Compositional recurrence analysis revisited

Kincaid, Zachary; Breck, Jason; Boroujeni, Ashkan Forouhi; Reps, Thomas

doi:10.1145/3062341.3062373

Cited by 49 publications

(47 citation statements)

References 31 publications

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“…Beyond AARA there exists many other approaches to automatic worst-case resource bound analysis for deterministic programs. They are based on sized types [89], linear dependent types [68,69], refinement types [29,92], annotated type systems [31,32], defunctionalization [7], recurrence relations [3,4,13,33,38,46,66], abstract interpretation [14,22,47,87,91], template based assume-guarantee reasoning [71], measure functions [27], and techniques from term rewriting [8,17,39,82]. These techniques do not apply to probabilistic programs and do not derive bounds on expected resource usage.…”

Section: Related Workmentioning

confidence: 99%

“…One important property that is often part of the formal and informal analysis of programs is resource bound analysis: What is the amount of resources such as time, memory or energy that is required to execute a program? Over the past decade, the programming language community has developed numerous tools that can be used to (semi-)automatically derive non-trivial symbolic resource bounds for imperative [17,47,66,87] and functional programs [7,33,55,92].…”

Section: Introductionmentioning

confidence: 99%

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Bounded expectations: resource analysis for probabilistic programs

Ngo

Carbonneaux

Hoffmann

2018

Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation

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This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials in the inputs. The new technique combines manual state-of-theart reasoning techniques for probabilistic programs with an effective method for automatic resource-bound analysis of deterministic programs. It can be seen as both, an extension of automatic amortized resource analysis (AARA) to probabilistic programs and an automation of manual reasoning for probabilistic programs that is based on weakest preconditions. An advantage of the technique is that it combines the clarity and compositionality of a weakest-precondition calculus with the efficient automation of AARA. As a result, bound inference can be reduced to off-the-shelf LP solving in many cases and automatically-derived bounds can be interactively extended with standard program logics if the automation fails. Building on existing work, the soundness of the analysis is proved with respect to an operational semantics that is based on Markov decision processes. The effectiveness of the technique is demonstrated with a prototype implementation that is used to automatically analyze 39 challenging probabilistic programs and randomized algorithms. Experiments indicate that the derived constant factors in the bounds are very precise and even optimal for some programs.CCS Concepts · Software and its engineering → General programming languages; · Social and professional topics → History of programming languages;

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bounded expectations: resource analysis for probabilistic programs

Ngo

Carbonneaux

Hoffmann

2018

Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation

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“…Static resource bound analysis for sequential programs has been extensively studied. Successful approaches are based on refinement types [18,15], linear dependent types [37], abstract interpretation [46,25,5,16], deriving and solving recurrence relations [19,20,4,36], term rewriting [11,8]. These works do not consider message-passing programs nor concurrent or parallel evaluation.…”

Section: Related Workmentioning

confidence: 99%

Work Analysis with Resource-Aware Session Types

Das

Hoffmann

Pfenning

2018

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science

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While there exist several successful techniques for supporting programmers in deriving static resource bounds for sequential code, analyzing the resource usage of message-passing concurrent processes poses additional challenges. To meet these challenges, this article presents an analysis for statically deriving worst-case bounds on the total work performed by message-passing processes. To decompose interacting processes into components that can be analyzed in isolation, the analysis is based on novel resource-aware session types, which describe protocols and resource contracts for inter-process communication. A key innovation is that both messages and processes carry potential to share and amortize cost while communicating. To symbolically express resource usage in a setting without static data structures and intrinsic sizes, resource contracts describe bounds that are functions of interactions between processes. Resource-aware session types combine standard binary session types and type-based amortized resource analysis in a linear type system. This type system is formulated for a core session-type calculus of the language SILL and proved sound with respect to a multiset-based operational cost semantics that tracks the total number of messages that are exchanged in a system. The effectiveness of the analysis is demonstrated by analyzing standard examples from amortized analysis and the literature on session types and by a comparative performance analysis of different concurrent programs implementing the same interface. arXiv:1712.08310v2 [cs.PL] 27 Apr 2018components that can be analyzed in isolation. After all, the resource usage of each component crucially depends on its interactions with the world.In this paper, we study the foundations of worst-case resource analysis for message-passing processes. A key idea of our approach is to rely on resourceaware session types to describe structure, protocols, and resource bounds for inter-process communication that we can use to perform a compositional and precise amortized analysis. Session types [32,33,12,13,45] prescribe bidirectional communication protocols for message-passing processes. Binary session types govern the interaction of two processes along a single channel, prescribing complementary send and receive actions for the processes at the two endpoints of a channel. We use such protocols as the basis of resource usage contracts that not only specify the type but also the potential of a message that is sent along a channel. The potential (in the sense of classic amortized analysis [43]) may be spent sending other messages as part of the network of interacting processes, or maintained locally for future interactions. Resource analysis is static, using the type system, and the runtime behavior of programs is not affected.

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“…Acceleration-like techniques are also used in over-approximating settings (see, e.g., [10,19,20,24,25,28,31,32]), whereas we consider exact and under-approximating loop acceleration techniques. As many related approaches have already been discussed in Sec.…”

Section: Related Workmentioning

confidence: 99%

A Calculus for Modular Loop Acceleration

Frohn

2020

Lecture Notes in Computer Science

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Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic: Either they accelerate a loop successfully or they fail completely. In contrast, we present a calculus that allows for combining acceleration techniques in a modular way and we show how to integrate many existing acceleration techniques into our calculus. Moreover, we propose two novel acceleration techniques that can be incorporated into our calculus seamlessly. An empirical evaluation demonstrates the applicability of our approach.⋆ This work has been funded by DFG grant 389792660 as part of TRR 248 (see https://perspicuous-computing.science).

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Compositional recurrence analysis revisited

Cited by 49 publications

References 31 publications

Bounded expectations: resource analysis for probabilistic programs

Bounded expectations: resource analysis for probabilistic programs

Work Analysis with Resource-Aware Session Types

A Calculus for Modular Loop Acceleration

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