The 16 reference contexts in paper A. Husainov A., E. Kudryashova S., А. Хусаинов А., Е. Кудряшова С. (2016) “Временные оценки и гомоморфизмы асинхронных систем // Timed estimates and homomorphisms of asynchronous systems” / spz:neicon:technomag:y:2014:i:1:p:134-149

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    ¬ÂÏÂÌÌ ̊ ӈÂÌÍË Ë „ÓÏÓÏÓÙËÁÏ ̊ ‡ÒËÌıÓÌÌ ̊ı ÒËÒÚÂÏ # 01, ˇÌ‚‡ ̧ 2014 DOI:10.7463/0114.0695993 Û‰ˇ ̄Ó‚‡ ≈. —., ’ÛÒ‡ËÌÓ‚ ¿. ¿. ”ƒ 519.7 –ÓÒÒˡ, Ã√“” ËÏ. Õ.›. ¡‡Ûχ̇ ekatt@inbox.ru husainov51@yandex.ru ¬‚‰ÂÌË ¬ ‡·ÓÚÂ
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    · ̊ÎË ‚‚‰ÂÌ ̊ ‡ÒËÌıÓÌÌ ̊ ÒËÒÚÂÏ ̊ ‰Îˇ ÏÓ‰ÂÎËÓ‚‡Ìˡ Ô‡‡ÎÎÂÎ ̧Ì ̊ı ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊ı ÒËÒÚÂÏ. ¬ [1,2] ‡ÒÒχÚË‚‡ÎËÒ ̧ ͇Ú„ÓËË ‡ÒËÌıÓÌÌ ̊ı ÒËÒÚÂÏ. ÃÓÙËÁÏ ̊ ‡ÒËÌıÓÌÌ ̊ı ÒËÒÚÂÏ(S, s0, E, I, T ran)→(S′, s′0, E′, I′, T ran′)ÓÔ‰ÂΡÎËÒ ̧ Í‡Í Ô‡ ̊ ÓÚÓ·‡ÊÂÌËÈ(η, σ), ‚ ÍÓÚÓ ̊ıη:E ⇀ E′| ÌÂÍÓÚÓÓ ̃‡ÒÚË ̃ÌÓ ÓÚÓ·‡ÊÂÌË ÏÌÓÊÂÒÚ‚ ÒÓ· ̊ÚËÈ, ‡σ:S→S′| ÓÚÓ·‡ÊÂÌË ÏÌÓÊÂÒÚ‚ ÒÓÒÚÓˇÌËÈ, Û‰Ó‚ÎÂÚ‚Óˇ ̨
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    —., ’ÛÒ‡ËÌÓ‚ ¿. ¿. ”ƒ 519.7 –ÓÒÒˡ, Ã√“” ËÏ. Õ.›. ¡‡Ûχ̇ ekatt@inbox.ru husainov51@yandex.ru ¬‚‰ÂÌË ¬ ‡·ÓÚ [1] · ̊ÎË ‚‚‰ÂÌ ̊ ‡ÒËÌıÓÌÌ ̊ ÒËÒÚÂÏ ̊ ‰Îˇ ÏÓ‰ÂÎËÓ‚‡Ìˡ Ô‡‡ÎÎÂÎ ̧Ì ̊ı ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊ı ÒËÒÚÂÏ. ¬
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    [1,2]
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    ‡ÒÒχÚË‚‡ÎËÒ ̧ ͇Ú„ÓËË ‡ÒËÌıÓÌÌ ̊ı ÒËÒÚÂÏ. ÃÓÙËÁÏ ̊ ‡ÒËÌıÓÌÌ ̊ı ÒËÒÚÂÏ(S, s0, E, I, T ran)→(S′, s′0, E′, I′, T ran′)ÓÔ‰ÂΡÎËÒ ̧ Í‡Í Ô‡ ̊ ÓÚÓ·‡ÊÂÌËÈ(η, σ), ‚ ÍÓÚÓ ̊ıη:E ⇀ E′| ÌÂÍÓÚÓÓ ̃‡ÒÚË ̃ÌÓ ÓÚÓ·‡ÊÂÌË ÏÌÓÊÂÒÚ‚ ÒÓ· ̊ÚËÈ, ‡σ:S→S′| ÓÚÓ·‡ÊÂÌË ÏÌÓÊÂÒÚ‚ ÒÓÒÚÓˇÌËÈ, Û‰Ó‚ÎÂÚ‚Óˇ ̨ ̆ ‰ÓÔÓÎÌËÚÂÎ ̧Ì ̊Ï ÛÒÎӂˡÏ.
