A note on the computational complexity of a string orbit problem (DRAFT)
نویسنده
چکیده
It is proven that finding the lexicographically greatest (smallest) string in the orbit of a given string under the position permuting action of a permutation group is an FP-complete problem. This gives an affirmative answer to an open problem of Babai and Luks (1983, Proc. 15th Annual ACM STOC): determining the value of the element at a given position in the lexicographically greatest (smallest) string in the orbit of a string is a ∆2P-complete problem. It is also shown that verifying whether a string is the lexicographical leader in its own orbit is a co-NP-complete problem. A generalized case of arbitrary polynomial time actions is also briefly discussed and an open problem is presented.
منابع مشابه
Reduction of Computational Complexity in Finite State Automata Explosion of Networked System Diagnosis (RESEARCH NOTE)
This research puts forward rough finite state automata which have been represented by two variants of BDD called ROBDD and ZBDD. The proposed structures have been used in networked system diagnosis and can overcome cominatorial explosion. In implementation the CUDD - Colorado University Decision Diagrams package is used. A mathematical proof for claimed complexity are provided which shows ZBDD ...
متن کاملThree Meta-heuristic Algorithms for the Single-item Capacitated Lot-sizing Problem (RESEARCH NOTE)
This paper proposes a mixed integer programming model for single-item capacitated lot-sizing problem with setup times, safety stock, demand shortages, outsourcing and inventory capacity. Due to the complexity of problem, three meta-heuristics algorithms named simulated annealing (SA), vibration damping optimization (VDO) and harmony search (HS) have been used to solve this model. Additionally, ...
متن کاملModeling of Partial Digest Problem as a Network flows problem
Restriction Site Mapping is one of the interesting tasks in Computational Biology. A DNA strand can be thought of as a string on the letters A, T, C, and G. When a particular restriction enzyme is added to a DNA solution, the DNA is cut at particular restriction sites. The goal of the restriction site mapping is to determine the location of every site for a given enzyme. In partial digest metho...
متن کاملOn the computational complexity of finding a minimal basis for the guess and determine attack
Guess-and-determine attack is one of the general attacks on stream ciphers. It is a common cryptanalysis tool for evaluating security of stream ciphers. The effectiveness of this attack is based on the number of unknown bits which will be guessed by the attacker to break the cryptosystem. In this work, we present a relation between the minimum numbers of the guessed bits and uniquely restricted...
متن کاملOn the Computational Complexity of the Domination Game
The domination game is played on an arbitrary graph $G$ by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer $k$ is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph $G$ in $mathcal O(Delta(G)cdot |V(G)|^k)$ time. In the special case when $k=3$ and the...
متن کامل