Implicit computation complexity in higher-order programming languages

Lago, Ugo Dal

doi:10.1017/s0960129521000505

Cited by 2 publications

(2 citation statements)

References 107 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…ICC has been an area of interest since, at least, the 1960s (Cobham, 1965), with a resurgence in the last 30 years since the groundbreaking work of Bellantoni & Cook (1992). There are multiple approaches to ICC, see, e.g., the survey (Hofmann, 2000) for early developments pre-2000, andDal Lago (2022) for a recent survey about methods involving higher-order programs. Recently, implicit characterizations have been furnished for complexity classes using different modes of computation, or using different modes of computation as a means of characterizing standard complexity classes; in particular, this includes probabilistic computation (Lago & Toldin, 2015;Lago et al, 2021), reversible computation (Kristiansen, 2022), parallel computation (Baillot & Ghyselen, 2022), and higher-order complexity (Hainry et al, 2022).…”

Section: Related Workmentioning

confidence: 99%

Read/write factorizable programs

Bhaskar¹,

Simonsen²

2023

J. Funct. Prog.

View full text Add to dashboard Cite

In the cons-free programming paradigm, we eschew constructors and program using only destructors. Cons-free programs in a simple first-order language with string data capture exactly P, the class of polynomial-time relations. By varying the underlying language and considering other data types, we can capture several other complexity classes. However, no cons-free programming language captures any functional complexity class for fundamental reasons. In this paper, we cleanly extend the cons-free paradigm to encompass functional complexity classes. Namely, we introduce programs with data that can either only be destructed or only be constructed, which we enforce by a type system on the program variables. We call the resulting programs read/write- (or RW-)factorizable, show that RW-factorizable string programs capture exactly the class FP of polynomial-time functions, and that tail-recursive RW-factorizable programs capture exactly the class FL of logarithmic-space functions. Finally, we state and solve the nontrivial problem of syntactic composition of two RW-factorizable programs.

show abstract

Section: Related Workmentioning

confidence: 99%

Read/write factorizable programs

Bhaskar¹,

Simonsen²

2023

J. Funct. Prog.

View full text Add to dashboard Cite

show abstract

“…In a series of articles (Hofmann 1999; Hofmann 2002; Hofmann 2003), he was able to prove a beautiful and ingenious result: PTIME corresponds to higher-order programs with structural recursion if the computation is non-size-increasing , a property that could be elegantly encoded with local type rules based on linear logic. More information about ICC and Hofmann’s work in the area can be found in the survey articles by Hofmann (2000a) and Dal Lago (2022).…”

Section: Setting the Stagementioning

confidence: 99%

Two decades of automatic amortized resource analysis

Hoffmann

Jost

2022

Math. Struct. Comp. Sci.

View full text Add to dashboard Cite

This article gives an overview of automatic amortized resource analysis (AARA), a technique for inferring symbolic resource bounds for programs at compile time. AARA has been introduced by Hofmann and Jost in 2003 as a type system for deriving linear worst-case bounds on the heap-space consumption of first-order functional programs with eager evaluation strategy. Since then AARA has been the subject of dozens of research articles, which extended the analysis to different resource metrics, other evaluation strategies, non-linear bounds, and additional language features. All these works preserved the defining characteristics of the original paper: local inference rules, which reduce bound inference to numeric (usually linear) optimization; a soundness proof with respect to an operational cost semantics; and the support of amortized analysis with the potential method.

show abstract

Implicit computation complexity in higher-order programming languages

Cited by 2 publications

References 107 publications

Read/write factorizable programs

Read/write factorizable programs

Two decades of automatic amortized resource analysis

Contact Info

Product

Resources

About