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    ÃÓÙËÁÏ ̊ ‡ÒËÌıÓÌÌ ̊ı ÒËÒÚÂÏ(S, s0, E, I, T ran)→(S′, s′0, E′, I′, T ran′)ÓÔ‰ÂΡÎËÒ ̧ Í‡Í Ô‡ ̊ ÓÚÓ·‡ÊÂÌËÈ(η, σ), ‚ ÍÓÚÓ ̊ıη:E ⇀ E′| ÌÂÍÓÚÓÓ ̃‡ÒÚË ̃ÌÓ ÓÚÓ·‡ÊÂÌË ÏÌÓÊÂÒÚ‚ ÒÓ· ̊ÚËÈ, ‡σ:S→S′| ÓÚÓ·‡ÊÂÌË ÏÌÓÊÂÒÚ‚ ÒÓÒÚÓˇÌËÈ, Û‰Ó‚ÎÂÚ‚Óˇ ̨ ̆ ‰ÓÔÓÎÌËÚÂÎ ̧Ì ̊Ï ÛÒÎӂˡÏ. ¬ ‡·ÓÚÂ
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    ËÒÒΉӂ‡ÎËÒ ̧ ÏÓÙËÁÏ ̊, ‚ ÍÓÚÓ ̊ıηÒÓÔÓÒÚ‡‚ΡÂÚ Í‡Ê‰ÓÏÛ ÒÓ· ̊ÚË ̨ ÔÓËÁ‚‰ÂÌË ÔÓÔ‡ÌÓ ÌÂÁ‡‚ËÒËÏ ̊ı ÒÓ· ̊ÚËÈ. ¬ ‰‡ÌÌÓÈ ‡·ÓÚÂ Ï ̊ ËÁÛ ̃‡ÂÏ ÏÓÙËÁÏ ̊, ‚‚‰ÂÌÌ ̊ ‚ ‡·ÓÚ [4] Ë ÔËÏÂÌÂÌÌ ̊ ‚ [5] ‰Îˇ ÓˆÂÌÍË ÔÓËÁ‚Ó‰ËÚÂÎ ̧ÌÓÒÚË Ô‡‡ÎÎÂÎ ̧Ì ̊ı ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊ı ÒËÒÚÂÏ.
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    I′, T ran′)ÓÔ‰ÂΡÎËÒ ̧ Í‡Í Ô‡ ̊ ÓÚÓ·‡ÊÂÌËÈ(η, σ), ‚ ÍÓÚÓ ̊ıη:E ⇀ E′| ÌÂÍÓÚÓÓ ̃‡ÒÚË ̃ÌÓ ÓÚÓ·‡ÊÂÌË ÏÌÓÊÂÒÚ‚ ÒÓ· ̊ÚËÈ, ‡σ:S→S′| ÓÚÓ·‡ÊÂÌË ÏÌÓÊÂÒÚ‚ ÒÓÒÚÓˇÌËÈ, Û‰Ó‚ÎÂÚ‚Óˇ ̨ ̆ ‰ÓÔÓÎÌËÚÂÎ ̧Ì ̊Ï ÛÒÎӂˡÏ. ¬ ‡·ÓÚ [3] ËÒÒΉӂ‡ÎËÒ ̧ ÏÓÙËÁÏ ̊, ‚ ÍÓÚÓ ̊ıηÒÓÔÓÒÚ‡‚ΡÂÚ Í‡Ê‰ÓÏÛ ÒÓ· ̊ÚË ̨ ÔÓËÁ‚‰ÂÌË ÔÓÔ‡ÌÓ ÌÂÁ‡‚ËÒËÏ ̊ı ÒÓ· ̊ÚËÈ. ¬ ‰‡ÌÌÓÈ ‡·ÓÚÂ Ï ̊ ËÁÛ ̃‡ÂÏ ÏÓÙËÁÏ ̊, ‚‚‰ÂÌÌ ̊ ‚ ‡·ÓÚÂ
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    Ë ÔËÏÂÌÂÌÌ ̊ ‚ [5] ‰Îˇ ÓˆÂÌÍË ÔÓËÁ‚Ó‰ËÚÂÎ ̧ÌÓÒÚË Ô‡‡ÎÎÂÎ ̧Ì ̊ı ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊ı ÒËÒÚÂÏ. ›ÚË ÏÓÙËÁÏ ̊ Á‡‰‡ ̨ÚÒˇ Í‡Í Ô‡ ̊(η, σ), ‚ ÍÓÚÓ ̊ıηÒÓÔÓÒÚ‡‚ΡÂÚ Í‡Ê‰ÓÏÛ ÒÓ· ̊ÚË ̨ ÌÂÍÓÚÓÛ ̨ Ú‡ÒÒÛ Ë ÏÓÊÂÚ ËÌÚÂÔÂÚËÓ‚‡Ú ̧Òˇ Í‡Í ‡ÁÎÓÊÂÌË ÒÓ· ̊Úˡ ‚ ÍÓÏÔÓÁËˆË ̨ ÓÔÂ‡ˆËÈ.
