Geodesic
Delay Games with WMSO+U Winning Conditions
Zimmermann, Martin1
1 Reactive Systems Group, Saarland University, 66123 Saarbrücken, Germany.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 2, pp. 145-165

Voir la notice de l'article provenant de la source Numdam

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. We consider delay games with winning conditions expressed in weak monadic second order logic with the unbounding quantifier, which is able to express (un)boundedness properties. We show that it is decidable whether the delaying player has a winning strategy using bounded lookahead and give a doubly-exponential upper bound on the necessary lookahead. In contrast, we show that bounded lookahead is not always sufficient: we present a game that can be won with unbounded lookahead, but not with bounded lookahead. Then, we consider such games with unbounded lookahead and show that the exact evolution of the lookahead is irrelevant: the winner is always the same, as long as the initial lookahead is large enough and the lookahead is unbounded.

Reçu le :
Accepté le :
DOI : 10.1051/ita/2016018
Classification : 68Q45
Keywords: Delay games, infinite games, unbounding quantifier, max-regular languages

Zimmermann, Martin 1

1 Reactive Systems Group, Saarland University, 66123 Saarbrücken, Germany. 
@article{ITA_2016__50_2_145_0,
     author = {Zimmermann, Martin},
     title = {Delay {Games} with {WMSO}$+${U} {Winning} {Conditions}},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {145--165},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {2},
     year = {2016},
     doi = {10.1051/ita/2016018},
     mrnumber = {3580108},
     zbl = {1356.68138},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2016018/}
}
TY  - JOUR
AU  - Zimmermann, Martin
TI  - Delay Games with WMSO$+$U Winning Conditions
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2016
SP  - 145
EP  - 165
VL  - 50
IS  - 2
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ita/2016018/
DO  - 10.1051/ita/2016018
LA  - en
ID  - ITA_2016__50_2_145_0
ER  - 
%0 Journal Article
%A Zimmermann, Martin
%T Delay Games with WMSO$+$U Winning Conditions
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2016
%P 145-165
%V 50
%N 2
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ita/2016018/
%R 10.1051/ita/2016018
%G en
%F ITA_2016__50_2_145_0
Zimmermann, Martin. Delay Games with WMSO$+$U Winning Conditions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 2, pp. 145-165. doi: 10.1051/ita/2016018

Cité par Sources :