Resource control of object-oriented programs

A sup-interpretation is a tool which provides an upper bound on the size of a value computed by some symbol of a program. Sup-interpretations have shown their interest to deal with the complexity of first order functional programs. For instance, they allow to characterize all the functions bitwise computable in Alogtime. This paper is an attempt to adapt the framework of sup-interpretations to a fragment of oriented-object programs, including distinct encodings of numbers through the use of constructor symbols, loop and while constructs and non recursive methods with side effects. We give a criterion, called brotherly criterion, which ensures that each brotherly program computes objects whose size is polynomially bounded by the inputs sizes

Quasi-friendly sup-interpretations

In a previous paper, the sup-interpretation method was proposed as a new tool to control memory resources of first order functional programs with pattern matching by static analysis. Basically, a sup-interpretation provides an upper bound on the size of function outputs. In this former work, a criterion, which can be applied to terminating as well as non-terminating programs, was developed in order to bound polynomially the stack frame size. In this paper, we suggest a new criterion which captures more algorithms computing values polynomially bounded in the size of the inputs. Since this work is related to quasi-interpretations, we compare the two notions obtaining two main features. The first one is that, given a program, we have heuristics for finding a sup-interpretation when we consider polynomials of bounded degree. The other one consists in the characterizations of the set of function computable in polynomial time and in polynomial space

Analyzing the Implicit Computational Complexity of object-oriented programs

A sup-interpretation is a tool which provides upper bounds on the size of the values computed by the function symbols of a program. Sup-interpretations have shown their interest to deal with the complexity of first order functional programs. This paper is an attempt to adapt the framework of sup-interpretations to a fragment of object-oriented programs, including loop and while constructs and methods with side effects. We give a criterion, called brotherly criterion, which uses the notion of sup-interpretation to ensure that each brotherly program computes objects whose size is polynomially bounded by the inputs sizes. Moreover we give some heuristics in order to compute the sup-interpretation of a given method

Automatic Inference of Upper Bounds for Recurrence Relations in Cost Analysis

The classical approach to automatic cost analysis consists of two phases. Given a program and some measure of cost, we first produce recurrence relations (RRs) which capture the cost of our program in terms of the size of its input data. Second, we convert such RRs into closed form (i.e., without recurrences). Whereas the first phase has received considerable attention, with a number of cost analyses available for a variety of programming languages, the second phase has received comparatively little attention. In this paper we first study the features of RRs generated by automatic cost analysis and discuss why existing computer algebra systems are not appropriate for automatically obtaining closed form solutions nor upper bounds of them. Then we present, to our knowledge, the first practical framework for the fully automatic generation of reasonably accurate upper bounds of RRs originating from cost analysis of a wide range of programs. It is based on the inference of ranking functions and loop invariants and on partial evaluation

Quasi-interpretations a way to control resources

International audienceThis paper presents in a reasoned way our works on resource analysis by quasi- interpretations. The controlled resources are typically the runtime, the runspace or the size of a result in a program execution. Quasi-interpretations allow analyzing system complexity. A quasi-interpretation is a numerical assignment, which provides an upper bound on computed func- tions and which is compatible with the program operational semantics. Quasi- interpretation method offers several advantages: (i) It provides hints in order to optimize an execution, (ii) it gives resource certificates, and (iii) finding quasi- interpretations is decidable for a broad class which is relevant for feasible com- putations. By combining the quasi-interpretation method with termination tools (here term orderings), we obtained several characterizations of complexity classes starting from Ptime and Pspace

A characterization of polynomial complexity classes using dependency pairs

The dependency pair method has already shown its power in proving termination of term rewriting systems. We adapt this framework using polynomial assignments in order to characterize with two distinct criteria the set of the functions computable in polynomial time and the set of the functions computable in polynomial space. To our knowledge, this is a first attempt to capture complexity classes using of the dependency pair method. The characterizations presented are inspired by previous works on implicit computational complexity, and, particularly, by the notions of quasi-interpretation and sup-interpretation. Both criteria are decidable so that we can synthesize resource upper-bounds

Global and local space properties of stream programs

The original publication is available at www.springerlink.comInternational audienceIn this paper, we push forward the approach proposed in [1] aiming at studying semantic interpretation criteria for the purpose of ensuring safety and complexity properties of programs working on streams. The paper improves the previous results by considering global and local upper bounds properties of both theoretical and practical interests guaranteeing that the size of each output stream element is bounded by a function in the maximal size of the input stream elements. Moreover, in contrast to previous studies, these properties also apply to a wide class of stream definitions, that is functions that do not have streams in the input but produce an output stream

Characterizations of Polynomial Complexity Classes with a Better Intensionality

ISBN : 978-1-60558-117-0International audienceIn this paper, we study characterizations of polynomial complexity classes using first order functional programs and we try to improve their intensionality, that is the number of natural algorithms captured. We use polynomial assignments over the reals. The polynomial assignments used are inspired by the notions of quasi-interpretation and sup-interpretation, and are decidable when considering polynomials of bounded degree ranging over real numbers. Contrarily to quasi-interpretations, the considered assignments are not required to have the subterm property. Consequently, they capture a strictly larger number of natural algorithms (including quotient, gcd, duplicate elimination from a list) than previous characterizations using quasi-interpretations

Quasi-interpretation Synthesis by Decomposition : An application to higher-order programs

International audienceQuasi-interpretations have shown their interest to deal with resource analysis of first order functional programs. There are at least two reasons to study the question of modularity of quasi-interpretations. Firstly, modularity allows to decrease the complexity of the quasi-inter\-pretation search algorithms. Secondly, modularity allows to increase the intentionality of the quasi-interpretation method, that is the number of captured programs. In particular, we take advantage of modularity conditions to extend smoothly quasi-interpretations to higher order programs. In this paper, we study the modularity of quasi-interpretations through the notions of constructor-sharing and hierarchical unions. We show that in the case of constructor-sharing and hierarchical unions, the existence of quasi-interpretations is no longer a modular property. However, we can still certify the complexity of programs

Proof Theory at Work: Complexity Analysis of Term Rewrite Systems

This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present the main ideas in an easily accessible fashion to make the result presented accessible to the general public. Necessarily some technical points are stated in an over-simplified way.Comment: Cumulative Habilitation Thesis, submitted to the University of Innsbruc