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    ¬ ‡·ÓÚ [3] ËÒÒΉӂ‡ÎËÒ ̧ ÏÓÙËÁÏ ̊, ‚ ÍÓÚÓ ̊ıηÒÓÔÓÒÚ‡‚ΡÂÚ Í‡Ê‰ÓÏÛ ÒÓ· ̊ÚË ̨ ÔÓËÁ‚‰ÂÌË ÔÓÔ‡ÌÓ ÌÂÁ‡‚ËÒËÏ ̊ı ÒÓ· ̊ÚËÈ. ¬ ‰‡ÌÌÓÈ ‡·ÓÚÂ Ï ̊ ËÁÛ ̃‡ÂÏ ÏÓÙËÁÏ ̊, ‚‚‰ÂÌÌ ̊ ‚ ‡·ÓÚ [4] Ë ÔËÏÂÌÂÌÌ ̊ ‚
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    ‰Îˇ ÓˆÂÌÍË ÔÓËÁ‚Ó‰ËÚÂÎ ̧ÌÓÒÚË Ô‡‡ÎÎÂÎ ̧Ì ̊ı ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊ı ÒËÒÚÂÏ. ›ÚË ÏÓÙËÁÏ ̊ Á‡‰‡ ̨ÚÒˇ Í‡Í Ô‡ ̊(η, σ), ‚ ÍÓÚÓ ̊ıηÒÓÔÓÒÚ‡‚ΡÂÚ Í‡Ê‰ÓÏÛ ÒÓ· ̊ÚË ̨ ÌÂÍÓÚÓÛ ̨ Ú‡ÒÒÛ Ë ÏÓÊÂÚ ËÌÚÂÔÂÚËÓ‚‡Ú ̧Òˇ Í‡Í ‡ÁÎÓÊÂÌË ÒÓ· ̊Úˡ ‚ ÍÓÏÔÓÁËˆË ̨ ÓÔÂ‡ˆËÈ.
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    ‰ ÒÎÓ‚ ‡ÎÙ‡‚ËÚ‡E, ‚ÍÎ ̨ ̃‡ ̨ ̆ËÈ ÔÛÒÚÓ ÒÎÓ‚Ó1. ƒÎˇ ÔÓËÁ‚ÓÎ ̧ÌÓ„Ó ÓÚÌÓ ̄ÂÌˡ ÌÂÁ‡‚ËÒËÏÓÒÚËİEÓÔ‰ÂÎÂÌ ÏÓÌÓˉM(E, I), ‡‚Ì ̊È Ù‡ÍÚÓ-ÏÓÌÓË‰Û ÏÓÌÓˉ‡ ÒÎÓ‚E∗, ÔÓÎÛ ̃ÂÌÌÓ„Ó ÓÚÓʉÂÒÚ‚ÎÂÌËÂÏ ÒÎÓ‚, ÓÚÎË ̃‡ ̨ ̆ËıÒˇ ÔÂÂÒÚ‡ÌÓ‚ÍÓÈ ˇ‰ÓÏ ÒÚÓˇ ̆Ëı ÌÂÁ‡‚ËÒËÏ ̊ı ·ÛÍ‚. ›ÚÓÚ ÏÓÌÓˉ ̇Á ̊‚‡ÂÚÒˇÒ‚Ó·Ó‰Ì ̊Ï ̃‡ÒÚË ̃ÌÓ ÍÓÏÏÛÚ‡ÚË‚Ì ̊ÏËÎËÏÓÌÓˉÓÏ Ú‡ÒÒ. ŒÌ · ̊Î ‚‚‰ÂÌ Ë ËÒÒΉӂ‡Ì ‚ ‡·ÓÚ œ. ‡Ú ̧Â Ë ƒ. ‘Ó‡Ú ̊
