Computer Science / Formal Languages

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The complexity of tangent words

The complexity of tangent words

์ด ๋…ผ๋ฌธ์€ ๋งค๋„๋Ÿฌ์šด ๊ณก์„ ๊ณผ ๊ทธ์— ๋Œ€ํ•œ ์ ‘์„  ๋‹จ์–ด์˜ ์–ธ์–ด์  ์ ‘๊ทผ๋ฒ•์„ ์ฒด๊ณ„์ ์œผ๋กœ ๋ถ„์„ํ•œ๋‹ค. ์ฃผ์š” ๋‚ด์šฉ์€ ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค: 1. ๋งค๋„๋Ÿฌ์šด ๊ณก์„ ์˜ ์ •์˜์™€ ํŠน์„ฑ : ๋งค๋„๋Ÿฌ์šด ๊ณก์„ ์€ ์‹ค์ˆ˜ ์ง์„  ์œ„์˜ ์ปดํŒฉํŠธ ๊ตฌ๊ฐ„ I์—์„œ ์ •์˜๋˜๋ฉฐ, ๋ชจ๋“  t โˆˆ I ์— ๋Œ€ํ•ด ||ฮณโ€ฒ(t)|| > 0 ์ด๋ผ๋Š” ๊ทœ์น™์„ฑ์„ ๋งŒ์กฑํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ๊ณก์„ ์€ ์›ํ•˜๋Š” ๋งŒํผ ์žฌ๋งค๊ฐœ๋ณ€์ˆ˜ํ™”๋  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์ผ๋ฐ˜์ ์œผ๋กœ ๊ฐ t ์— ๋Œ€ํ•ด ||ฮณโ€ฒ(t)|| 1 ์ด๋‹ค. ๋งค๋„๋Ÿฌ์šด ๊ณก์„ ์˜ ๊ทผ์‚ฌ ๋ฐฉ๋ฒ•์œผ๋กœ ํ‰๋ฉด์— ๊ฒฉ์ž๋ง์„ ๊ทธ๋ ค์„œ ๊ณก์„ ์ด ๋งŒ๋‚˜๋Š” ์‚ฌ๊ฐํ˜•์˜ ์ˆœ์„œ๋ฅผ ์‚ดํŽด๋ณธ๋‹ค. ์ด ์ ˆ๋‹จ ์ˆœ์„œ๋Š” ์ƒ, ํ•˜, ์ขŒ, ์šฐ ๋ฐฉํ–ฅ์œผ

Formal Languages Computational Geometry Computer Science Discrete Mathematics
Biologically Inspired Process Calculi, Petri Nets and Membrane Computing

Biologically Inspired Process Calculi, Petri Nets and Membrane Computing

: ์ด ์ฑ…์€ ๋ง‰ ๊ตฌ์กฐ ์ปดํ“จํŒ…(Membrane Computing) ๋ฐ ์ƒ๋ฌผํ•™์ ์œผ๋กœ ์˜๊ฐ์„ ๋ฐ›์€ ํ”„๋กœ์„ธ์Šค ๊ณ„์‚ฐ(Biologically Inspired Process Calculus) ๋ถ„์•ผ์—์„œ ์ค‘์š”ํ•œ ์—ฐ๊ตฌ ์„ฑ๊ณผ๋“ค์„ ๋ชจ์•„๋†“์€ ๊ธฐ๋ก์ž…๋‹ˆ๋‹ค. ํŠนํžˆ, ํŽ˜ํŠธ๋ฆฌ ๋„คํŠธ(Petri Net)๋ฅผ ํ™œ์šฉํ•œ ์—ฐ๊ตฌ๊ฐ€ ๊ฐ•์กฐ๋˜์–ด ์žˆ์–ด ์ด ์„ธ ๊ฐ€์ง€ ์ฃผ์ œ ์‚ฌ์ด์˜ ์ƒํ˜ธ์ž‘์šฉ์„ ์ž˜ ๋ณด์—ฌ์ฃผ๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. ๋ง‰ ๊ตฌ์กฐ ์ปดํ“จํŒ…์€ ์ƒ๋ฌผํ•™์  ์‹œ์Šคํ…œ์—์„œ ์˜๊ฐ์„ ๋ฐ›์•„ ๊ฐœ๋ฐœ๋œ ๊ณ„์‚ฐ ๋ชจ๋ธ๋กœ, ํŠนํžˆ ์„ธํฌ ๋‚ด์—์„œ ๋ฐœ์ƒํ•˜๋Š” ๋ณต์žกํ•œ ํ™”ํ•™ ๋ฐ˜์‘๊ณผ ์ •๋ณด ํ๋ฆ„์„ ๋ชจ๋ธ๋งํ•˜๋Š”๋ฐ ์‚ฌ์šฉ๋ฉ๋‹ˆ๋‹ค. ์ด ๋ถ„์•ผ๋Š” ์ž๋™ํ™”, ํ˜•

