5 results
Thomas Colcombet ; Christof Löding.
We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of […]
Published on May 4, 2007
Thomas Colcombet.
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to each input the two values "inside" and "outside". This theory […]
Published on August 13, 2013
Thomas Colcombet ; Daniela Petrişan.
In this paper we regard languages and their acceptors - such as deterministic or weighted automata, transducers, or monoids - as functors from input categories that specify the type of the languages and of the machines to categories that specify the type of outputs. Our results are as follows: A) […]
Published on March 23, 2020
Thomas Colcombet ; Nathanaël Fijalkow ; Pierre Ohlmann.
Bertrand et al. introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all agents to a target state? They showed that the problem is […]
Published on November 24, 2021
Thomas Colcombet ; Nathanaël Fijalkow ; Paweł Gawrychowski ; Pierre Ohlmann.
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals: showing an equivalence and normalisation result between […]
Published on September 7, 2022