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    . »ÏÂÂÚ ÏÌÓ„Ó ̃ËÒÎÂÌÌ ̊ ÔËÎÓÊÂÌˡ ‚ Ô‡‡ÎÎÂÎ ̧ÌÓÏ ÔÓ„‡ÏÏËÓ‚‡ÌËË [7,8,9]. œÓÒÚ‡ÌÒÚ‚‡ ÒÓÒÚÓˇÌËÈ.œÓÒÚ‡ÌÒÚ‚Ó ÒÓÒÚÓˇÌËÈ(S, E, I, T ran)ÒÓÒÚÓËÚ ËÁ ÔÓËÁ‚ÓÎ ̧Ì ̊ı ÏÌÓÊÂÒÚ‚S,E, ÒËÏÏÂÚË ̃ÌÓ„Ó ‡ÌÚËÂÙÎÂÍÒË‚ÌÓ„Ó ÓÚÌÓ ̄ÂÌˡI⊆E×EË ÏÌÓÊÂÒÚ‚‡T ran⊆S×E×S, ӷ·‰‡ ̨ ̆Ëı Ò‚ÓÈÒÚ‚‡ÏË: 1) ÂÒÎË(s, a, s′)∈T ran& (s, a, s′′)∈T ran, ÚÓs′=s′′; 2) ÂÒÎË(a, b)∈I& (s, a, s′)∈T ran& (s′, b, s′′)∈T ran, ÚÓ ÒÛ ̆ÂÒÚ‚ÛÂÚ Ú
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    ›ÚÓÚ ÏÓÌÓˉ ̇Á ̊‚‡ÂÚÒˇÒ‚Ó·Ó‰Ì ̊Ï ̃‡ÒÚË ̃ÌÓ ÍÓÏÏÛÚ‡ÚË‚Ì ̊ÏËÎËÏÓÌÓˉÓÏ Ú‡ÒÒ. ŒÌ · ̊Î ‚‚‰ÂÌ Ë ËÒÒΉӂ‡Ì ‚ ‡·ÓÚ œ. ‡Ú ̧Â Ë ƒ. ‘Ó‡Ú ̊ [6]. »ÏÂÂÚ ÏÌÓ„Ó ̃ËÒÎÂÌÌ ̊ ÔËÎÓÊÂÌˡ ‚ Ô‡‡ÎÎÂÎ ̧ÌÓÏ ÔÓ„‡ÏÏËÓ‚‡ÌËË
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    . œÓÒÚ‡ÌÒÚ‚‡ ÒÓÒÚÓˇÌËÈ.œÓÒÚ‡ÌÒÚ‚Ó ÒÓÒÚÓˇÌËÈ(S, E, I, T ran)ÒÓÒÚÓËÚ ËÁ ÔÓËÁ‚ÓÎ ̧Ì ̊ı ÏÌÓÊÂÒÚ‚S,E, ÒËÏÏÂÚË ̃ÌÓ„Ó ‡ÌÚËÂÙÎÂÍÒË‚ÌÓ„Ó ÓÚÌÓ ̄ÂÌˡI⊆E×EË ÏÌÓÊÂÒÚ‚‡T ran⊆S×E×S, ӷ·‰‡ ̨ ̆Ëı Ò‚ÓÈÒÚ‚‡ÏË: 1) ÂÒÎË(s, a, s′)∈T ran& (s, a, s′′)∈T ran, ÚÓs′=s′′; 2) ÂÒÎË(a, b)∈I& (s, a, s′)∈T ran& (s′, b, s′′)∈T ran, ÚÓ ÒÛ ̆ÂÒÚ‚ÛÂÚ Ú‡ÍÓÈs1∈S, ̃ÚÓ (s, b, s1)∈T ran& (s1, a, s′′)∈T ran(ËÒ.1).
