Complexity of Model-Checking Call-by-Value Programs

Tsukada, Takeshi; Kobayashi, Naoki

doi:10.1007/978-3-642-54830-7_12

Cited by 4 publications

(5 citation statements)

References 24 publications

(41 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, we investigate a call-by-value framework. Here the associated reachability problem was shown to be n-EXPTIME-complete for programs of depth-n in Tsukada and Kobayashi [2014]. We consider the more general resource usage verification problem and also show its n-EXPTIMEcompleteness.…”

Section: Introductionmentioning

confidence: 94%

“…To avoid the complexity blow-up due to CPS translation, Tsukada and Kobayashi [2014] gave a direct intersection type system to show that the reachability problem for depth-n call-by-value programs is n-EXPTIME-complete. We show that, using Theorem 34, one can recover their result through a linear CPS transformation, and the refined complexity analysis afforded by the Theorem does yield the optimal bound.…”

Section: Call-by-value Programsmentioning

confidence: 99%

“…Now, we enrich our operational semantics to track resource usage. As in [Tsukada and Kobayashi 2014], resources can be dynamically created and the properties we aim to verify are resource-conscious: each resource, taken separately, must be accessed according to A. To track usage of the r th initialized resource we build a labelled transition system L(r ).…”

Section: :22mentioning

confidence: 99%

“…with types as indicated before. Note that we insisted (as in [Tsukada and Kobayashi 2014]) that in such definitions, each abstraction be non-empty, i.e. for all 1 ≤ i ≤ n, p i ≥ 1.…”

Section: Translation Of Definitions and Programs Assume We Have A Dementioning

confidence: 99%

“…We consider the more general resource usage verification problem and also show its n-EXPTIMEcompleteness. In contrast to Tsukada and Kobayashi [2014], our result is obtained through a linear variant of a CPS transformation, which maps call-by-value programs of depth n to call-by-name λℓY -terms of linear order n. CPS translations are known to cause an increase in type order, but in our case linear order does not increase. As the linear depth of the types involved turns out to be constant (equal to 2), our result for LHORS implies the desired complexity.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Linearity in higher-order recursion schemes

Clairambault

Grellois

Murawski

2017

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

Higher-order recursion schemes (HORS) have recently emerged as a promising foundation for higher-order program verification. We examine the impact of enriching HORS with linear types. To that end, we introduce two frameworks that blend non-linear and linear types: a variant of the λY-calculus and an extension of HORS, called linear HORS (LHORS). First we prove that the two formalisms are equivalent and there exist polynomial-time translations between them. Then, in order to support model-checking of (trees generated by) LHORS, we propose a refined version of alternating parity tree automata, called LNAPTA, whose behaviour depends on information about linearity. We show that the complexity of LNAPTA model-checking for LHORS depends on two type-theoretic parameters: linear order and linear depth. The former is in general smaller than the standard notion of order and ignores linear function spaces. In contrast, the latter measures the depth of linear clusters inside a type. Our main result states that LNAPTA model-checking of LHORS of linear order n is n-EXPTIME-complete, when linear depth is fixed. This generalizes and improves upon the classic result of Ong, which relies on the standard notion of order. To illustrate the significance of the result, we consider two applications: the MSO model-checking problem on variants of HORS with case distinction (RSFD and HORSC) on a finite domain and a call-by-value resource verification problem. In both cases, decidability can be established by translation into HORS, but the implied complexity bounds will be suboptimal due to increases in type order. In contrast, we show that the complexity bounds derived by translations into LHORS and appealing to our result are optimal in that they match the respective hardness results. CCS Concepts: • Software and its engineering → Model checking; • Theory of computation → Linear logic;

show abstract

Section: Introductionmentioning

confidence: 94%

Section: Call-by-value Programsmentioning

confidence: 99%

Section: :22mentioning

confidence: 99%

“…with types as indicated before. Note that we insisted (as in [Tsukada and Kobayashi 2014]) that in such definitions, each abstraction be non-empty, i.e. for all 1 ≤ i ≤ n, p i ≥ 1.…”

Section: Translation Of Definitions and Programs Assume We Have A Dementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Linearity in higher-order recursion schemes

Clairambault

Grellois

Murawski

2017

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

show abstract

Monadic Intersection Types, Relationally

Gavazzo,

Treglia,

Vanoni

2024

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We extend intersection types to a computational $$\lambda $$ λ -calculus with algebraic operations à la Plotkin and Power. We achieve this by considering monadic intersections—whereby computational effects appear not only in the operational semantics, but also in the type system. Since in the effectful setting termination is not anymore the only property of interest, we want to analyze the interactive behavior of typed programs with the environment. Indeed, our type system is able to characterize the natural notion of observation, both in the finite and in the infinitary setting, and for a wide class of effects, such as output, cost, pure and probabilistic nondeterminism, and combinations thereof. The main technical tool is a novel combination of syntactic techniques with abstract relational reasoning, which allows us to lift all the required notions, e.g. of typability and logical relation, to the monadic setting.

show abstract