Public lecture by Hans van Ditmarsch
One Hundred Prisoners and a Lightbulb
A public lecture by Hans van Ditmarsch, Senior Researcher, Centre National de la Recherche Scientifique, France
Consider this riddle:
"A group of 100 prisoners, all together in the prison dining area, are told that they will be all put in isolation cells and then will be interrogated one by one in a room containing a light with an on/off switch. The prisoners may communicate with one another by toggling the light-switch (and that is the only way in which they can communicate). The light is initially switched off. There is no fixed order of interrogation, or interval between interrogations, and the same prisoner will be interrogated again at any stage. When interrogated, a prisoner can either do nothing, or toggle the light-switch, or announce that all prisoners have been interrogated. If that announcement is true, the prisoners will (all) be set free, but if it is false, they will all be executed. While still in the dining room, and before the prisoners go to their isolation cells (forever), can the prisoners agree on a protocol that will set them free?"
Dr van Ditmarsch's talk will present a solution, however his talk will mainly address such puzzles of knowledge in general. There are many others, such as the ‘Muddy Children Puzzle’ (also known as the ‘Wisemen Puzzle’), ‘Surprise Examination’, ‘Monty Hall’, etc. They often involve a (seemingly) paradoxical aspect making agents knowledgeable by announcements of their ignorance. More information on such puzzles is found on https://personal.us.es/hvd/lightbulb.html. This also refers to the book entitled One Hundred Prisoners and a Light Bulb, co-authored by Hans van Ditmarsch and Barteld Kooi (Groningen). There is a relation with the area in logic known as ‘dynamic epistemic logic’.
Hans van Ditmarsch is a senior researcher at CNRS (the French National Research Organization), and based at LORIA in Nancy, where he is heading the research team CELLO (Computational Epistemic Logic in Lorraine). He is also affiliated to IMSc (Institute for Mathematical Sciences), in Chennai. He is the recipient of an ERC (European Research Council) starting grant Epistemic Protocol Synthesis. His research is on the dynamics of knowledge and belief, information-based security protocols, modal logics, and combinatorics. He has been an editor of the Journal of Philosophical Logic. He is an author of the book Dynamic Epistemic Logic, an editor of the Handbook of Epistemic Logic, and an author of the puzzlebook One Hundred Prisoners and a Light Bulb. He is currently an Institute of Advanced Studies Visiting Fellow at The University of Western Australia, working with Dr Tim French, Senior Lecturer in Computer Science and Software Engineering.