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    ÂÒÎË(a, b)∈I& (s, a, s′)∈T ran& (s′, b, s′′)∈T ran, ÚÓ ÒÛ ̆ÂÒÚ‚ÛÂÚ Ú‡ÍÓÈs1∈S, ̃ÚÓ (s, b, s1)∈T ran& (s1, a, s′′)∈T ran(ËÒ.1).ËÒ.1 ›ÎÂÏÂÌÚ ̊ ËÁṠÁ ̊‚‡ ̨ÚÒˇÒÓÒÚÓˇÌˡÏË, ËÁE|ÒÓ· ̊ÚˡÏË,I⊆E×E|ÓÚÌÓ ̄ÂÌËÂÏ ÌÂÁ‡‚ËÒËÏÓÒÚË, ̋ÎÂÏÂÌÚ ̊(s, a, s′)∈T ran| ÔÂÂıÓ‰‡ÏË. –ËÒ. 1.—‚ÓÈÒÚ‚Ó 2 œÓÒÚ‡ÌÒÚ‚Ó ÒÓÒÚÓˇÌËÈ ÏÓÊÌÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ÏÌÓÊÂÒÚ‚ÓSÒ ̃‡ÒÚË ̃Ì ̊Ï ‰ÂÈÒÚ‚ËÂÏ ÏÓÌÓˉ‡ Ú‡ÒÒM(E, I). ’ÓÓ ̄Ó ËÁ‚ÂÒÚÌÓ
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    , ̃ÚÓ ̃‡ÒÚË ̃ÌÓ ÓÚÓ·‡ÊÂÌËÂf:A ⇀ BÏÓÊÌÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ÚÓڇΠ̧ÌÓÂ̂f:A∪{∗}→B∪{∗}, ‰Ó·‡‚Ρˇ Í Í‡Ê‰ÓÏÛ ÏÌÓÊÂÒÚ‚Û <·ÂÒÍÓÌ ̃ÌÓ Û‰‡ÎÂÌÌÛ ̨> ÚÓ ̃ÍÛ∗Ë ÔÓ·„‡ˇ ‰Îˇx∈A f̂(x) = { f(x),ÂÒÎËf(x)ÓÔ‰ÂÎÂÌÓ; ∗,‚ ‰Û„Ëı ÒÎÛ ̃‡ˇı. ƒÎˇx=∗ÔÓÎÓÊËÏ̂f(x) =∗. œÓÎÓÊËÏA∗=A∪{∗}.
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    ̄ÂÌËˇÏ •(∀s∈S∗)(∀μ1∈M(E, I))(∀μ2∈M(E, I)) (s·μ1)·μ2=s·(μ1μ2); •(∀s∈S∗)s·1 =s; •(∀μ∈M(E, I))∗·μ=∗. ¬ ̃‡ÒÚÌÓÒÚË, ͇ʉÓ Ô‡‚ÓÂM(E, I)-ÏÌÓÊÂÒÚ‚Ó ÏÓÊÌÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ÔÛÌÍÚËÓ‚‡ÌÌ ̊È ÔÓÎË„ÓÌ Ì‡‰ ÏÓÌÓˉÓÏ Ú‡ÒÒ, ‰Ó·‡‚Ρˇ Í ÏÌÓÊÂÒÚ‚Û ÒÓÒÚÓˇÌËÈ ÒÓÒÚÓˇÌËÂ∗Ë ÓÔ‰ÂΡˇ ̇ ÌÂÏ ‰ÂÈÒÚ‚Ë ͇Í∗·μ=∗. —ÓÓÚÌÓ ̄ÂÌˡ ÔÓ͇Á ̊‚‡ ̨Ú, ̃ÚÓ ‰ÂÈÒڂˡ(s, a)7→s·a‰ÓÒÚ‡ÚÓ ̃ÌÓ ÓÔ‰ÂÎËÚ ̧ ‰Îˇ ‚ÒÂı s∈S∗Ëa∈E. œ‰ÎÓÊÂÌË 1.
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    [10, “ÂÓÂχ 2.3.5]
