33 research outputs found
Newton series, coinductively
We present a comparative study of four product operators on weighted languages: (i) the convolution, (ii) the shue, (iii) the inltration, and (iv) the Hadamard product. Exploiting the fact that the set of weighted languages is a nal coalgebra, we use coinduction to prove that a classical operator from dierence calculus in mathematics: the Newton transform, generalises (from innite sequences) to weighted lan- guages. We show that the Newton transform is an isomorphism of rings that transforms the Hadamard product of two weighted languages into an inltration product, and we develop various representations for the Newton transform of a language, together with concrete calculation rules for computing them
Rationality and Escalation in Infinite Extensive Games
The aim of this of this paper is to study infinite games and to prove
formally some properties in this framework. As a consequence we show that the
behavior (the madness) of people which leads to speculative crashes or
escalation can be fully rational. Indeed it proceeds from the statement that
resources are infinite. The reasoning is based on the concept of coinduction
conceived by computer scientists to model infinite computations and used by
economic agents unknowingly. When used consciously, this concept is not as
simple as induction and we could paraphrase Newton: "Modeling the madness of
people is more difficult than modeling the motion of planets".Comment: arXiv admin note: substantial text overlap with arXiv:1004.5257,
arXiv:0904.3528, and arXiv:0912.174
Sequentiality vs. Concurrency in Games and Logic
Connections between the sequentiality/concurrency distinction and the
semantics of proofs are investigated, with particular reference to games and
Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc
Behavioural differential equations : a coinductive calculus of streams, automata, and power series
Streams, (automata and) languages, and formal power series are viewed coalgebraically. In summary, this amounts to supplying these sets with a deterministic automaton structure, which has the universal property of being final. Finality then forms the basis for both definitions and proofs by coinduction, the coalgebraic counterpart of induction