On convergence-sensitive bisimulation and the embedding of CCS in timed CCS

We propose a notion of convergence-sensitive bisimulation that is built just over the notions of (internal) reduction and of (static) context. In the framework of timed CCS, we characterise this notion of `contextual' bisimulation via the usual labelled transition system. We also remark that it provides a suitable semantic framework for a fully abstract embedding of untimed processes into timed ones. Finally, we show that the notion can be refined to include sensitivity to divergence

Enumeration of the Monomials of a Polynomial and Related Complexity Classes

We study the problem of generating monomials of a polynomial in the context of enumeration complexity. In this setting, the complexity measure is the delay between two solutions and the total time. We present two new algorithms for restricted classes of polynomials, which have a good delay and the same global running time as the classical ones. Moreover they are simple to describe, use little evaluation points and one of them is parallelizable. We introduce three new complexity classes, TotalPP, IncPP and DelayPP, which are probabilistic counterparts of the most common classes for enumeration problems, hoping that randomization will be a tool as strong for enumeration as it is for decision. Our interpolation algorithms proves that a lot of interesting problems are in these classes like the enumeration of the spanning hypertrees of a 3-uniform hypergraph. Finally we give a method to interpolate a degree 2 polynomials with an acceptable (incremental) delay. We also prove that finding a specified monomial in a degree 2 polynomial is hard unless RP = NP. It suggests that there is no algorithm with a delay as good (polynomial) as the one we achieve for multilinear polynomials

A note on the enumeration of directed animals via gas considerations

In the literature, most of the results about the enumeration of directed animals on lattices via gas considerations are obtained by a formal passage to the limit of enumeration of directed animals on cyclical versions of the lattice. Here we provide a new point of view on this phenomenon. Using the gas construction given in [Electron. J. Combin. (2007) 14 R71], we describe the gas process on the cyclical versions of the lattices as a cyclical Markov chain (roughly speaking, Markov chains conditioned to come back to their starting point). Then we introduce a notion of convergence of graphs, such that if $(G_n)\to G$ then the gas process built on $G_n$ converges in distribution to the gas process on $G$. That gives a general tool to show that gas processes related to animals enumeration are often Markovian on lines extracted from lattices. We provide examples and computations of new generating functions for directed animals with various sources on the triangular lattice, on the $\mathcal {T}_n$ lattices introduced in [Ann. Comb. 4 (2000) 269--284] and on a generalization of the \mathcaligr {L}_n lattices introduced in [J. Phys. A 29 (1996) 3357--3365].Comment: Published in at http://dx.doi.org/10.1214/08-AAP580 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org