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

Developing a critical realist positional approach to intersectionality

This article identifies philosophical tensions and limitations within contemporary intersectionality theory which, it will be argued, have hindered its ability to explain how positioning in multiple social categories can affect life chances and influence the reproduction of inequality. We draw upon critical realism to propose an augmented conceptual framework and novel methodological approach that offers the potential to move beyond these debates, so as to better enable intersectionality to provide causal explanatory accounts of the ‘lived experiences’ of social privilege and disadvantage

On Sharing, Memoization, and Polynomial Time (Long Version)

We study how the adoption of an evaluation mechanism with sharing and memoization impacts the class of functions which can be computed in polynomial time. We first show how a natural cost model in which lookup for an already computed value has no cost is indeed invariant. As a corollary, we then prove that the most general notion of ramified recurrence is sound for polynomial time, this way settling an open problem in implicit computational complexity

The Last Scientific Revolution

Critically growing problems of fundamental science organisation and content are analysed with examples from physics and emerging interdisciplinary fields. Their origin is specified and new science structure (organisation and content) is proposed as a unified solution

Money makes the world go round: Shakespeare, commerce and community

In early modern England money was of central importance to areas of social life that are in the modern world separate from the study of economics. The demand for liquid capital and the practical problems associated with the devising of a monetary system that was reliable exercised the minds of philosophers, social commentators, and dramatists. The template for discussion was laid down by Aristotle, who perceived financial activity as part of the larger community and its various modes of social interaction. Copernicus wrote a treatise on money, as had Nicholas of Oresme before him. But in the sixteenth century dramatists turned their attention to what we would call “economics” and its impact on social life. Writers such as Thomas Lupton, Christopher Marlowe, Ben Jonson, and Shakespeare all dealt with related issues of material greed, usury, hospitality and friendship and the ways in which they transformed, and were transformed by particular kinds of social and economic practice. These concerns fed into the investigation of different kinds of society, particularly turning their attention to their strengths and weaknesses, and in the case of dramatists providing imaginative accounts of the kinds of life that these innovations produced