Formal Languages Distributed Computing Computer Science
No Image

Multiscale Modelling: A Mobile Membrane Approach

: ๋ณธ ๋…ผ๋ฌธ์€ ์ƒ๋ฌผํ•™์  ๊ณผ์ • ์—ฐ๊ตฌ์— ์žˆ์–ด ๋‹ค์ค‘ ๊ทœ๋ชจ ๋ชจ๋ธ๋ง์˜ ์ค‘์š”์„ฑ๊ณผ ๊ทธ ๊ตฌํ˜„ ๋ฐฉ๋ฒ•์„ ํƒ๊ตฌํ•˜๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. ํŠนํžˆ, ์ด๋™์„ฑ ๋ง‰ ์‹œ์Šคํ…œ์ด ์ด๋Ÿฌํ•œ ๋ชจ๋ธ๋ง ์ ‘๊ทผ๋ฒ•์—์„œ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•˜๋Š”๋ฐ ์ดˆ์ ์„ ๋งž์ถ”๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. 1. ๋‹ค์ค‘ ๊ทœ๋ชจ ๋ชจ๋ธ๋ง์˜ ํ•„์š”์„ฑ ์ž์—ฐ ํ˜„์ƒ์€ ๋‹ค์–‘ํ•œ ๊ณต๊ฐ„์  ๋ฐ ์‹œ๊ฐ„์  ๊ทœ๋ชจ์—์„œ ์ƒํ˜ธ์ž‘์šฉํ•˜๋ฉฐ ๋ฐœ์ƒํ•ฉ๋‹ˆ๋‹ค. ๋”ฐ๋ผ์„œ, ์ด๋ฅผ ํšจ๊ณผ์ ์œผ๋กœ ์—ฐ๊ตฌํ•˜๋ ค๋ฉด ๋‹ค์ค‘ ๊ทœ๋ชจ ๋ชจ๋ธ๋ง์ด ํ•„์ˆ˜์ ์ž…๋‹ˆ๋‹ค. ๋ณต์žก ์ž๋™๋ฌธ(CxA)์€ ์ด๋Ÿฌํ•œ ๋‹ค์ค‘ ๊ทœ๋ชจ ์ ‘๊ทผ๋ฒ•์„ ๊ตฌํ˜„ํ•˜๋Š” ๋ฐ ๊ฐ€์žฅ ์ ํ•ฉํ•œ ์‹œ์Šคํ…œ์œผ๋กœ ๊ฐ„์ฃผ๋ฉ๋‹ˆ๋‹ค. 2. ์ด๋™์„ฑ ๋ง‰ ์‹œ์Šคํ…œ์˜ ํ™œ์šฉ ์ด๋™์„ฑ ๋ง‰ ์‹œ์Šคํ…œ์€ ์ƒ๋ฌผํ•™์  ์›€

Formal Languages Quantitative Biology Model Computer Science Emerging Technologies
Petri Nets and Bio-Modelling - and how to benefit from their synergy

