Jamie Seol
Yonsei University, Mathematics, Undergraduate
- Geometry And Topology, Differential Geometry, Automata Theory (Formal Languages), Threory of Computaion, UI/UX Design, Mathematics, and 20 moreMathematics and Computer Science, Probability Theory, Probability and statistics, Hanoi, Hanoi Tower, Cellular Automata, Matematica, Applied Mathematics, Computer Science, Cryptography, Cryptographic Hash Function, Life-like Cellular Automata, Computer Graphics, Optics, Reflection, Refraction, Rainbow, Mathematical Physics, Classical Mechanics, and Engineeringedit
Research Interests:
Cryptographic Hash Function (in short, CHF) is a useful tool for implementing one-wayencryptionthatishardtorestoretheplaintext. CHFisdefinedasafunctionfromsome set X to fixed sized string, with almost-injective property and hard to... more
Cryptographic Hash Function
(in short, CHF) is a useful tool for implementing one-wayencryptionthatishardtorestoretheplaintext. CHFisdefinedasafunctionfromsome set X to fixed sized string, with almost-injective property and hard to restore theoriginal input. There are many famous algorithms such as
SHA-1
, commonly usedfor encrypting plain text into a string composed of alphabet and numbers, with size40. One interesting thing is, a
Cellular Automata
(in short, CA) has similar behavioras CHF. CA is deterministic to initial state so it’s well-defined function, and differentinitial state generates almost different output. If we take CA rule as
Life-Like Cellular Automata
(in short, LLCA), then it would be hard to guess initial state from generatedoutput since LLCA has non-deterministic property for inverse mapping, i.e., it’s
NP
problem. Therefore if we can encode given input to appropriate CA initial state andthe result, then LLCA would be suitable CHF
(in short, CHF) is a useful tool for implementing one-wayencryptionthatishardtorestoretheplaintext. CHFisdefinedasafunctionfromsome set X to fixed sized string, with almost-injective property and hard to restore theoriginal input. There are many famous algorithms such as
SHA-1
, commonly usedfor encrypting plain text into a string composed of alphabet and numbers, with size40. One interesting thing is, a
Cellular Automata
(in short, CA) has similar behavioras CHF. CA is deterministic to initial state so it’s well-defined function, and differentinitial state generates almost different output. If we take CA rule as
Life-Like Cellular Automata
(in short, LLCA), then it would be hard to guess initial state from generatedoutput since LLCA has non-deterministic property for inverse mapping, i.e., it’s
NP
problem. Therefore if we can encode given input to appropriate CA initial state andthe result, then LLCA would be suitable CHF
Research Interests:
Let p be probability of event occurence for each trigger. Then one would expect that event can not be not occur in ⌈1/p⌉ triggers in a row. Similarly, event can not be occured in ⌈1/(1 − p)⌉ triggers in a row. One will also expect pn... more
Let p be probability of event occurence for each trigger. Then one would expect that event can not be not occur in ⌈1/p⌉ triggers in a row. Similarly, event can not be occured in ⌈1/(1 − p)⌉ triggers in a row. One will also expect pn event occurences among n triggers. The former is local property and the other is global property. To make this happen, we should adjust probability manually. This paper introduces simple algorithm to construct ideal result for given probability, that fits well even in low n. This idea can be applied in many fields, for example, critical reward system from online game "League of Legends", and item reward system from MMO RPG "World of Warcraft", which shortly can be expressed as "1% guarantees at least 1 event among 100 triggers".
Research Interests:
”Tower of Hanoi”, or simply ”Hanoi Tower” is mathematical game which is mov- ing some size-ordered disks from one peg to the other without stacking inverse order due to size. Traditional game has 3 pegs on condition, but many people... more
”Tower of Hanoi”, or simply ”Hanoi Tower” is mathematical game which is mov- ing some size-ordered disks from one peg to the other without stacking inverse order due to size. Traditional game has 3 pegs on condition, but many people started to study about p ≥ 4 case where p is number of pegs. Solving the 3-peg game in least movements has been simply solved in many ways, but p ≥ 4 version of this prob- lem has yet not solved, know as ”Frame-Stewart Conjecture”. [?, ?] This paper has 2 try-outs to solve least movement requirement between two general states on Hanoi Tower. It starts with defining term ”general state” using regular expression from au- tomata theory, and illustrates two try-outs, which has failed.