Shrinking games and local formulas

Shrinking games and local formulas

Gaifman’s normal form theorem showed that every first order sentence of quantifier rank n is equivalent to a Boolean combination of “scattered local sentences”, where the local neighborhoods have radius at most 7n−1. This bound was improved by Lifsches and Shelah to 3 · 4n−1. We use Ehrenfeucht-Fräıssé type games with a “shrinking horizon” to get a spectrum of normal form theorems of the Gaifma...

Valid formulas, games and network protocols

We describe a remarkable relation between a fundamental notion of mathematical logic – that is valid formula of predicate calculus – and the specification of network protocols. We explain here in detail several simple examples : the acknowledgement of one or two packets, and then of an arbitrary number. We show that, using this method, it is possible to specify the composition of protocols. We ...

2 00 7 Valid formulas , games and network protocols

We describe a remarkable relation between a fundamental notion of mathematical logic – that is valid formula of predicate calculus – and the specification of network protocols. We explain here in detail several simple examples : the acknowledgement of one or two packets, and then of an arbitrary number. We tried to write a self-contained paper, as far as possible, in what concerns the basic not...

On Local and Network Games

Evolutionary Games and Local Dynamics

Evolutionary games have been introduced by Maynard Smith and Price [1973] in the early 70’s with the aim to study the stability of populations in time. In the general model, a population consists of finitely many different types that interact randomly with each other, where each interaction leads to fitness payoffs for each of the types involved. Consequently, the population distribution over t...