Petri Nets and Bio-Modelling - and how to benefit from their synergy

: ๋ณธ ๋…ผ๋ฌธ์€ ํŽ˜ํŠธ๋ฆฌ๋„ท๊ณผ ์ƒ๋ฌผํ•™์  ์‹œ์Šคํ…œ ๊ฐ„์˜ ์ƒํ˜ธ์ž‘์šฉ์„ ํ†ตํ•ด ์–ป์„ ์ˆ˜ ์žˆ๋Š” ์ด์ ์„ ํƒ๊ตฌํ•ฉ๋‹ˆ๋‹ค. ํŽ˜ํŠธ๋ฆฌ๋„ท์€ ๋™์‹œ์„ฑ๊ณผ ๋ถ„์‚ฐ ๊ณ„์‚ฐ์„ ์œ„ํ•œ ๊ฐ•๋ ฅํ•œ ๋„๊ตฌ๋กœ, ํ–‰๋™ ํŠน์„ฑ์„ ๋ถ„์„ํ•˜๊ณ  ๊ฒ€์ฆํ•˜๋Š” ๋ฐ ์‚ฌ์šฉ๋ฉ๋‹ˆ๋‹ค. ์ƒ๋ฌผํ•™์  ๊ณผ์ •์„ ์ดํ•ดํ•˜๊ธฐ ์œ„ํ•ด ์ œ์•ˆ๋œ ๋ง‰ ์‹œ์Šคํ…œ๊ณผ ๋ฐ˜์‘ ์‹œ์Šคํ…œ์€ ์„ธํฌ ๋‚ด ํ™”ํ•™ ๋ฐ˜์‘์„ ์ถ”์ƒํ™”ํ•œ ๋ชจ๋ธ์ž…๋‹ˆ๋‹ค. ํŽ˜ํŠธ๋ฆฌ๋„ท์˜ ์›์ธ๊ณผ ๋™์‹œ์„ฑ ์˜๋ฏธ๋ก ์— ๋Œ€ํ•œ ์ดํ•ด๋Š” ํŽ˜ํŠธ๋ฆฌ๋„ท์ด ์–ด๋–ป๊ฒŒ ์ƒ๋ฌผํ•™์  ๊ณผ์ •์„ ์ •ํ™•ํžˆ ๋ชจ๋ธ๋งํ•  ์ˆ˜ ์žˆ๋Š”์ง€ ์„ค๋ช…ํ•˜๋Š” ๋ฐ ์ค‘์š”ํ•ฉ๋‹ˆ๋‹ค. ๋ง‰ ์‹œ์Šคํ…œ์€ ์„ธํฌ ๋‚ด ํ™”ํ•™ ๋ฐ˜์‘์—์„œ ์˜๊ฐ์„ ๋ฐ›์•„ ๊ฐœ๋ฐœ๋˜์—ˆ์œผ๋ฉฐ, ์ด๋Š” ํŽ˜ํŠธ๋ฆฌ๋„ท๊ณผ ์œ ์‚ฌํ•œ ๋‹ค์ค‘ ์ง‘ํ•ฉ ์žฌ๊ตฌ

Formal Languages Distributed Computing Model Computer Science
Superiority of exact quantum automata for promise problems

Superiority of exact quantum automata for promise problems

: ๋ณธ ๋…ผ๋ฌธ์€ ์–‘์ž ์ปดํ“จํŒ…๊ณผ ๊ณ ์ „์  ์ปดํ“จํŒ…์˜ ์„ฑ๋Šฅ ์ฐจ์ด์— ๋Œ€ํ•œ ์‹ฌ๋„ ์žˆ๋Š” ๋ถ„์„์„ ์ œ๊ณตํ•ฉ๋‹ˆ๋‹ค. ํŠนํžˆ, ์–‘์ž ์˜คํ† ๋งˆํƒ€์™€ ๊ฒฐ์ •์  ์œ ํ•œ ์˜คํ† ๋งˆํƒ€(DFA)๋ฅผ ๋น„๊ตํ•˜์—ฌ ์–‘์ž์˜ ์šฐ์›”์„ฑ์„ ์ž…์ฆํ•˜๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. 1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ์–‘์ž ๊ณ„์‚ฐ์€ ๋ถ€๋ถ„ ํ•จ์ˆ˜์™€ ์ „์ฒด ํ•จ์ˆ˜์— ๋Œ€ํ•œ ๊ด‘๋ฒ”์œ„ํ•œ ์—ฐ๊ตฌ๊ฐ€ ์ด๋ฃจ์–ด์ ธ ์™”์Šต๋‹ˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์ž๋™ํ™” ์ด๋ก ์—์„œ๋Š” ์–‘์ž ์œ ํ•œ ์˜คํ† ๋งˆํƒ€(QFA)์˜ ์„ฑ๋Šฅ์„ ๋ถ„์„ํ•˜๋Š” ๊ฒฐ๊ณผ๋Š” ๋งค์šฐ ์ œํ•œ์ ์ด์—ˆ์Šต๋‹ˆ๋‹ค. Klauck

Formal Languages Quantum Physics Computational Complexity Computer Science
Reversibility in Massive Concurrent Systems