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    . œÛÒÚ ̧(S∗, M(E, I),·)| ÔÛÌÍÚËÓ‚‡ÌÌ ̊È ÔÓÎË„ÓÌ Ì‡‰ ÏÓÌÓˉÓÏ Ú‡ÒÒ. œÓÎÓÊËÏ T ran={(s, a, s′)|s∈S, s′∈S, s·a=s′}. “Ó„‰‡ ̃ÂÚ‚Â͇(S, E, I, T ran)·Û‰ÂÚ ÔÓÒÚ‡ÌÒÚ‚ÓÏ ÒÓÒÚÓˇÌËÈ. » ̇ӷÓÓÚ, ‚ÒˇÍÓÏÛ ÔÓÒÚ‡ÌÒÚ‚Û ÒÓÒÚÓˇÌËÈ(S, E, I, T ran)·Û‰ÂÚ ÒÓÓÚ‚ÂÚÒÚ‚Ó‚‡Ú ̧ ÔÛÌÍÚËÓ‚‡ÌÌ ̊È ÔÓÎË„ÓÌ (S∗, M(E, I),·)Ò ‰ÂÈÒÚ‚ËÂÏs·a, ÓÔ‰ÂÎÂÌÌ ̊Ï ‰Îˇ ‚ÒÂıs∈S∗Ëe∈EÔÓ ÙÓÏÛΠs·a= { s′,ÂÒÎË ÒÛ ̆ÂÒÚ‚ÛÂÚ Ú‡ÍÓÈs′∈S, ̃ÚÓ
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    6138
    Prefix
    ¿ÒËÌıÓÌ̇ˇ ÒËÒÚÂχ Ò ÙÛÌ͈ËÂÈ ‚ÂÏÂÌË ƒÎˇ ‡ÒÔ‡‡ÎÎÂÎË‚‡Ìˡ ‚ ̊ ̃ËÒÎËÚÂÎ ̧ÌÓ„Ó ÔÓˆÂÒÒ‡ ̋ÚÓÚ ÔÓˆÂÒÒ Ò̇ ̃‡Î‡ ‡Á·„‡ ̨Ú ‚ ÍÓÏÔÓÁËˆË ̨ ÍÓÌ ̃ÌÓÈ ÔÓÒΉӂ‡ÚÂÎ ̧ÌÓÒÚË ÓÔÂ‡ÚÓÓ‚, Á‡ÚÂÏ Ì‡ıÓ‰ˇÚ Ô‡ ̊ ÌÂÁ‡‚ËÒËÏ ̊ı ÓÔÂ‡ÚÓÓ‚ Ë Ó· ̇‰ËÌˇ ̨Ú ÌÂÁ‡‚ËÒËÏ ̊ ÓÔÂ‡ÚÓ ̊ ‚ ·ÎÓÍË-ˇÛÒ ̊ Ô‡‡ÎÎÂÎ ̧ÌÓÈ ÙÓÏ ̊
    Exact
    [11]
    Suffix
    . à ̊ ·Û‰ÂÏ ËÒÔÓÎ ̧ÁÓ‚‡Ú ̧ ̋ÚÛ Ë‰Â ̨ ‰Îˇ ‚ ̊ ̃ËÒÎÂÌˡ ‚ÂÏÂÌË ‚ ̊ÔÓÎÌÂÌˡ. œÛÒÚ ̧A| ‡ÒËÌıÓÌ̇ˇ ÒËÒÚÂχ. à ̊ ·Û‰ÂÏ ËÌÚÂÔÂÚËÓ‚‡Ú ̧ ÒÓ· ̊Úˡa∈EÍ‡Í ‚ ̊ÔÓÎÌˇ ̨ ̆ËÂÒˇ ‚Ó ‚ÂÏÂÌË Ï‡ ̄ËÌÌ ̊ ÍÓχ̉ ̊, ËÌÒÚÛ͈ËË.
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  11. Start
    8099
    Prefix
    ŒÌ‡ ̇Á ̊‚‡ÂÚÒˇÌÓχΠ̧ÌÓÈ ÙÓÏÓÈ ‘Ó‡Ú ̊,  ‰ËÌÒÚ‚ÂÌÌÓÒÚ ̧ Ï ̊ ÛÒÚ‡ÌÓ‚ËÏ ÌËÊ (ÒΉÒÚ‚ËÂ1). Õ‡ÔËÏÂ, ‰Îˇ Í·ÒÒ‡[abba]‚ ÔÓÓʉÂÌÌÓÏ ‰‚ÛÏˇ ̋ÎÂÏÂÌÚ‡ÏË{a, b}ÏÓÌÓˉ Ú‡ÒÒ ÌÓχΠ̧̇ˇ ÙÓχ ‘Ó‡Ú ̊ ·Û‰ÂÚ ‡‚̇abab. œ‰ÎÓÊÂÌË 2.
    Exact
    [6]
    Suffix
    . ƒÎˇ Î ̨·Ó„Ó[w]∈M(E, I)ÒÛ ̆ÂÒÚ‚ÛÂÚ Â‰ËÌÒÚ‚ÂÌ̇ˇ ÔÓÒΉӂ‡ÚÂÎ ̧ÌÓÒÚ ̧ ÒÎÓ‚w1, . . . , wn, ͇ʉÓ ËÁ ÍÓÚÓ ̊ı ÒÓÒÚÓËÚ ËÁ ÔÓÔ‡ÌÓ ÌÂÁ‡‚ËÒËÏ ̊ı ·ÛÍ‚, Ú‡ÍËı, ̃ÚÓ[w] = [w1]···[wn]·Û‰ÂÚ ‡ÁÎÓÊÂÌËÂÏ ‘Ó‡Ú ̊.
