Theory of higher order interpretations and application to Basic Feasible Functions

Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional language. We develop a theory of higher order functions that is well-suited for the complexity analysis of this programming language. The interpretation domain is a complete lattice and, consequently, we express program interpretation in terms of a least fixpoint. As an application, by bounding interpretations by higher order polynomials, we characterize Basic Feasible Functions at any order

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

Characterizing polynomial time complexity of stream programs using interpretations

This paper provides a criterion based on interpretation methods on term rewrite systems in order to characterize the polynomial time complexity of second order functionals. For that purpose it introduces a first order functional stream language that allows the programmer to implement second order functionals. This characterization is extended through the use of exp-poly interpretations as an attempt to capture the class of Basic Feasible Functionals (bff). Moreover, these results are adapted to provide a new characterization of polynomial time complexity in computable analysis. These characterizations give a new insight on the relations between the complexity of functional stream programs and the classes of functions computed by Oracle Turing Machine, where oracles are treated as inputs

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

State and multilateralism, a theoretical approach. Transformations in a globalized international society

The State, classical international actor, has had to readaption to the new dynamics in the International Society and has given prominence to other actors. In this logic, it´s relevant to analyze the role in the international system after the Cold War to evaluare whether it is still an actor capable of responding to the functional needs of the society. For this, reaffirms its commitment to multilateralism as a response to the main issue on the international agenda. Namely, is reactivated as an ideal tool to manage structural changes, despite the different interpretations of United States, the European Union or the BRICS. The object of this analysis contribute to the academic debate and focuses on studying the transformations of the State in the globalized international society where multilateralism has become a concept discussed and a common practice in the international discourse, despite its complexity and the different visions and interpretations by different actors. Multilateralism granted the State a path of cooperation and understanding as a guiding principle and foreign policy legitimizing discours

12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto

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

On Quasi-Interpretations, Blind Abstractions and Implicit Complexity

Quasi-interpretations are a technique to guarantee complexity bounds on first-order functional programs: with termination orderings they give in particular a sufficient condition for a program to be executable in polynomial time, called here the P-criterion. We study properties of the programs satisfying the P-criterion, in order to better understand its intensional expressive power. Given a program on binary lists, its blind abstraction is the nondeterministic program obtained by replacing lists by their lengths (natural numbers). A program is blindly polynomial if its blind abstraction terminates in polynomial time. We show that all programs satisfying a variant of the P-criterion are in fact blindly polynomial. Then we give two extensions of the P-criterion: one by relaxing the termination ordering condition, and the other one (the bounded value property) giving a necessary and sufficient condition for a program to be polynomial time executable, with memoisation.Comment: 18 page