A flow calculus of<i>mwp</i>-bounds for complexity analysis

Jones, Neil D.; Kristiansen, Lars

doi:10.1145/1555746.1555752

Cited by 23 publications

(27 citation statements)

References 21 publications

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“…In [17] Jones characterizes PTIME by means of simple constructor free programs. Data flow analysis to bound variables growth rate is performed by matrix calculus in Jones & Kristiansen [18], Niggl & Wunderlich [19], and Ben-Amram, Jones & Kristiansen [20]. However the language is restricted to loops of fixed length, and operators are successor-like functions.…”

Section: Related Workmentioning

confidence: 99%

A Type System for Complexity Flow Analysis

Marion¹

2011

2011 IEEE 26th Annual Symposium on Logic in Computer Science

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We propose a type system for an imperative programming language, which certifies program time bounds. This type system is based on secure flow information analysis. Each program variable has a level and we prevent information from flowing from low level to higher level variables. We also introduce a downgrading mechanism in order to delineate a broader class of programs. Thus, we propose a relation between security-typed language and implicit computational complexity. We establish a characterization of the class of polynomial time functions.

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Section: Related Workmentioning

confidence: 99%

A Type System for Complexity Flow Analysis

Marion¹

2011

2011 IEEE 26th Annual Symposium on Logic in Computer Science

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“…The two first transitions are an application of Rules (8) and (9) of Figure 4. The third one is Rule (14) as queue is a field of the current object. The first equality holds by definition of I ′ and its top stack frame ⊤I ′ = s H .…”

Section: Input and Sizementioning

confidence: 99%

A type-based complexity analysis of Object Oriented programs

Hainry

Péchoux

2018

Information and Computation

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A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound and complete characterization of the set of polynomial time computable functions is obtained. As a consequence, the heap-space and the stack-space requirements of typed programs are also bounded polynomially. This type system is inspired by previous works on Implicit Computational Complexity, using tiering and non-interference techniques. The presented methodology has several advantages. First, it provides explicit big O polynomial upper bounds to the programmer, hence its use could allow the programmer to avoid memory errors. Second, type checking is decidable in polynomial time. Last, it has a good expressivity since it analyzes most object oriented features like inheritance, overload, override and recursion. Moreover it can deal with loops guarded by objects and can also be extended to statements that alter the control flow like break or return. Init ::= BList b := new BList (); BList c := new BList ( true , b ); B d := new B ( c ); A e := new A (c , c );

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“…While these upper bounds are tight for the class of programs as a whole, many programs of the class have a lower complexity, so we can try to analyze a given program more precisely. Works of this kind include [11,1,14,18,10]. With a single exception, these works proposed syntactic criteria, or analysis algorithms, that are sufficient for ensuring that the program lies in a desired class (say, polynomial-time programs), but are not both necessary and sufficient: thus, they do not address the decidability question (the exception is [14] which has a decidability result for a "core" language).…”

Section: Related Workmentioning

confidence: 99%

On the Edge of Decidability in Complexity Analysis of Loop Programs

Ben-Amram

Kristiansen

2012

Int. J. Found. Comput. Sci.

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We investigate the decidability of the feasibility problem for imperative programs with bounded loops. A program is called feasible if all values it computes are polynomially bounded in terms of the input. The feasibility problem is representative of a group of related properties, like that of polynomial time complexity. It is well known that such properties are undecidable for a Turing-complete programming language. They may be decidable, however, for languages that are not Turing-complete. But if these languages are expressive enough, they do pose a challenge for analysis. We are interested in tracing the edge of decidability for the feasibility problem and similar problems.In previous work, we proved that such problems are decidable for a language where loops are bounded but indefinite (that is, the loops may exit before completing the given iteration count). In this paper, we consider definite loops. A second language feature that we vary, is the kind of assignment statements. With ordinary assignment, we prove undecidability of a very tiny language fragment. We also prove undecidability with lossy assignment (that is, assignments where the modified variable may receive any value bounded by the given expression, even zero). But we prove decidability with max assignments (that is, assignments where the modified variable never decreases its value).

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A flow calculus ofmwp-bounds for complexity analysis

Cited by 23 publications

References 21 publications

A Type System for Complexity Flow Analysis

A Type System for Complexity Flow Analysis

A type-based complexity analysis of Object Oriented programs

On the Edge of Decidability in Complexity Analysis of Loop Programs

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