NDLI: The Exact Query Complexity of Yes-No Permutation Mastermind

Please wait, while we are loading the content...

The Exact Query Complexity of Yes-No Permutation Mastermind

Content Provider	MDPI
Author	Ouali, Mourad El Sauerland, Volkmar
Copyright Year	2020
Abstract	Mastermind is famous two-player game. The first player (codemaker) chooses a secret code which the second player (codebreaker) is supposed to crack within a minimum number of code guesses (queries). Therefore, the codemaker’s duty is to help the codebreaker by providing a well-defined error measure between the secret code and the guessed code after each query. We consider a variant, called Yes-No AB-Mastermind, where both secret code and queries must be repetition-free and the provided information by the codemaker only indicates if a query contains any correct position at all. For this Mastermind version with n positions and $k \geq n$ colors and $ℓ : = k + 1 - n$ , we prove a lower bound of $\sum_{j = ℓ}^{k} {log}_{2} j$ and an upper bound of $n {log}_{2} n + k$ on the number of queries necessary to break the secret code. For the important case $k = n$ , where both secret code and queries represent permutations, our results imply an exact asymptotic complexity of $Θ (n log n)$ queries.
Starting Page	19
e-ISSN	20734336
DOI	10.3390/g11020019
Journal	Games
Issue Number	2
Volume Number	11
Language	English
Publisher	MDPI
Publisher Date	2020-04-13
Access Restriction	Open
Subject Keyword	Games Operations Research and Management Science Mastermind Permutation Query Complexity
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in