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  12. Start
    9954
    Prefix
    ≈ÒÎË ÌÂÍÓÚÓ‡ˇ ·ÛÍ‚‡ ËÁwi Ì Á‡‚ËÒËχ ÒÓ ‚ÒÂÏË ·ÛÍ‚‡ÏË ËÁwi−1, ÚÓ ÔË ÔÓÒÚÓÂÌËË ‡ÁÎÓÊÂÌˡ ‘Ó‡Ú ̊ Ó̇ ÔÂÂȉÂÚ ‚ Ó‰ËÌ ËÁ ·ÎÓÍÓ‚wj, „‰Âj < i. ÓÎË ̃ÂÒÚ‚Ó ·ÎÓÍÓ‚ ÓÚ ̋ÚÓ„Ó ÔÂÂÏ ̆ÂÌˡ Ì ۂÂÎË ̃ËÚÒˇ. œÓ ̋ÚÓÏÛ ̃ËÒÎÓ ˇÛÒÓ‚ ‚ ‡ÁÎÓÊÂÌËË ‘Ó‡Ú ̊ Ì ÏÂÌ ̧ ̄Â, ̃ÂÏn.I œ‰ÎÓÊÂÌË 3.
    Exact
    [7]
    Suffix
    .≈ÒÎË ‚ÂÏˇ ‚ ̊ÔÓÎÌÂÌˡ Í‡Ê‰Ó„Ó ÒÓ· ̊Úˡ ‡‚ÌÓ1, ÚÓ ÏËÌËχΠ̧ÌÓ ‚ÂÏˇ ‚ ̊ÔÓÎÌÂÌˡ Ú‡ÒÒ ̊ ‡‚ÌÓ ‚ ̊ÒÓڠ ÌÓχΠ̧ÌÓÈ ÙÓÏ ̊ ‘Ó‡Ú ̊. œ˂‰ÂÌË Ú‡ÒÒ ̊ Í ÌÓχΠ̧ÌÓÈ ÙÓÏ ‘Ó‡Ú ̊ ‡Ì‡ÎÓ„Ë ̃ÌÓ ÔÓÒÚÓÂÌË ̨ ͇ÌÓÌË ̃ÂÒÍÓÈ ˇÛÒÌÓ-Ô‡‡ÎÎÂÎ ̧ÌÓÈ ÌÓχΠ̧ÌÓÈ ÙÓÏ ̊ [11,12]. œÓÒÚÓÂÌË χÚÂχÚË ̃ÂÒÍÓÈ ÏÓ‰ÂÎË ‰Îˇ ‡Ò ̃ÂÚ‡ ‚ÂÏÂÌË.
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  13. Start
    10213
    Prefix
    ÓÎË ̃ÂÒÚ‚Ó ·ÎÓÍÓ‚ ÓÚ ̋ÚÓ„Ó ÔÂÂÏ ̆ÂÌˡ Ì ۂÂÎË ̃ËÚÒˇ. œÓ ̋ÚÓÏÛ ̃ËÒÎÓ ˇÛÒÓ‚ ‚ ‡ÁÎÓÊÂÌËË ‘Ó‡Ú ̊ Ì ÏÂÌ ̧ ̄Â, ̃ÂÏn.I œ‰ÎÓÊÂÌË 3.[7].≈ÒÎË ‚ÂÏˇ ‚ ̊ÔÓÎÌÂÌˡ Í‡Ê‰Ó„Ó ÒÓ· ̊Úˡ ‡‚ÌÓ1, ÚÓ ÏËÌËχΠ̧ÌÓ ‚ÂÏˇ ‚ ̊ÔÓÎÌÂÌˡ Ú‡ÒÒ ̊ ‡‚ÌÓ ‚ ̊ÒÓڠ ÌÓχΠ̧ÌÓÈ ÙÓÏ ̊ ‘Ó‡Ú ̊. œ˂‰ÂÌË Ú‡ÒÒ ̊ Í ÌÓχΠ̧ÌÓÈ ÙÓÏ ‘Ó‡Ú ̊ ‡Ì‡ÎÓ„Ë ̃ÌÓ ÔÓÒÚÓÂÌË ̨ ͇ÌÓÌË ̃ÂÒÍÓÈ ˇÛÒÌÓ-Ô‡‡ÎÎÂÎ ̧ÌÓÈ ÌÓχΠ̧ÌÓÈ ÙÓÏ ̊
    Exact
    [11,12]
    Suffix
    . œÓÒÚÓÂÌË χÚÂχÚË ̃ÂÒÍÓÈ ÏÓ‰ÂÎË ‰Îˇ ‡Ò ̃ÂÚ‡ ‚ÂÏÂÌË.–‡ÒÒÏÓÚËÏ ÚÂÔÂ ̧ Ó· ̆ËÈ ÒÎÛ ̃‡È. œÛÒÚ ̧ Á‡‰‡Ì‡ ‡ÒËÌıÓÌ̇ˇ ÒËÒÚÂχAÒ ÙÛÌ͈ËÂÈ ‚ÂÏÂÌË, ÔËÌËχ ̨ ̆ÂÈ ÔÓËÁ‚ÓÎ ̧Ì ̊ Á̇ ̃ÂÌˡτ(a)∈N+. œÓÔ ̊Ú‡ÂÏÒˇ ‡ÁÎÓÊËÚ ̧ ÔÂÂıÓ‰s a →s′‚ ÍÓÏÔÓÁËˆË ̨ ÔÂÂıÓ‰Ó‚, ËÏ ̨ ̆Ëı Á‡‚ËÒËÏ ̊ ËÌÒÚÛ͈ËËe1,e2, . . . ,ek, „‰Âk=τ(a).