Reversibility in Massive Concurrent Systems

: ๋ณธ ๋…ผ๋ฌธ์€ ๋Œ€๊ทœ๋ชจ ๋ณ‘๋ ฌ ์‹œ์Šคํ…œ์—์„œ ์—ญ์ „ ๊ฐ€๋Šฅ์„ฑ์˜ ๊ฐœ๋…๊ณผ ๊ทธ ์ ์šฉ ๋ฒ”์œ„๋ฅผ ํƒ๊ตฌํ•˜๊ณ  ์žˆ๋‹ค. ์—ญ์ „ ๊ฐ€๋Šฅ์„ฑ์€ ์ž…๋ ฅ ๋ฐ์ดํ„ฐ๊ฐ€ ์ˆœ์ฐจ์ ์œผ๋กœ ์ฒ˜๋ฆฌ๋˜๋ฉด์„œ, ์ฒซ ๋ฒˆ์งธ ์ž…๋ ฅ์ด ๋‘ ๋ฒˆ์งธ ์ž…๋ ฅ ์—†์ด๋„ ๋ฐฉ์ถœ๋˜์–ด ๋‹ค๋ฅธ ์—ฐ์‚ฐ์ž์— ์˜ํ•ด ์‚ฌ์šฉ๋  ์ˆ˜ ์žˆ๋Š” ๋Šฅ๋ ฅ์„ ์˜๋ฏธํ•œ๋‹ค. ์ด๋Š” ๋ณ‘๋ ฌ ์‹œ์Šคํ…œ์—์„œ ํšจ์œจ์ ์ธ ๋ฐ์ดํ„ฐ ์ฒ˜๋ฆฌ์™€ ํ”„๋กœ์„ธ์‹ฑ์„ ๊ฐ€๋Šฅํ•˜๊ฒŒ ํ•˜๋Š” ์ค‘์š”ํ•œ ํŠน์„ฑ์ด๋‹ค. ๋…ผ๋ฌธ์€ ์—ญ์ „ ๊ฐ€๋Šฅ์„ฑ์˜ ๊ตฌ์กฐ๋ฅผ ๋ถ„์„ํ•˜๋ฉด์„œ, ํŠนํžˆ ์ผ๊ด€์„ฑ ์ œ์•ฝ ์กฐ๊ฑด ํ•˜์—์„œ ๋‹ค์ค‘์„ฑ์ด ์ œ๊ฑฐ๋œ ์—ญ์ „ ๊ฐ€๋Šฅํ•œ ๊ตฌ์กฐ์— ์ดˆ์ ์„ ๋งž์ถ”๊ณ  ์žˆ๋‹ค. ์ด๋Š” ๋ณ‘๋ ฌ ์‹œ์Šคํ…œ ๋‚ด์—์„œ ๋ฐ์ดํ„ฐ ์ฒ˜๋ฆฌ ๊ณผ์ •์ด ์ผ๊ด€์„ฑ์„ ์œ ์ง€ํ•˜๋„๋ก ํ•˜๋Š” ์ค‘์š”ํ•œ

Formal Languages Distributed Computing Computer Science System
Jancars formal system for deciding bisimulation of first-order grammars and its non-soundness

Jancars formal system for deciding bisimulation of first-order grammars and its non-soundness

: 1. ์ฒซ ๋ฒˆ์งธ ์ˆœ์„œ ๋ฌธ๋ฒ•๊ณผ ํ–‰๋™ ์•ŒํŒŒ๋ฒณ์˜ ์ •์˜ ๋…ผ๋ฌธ์€ ์ฒซ ๋ฒˆ์งธ ์ˆœ์„œ ๋ฌธ๋ฒ•์— ๋Œ€ํ•œ ๋น„์‹œ๋ฎฌ๋ ˆ์ด์…˜ ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•ด Jancar์˜ ํ˜•์‹ ์‹œ์Šคํ…œ์„ ๊ฒ€ํ† ํ•œ๋‹ค. ์ด ๊ณผ์ •์—์„œ ํ–‰๋™ ์•ŒํŒŒ๋ฒณ A์™€ ์ค‘๊ฐ„ ๋ผ๋ฒจ ์•ŒํŒŒ๋ฒณ T, ๊ทธ๋ฆฌ๊ณ  ๋งต LAB A: T โ†’ A๋ฅผ ์ •์˜ํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ์ •์˜๋Š” ์ฒซ ๋ฒˆ์งธ ์ˆœ์„œ ๋ฌธ๋ฒ• G (N, A, R)์„ ๊ตฌ์„ฑํ•˜๋Š” ๋ฐ ํ•„์š”ํ•œ ๊ธฐ๋ณธ ์š”์†Œ๋ฅผ ์ œ๊ณตํ•˜๋ฉฐ, ์—ฌ๊ธฐ์„œ N์€ ๋น„ํ„ฐ๋ฏธ๋„ ์ง‘ํ•ฉ, A๋Š” ํ–‰๋™ ์•ŒํŒŒ๋ฒณ, ๊ทธ๋ฆฌ๊ณ  R์€ ๊ทœ์น™ ์ง‘ํ•ฉ์ด๋‹ค. 2. Jancar ํ˜•์‹ ์‹œ์Šคํ…œ์˜ ๊ฐœ์š” Jancar์˜ ํ˜•์‹ ์‹œ์Šคํ…œ์€

Computer Science Formal Languages Logic System

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