Skip to Main content Skip to Navigation
Theses

Logical foundations of games with imperfect information : uniform strategies

Bastien Maubert 1
1 LogicA - Logic and Applications
IRISA-D4 - LANGAGE ET GÉNIE LOGICIEL, UR1 - Université de Rennes 1, ENS Cachan - École normale supérieure - Cachan
Abstract : There are in the literature many examples of games where the desired strategies are submitted to ''transversal'' constraints involving sets of plays, related by some semantic relation. The most famous example is strategies for games with imperfect information, and games where the objective involves some epistemic aspect provide many more examples. Nevertheless, to the best of our knowledge, there has been no thorough study on this type of constraints in their generality. This is what this thesis intends to start. Therefore, we define a general notion of uniform strategies. Uniformity properties of strategies are expressed in a logical language that extends CTL∗ with two original quantifiers. These quantifiers are very close to the classic knowledge operators of epistemic logics, and they involve sets of plays related by binary relations. We show how this notion of uniform strategies captures the known examples from the literature, and we study in depth the problem of uniform strategy synthesis, assuming that the binary relations between plays can be recognized by finite automata (rational relations). We establish several decidability and complexity results, relying widely on automata techniques: in particular, we introduce as tools jumping tree automata and information sets automata. Moreover, our results enable us to improve existing results and establish new ones, in the domains of model checking epistemic temporal logics, and epistemic planning.
Document type :
Theses
Complete list of metadata

Cited literature [105 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00980490
Contributor : Abes Star :  Contact
Submitted on : Wednesday, May 7, 2014 - 4:00:15 PM
Last modification on : Tuesday, June 15, 2021 - 4:30:20 PM
Long-term archiving on: : Thursday, August 7, 2014 - 10:36:41 AM

File

MAUBERT_Bastien.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-00980490, version 1

Citation

Bastien Maubert. Logical foundations of games with imperfect information : uniform strategies. Other [cs.OH]. Université Rennes 1, 2014. English. ⟨NNT : 2014REN1S001⟩. ⟨tel-00980490⟩

Share

Metrics

Record views

787

Files downloads

653