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  14. Start
    25101
    Prefix
    –ËÒ. 4.«‡‚ËÒËÏÓÒÚ ̧ ‚ÂÏÂÌË Ó·‡·ÓÚÍËm ̋ÎÂÏÂÌÚÓ‚ Ó ̃ÂÂ‰Ë ¡ÓΠӷ ̆Ë ÒÚÛÍÚÛ ̊.¬ ÒÎÛ ̃‡Â ËÁÏÂÌÂÌˡ ÒÚÛÍÚÛ ̊ ÍÓÌ‚ÂÈÂÌÓÈ Ó·‡·ÓÚÍË, ‡·ÓÚ‡ ÔÓ„‡ÏÏ ̊ ÓÒÛ ̆ÂÒڂΡÂÚÒˇ ‡Ì‡ÎÓ„Ë ̃Ì ̊Ï Ó·‡ÁÓÏ. ›ÚÓ ÏÓÊÌÓ ÔËÏÂÌËÚ ̧, ̇ÔËÏÂ, Í‚ÓÎÌÓ‚ ̊Ï ÒËÒÚÂχÏ
    Exact
    [13]
    Suffix
    . ƒÎˇ ËÎÎ ̨ÒÚ‡ˆËË ̋ÚÓ„Ó ÛÚ‚ÂʉÂÌˡ ‡ÒÒÏÓÚËÏ ÒÂÚ ̧, Ô‰ÒÚ‡‚ÎÂÌÌÛ ̨ ̇ ËÒ.5.ËÒ.5 –ËÒ. 5.œËÏÂ Ó·‡·ÓÚÍË ÍÓÌ‚ÂÈÂÌÓ„Ó ÚËÔ‡ ¬ ̊ÔÓÎÌË‚ ÔÓÒÚÓÂÌË ÌÓχΠ̧ÌÓÈ ÙÓÏ ̊ ‘Ó‡Ú ̊, ÔÓÎÛ ̃ËÏ ‚ ̊‡ÊÂÌË ‰Îˇ ̇ıÓʉÂÌˡ ÏËÌËχΠ̧ÌÓ„Ó ‚ÂÏÂÌË ‚ ̊ÔÓÎÌÂÌˡ: [(a21a32a13)m] = [a1a2][a1a2][a2]([a3][a1a2][a1a2][a2])m−1[a3].
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  15. Start
    26847
    Prefix
    Õ‡ÎË ̃Ë ÔÓ„ ̄ÌÓÒÚË ÏÓÊÌÓ Ò‚ˇÁ‡Ú ̧ Ò ÚÂÏ, ̃ÚÓ ÔË Ï‡Î ̊ıτ(a)‚ÂÏÂÌÌ ̊ Á‡Ú‡Ú ̊ ̇ ÛÒÚ‡ÌÓ‚ÍÛ ÒÓ· ̊ÚËÈ Ë ÔÂ‰‡ ̃Û ÛÔ‡‚ÎÂÌˡ ÏÂÊ‰Û ÔÓÚÓ͇ÏË Ô‚ÓÒıÓ‰ˇÚ Á‡Ú‡Ú ̊ ̇ ÒÓ·ÒÚ‚ÂÌÌÓ ‚ ̊ ̃ËÒÎÂÌˡ. à ̊ ÌÂ Û ̃ËÚ ̊‚‡ÂÏ ̋ÚËı ÔÓ„ ̄ÌÓÒÚÂÈ. ›ÚÓÈ ÔÓ·ÎÂÏ ÔÓÒ‚ˇ ̆Â̇, ̇ÔËÏÂ, ‡·ÓÚ‡
    Exact
    [14]
    Suffix
    , ÌÓ ‚ ÌÂÈ ‡ÒