number.  ...  In the case of a uniformly distributed random variable the lower bound does not exceed the upper, i.e., the corresponding algorithm is optimal with respect to the sample size.  ... 

Tensor Network Complexity of Multilinear Maps

Per Austrin, Petteri Kaski, Kaie Kubjas, Michael Wagner
2018 Innovations in Theoretical Computer Science  
While powerful, the model still has limitations, and we are able to show a number of unconditional lower bounds for various multilinear maps, including: (a) an Ω(n bw(P ) ) time lower bound for counting  ...  (b) an Ω(2 0.918n ) time lower bound for the permanent of an n × n matrix.  ...  Acknowledgements We are grateful to Andreas Björklund for highlighting branchwidth to us as a natural parameter to generalize from clique-counting to counting homomorphisms.  ... 
doi:10.4230/lipics.itcs.2019.7 dblp:conf/innovations/AustrinKK19 fatcat:t4xmqd4rxfb27lgqzslpxtduli

A Simple and Scalable Static Analysis for Bound Analysis and Amortized Complexity Analysis [article]

Moritz Sinn, Florian Zuleger, Helmut Veith
2014 arXiv   pre-print
Our bound analysis first computes a lexicographic ranking function that proves the termination of a VASS, and then derives a bound from this ranking function.  ...  Rather, we derive bounds directly from abstract program models, which we obtain from programs by comparatively simple invariant generation and symbolic execution techniques.  ...  We thank Fabian Souczek and Thomas Pani for help with the experiments.  ... 
arXiv:1401.5842v2 fatcat:lya5sjc4gnbenlyzrfsb2e3bnm

Relational Cost Analysis for Functional-Imperative Programs [article]

Weihao Qu, Marco Gaboardi, Deepak Garg
2019 arXiv   pre-print
As a particular case, one can also use relational cost analysis to establish bounds on the difference in the evaluation cost of the same program on two different inputs.  ...  Relational cost analysis aims at formally establishing bounds on the difference in the evaluation costs of two programs.  ...  This typing has two kinds of costs: the lower bound L 1 and 92:16 Weihao , Marco Gaboardi, and Deepak Garg upper bound U 1 for the unary execution cost of t 1 , and the lower bound L and upper bound  ... 
arXiv:1812.04090v2 fatcat:sw4haewcm5f67gr2mvygc3ugjm
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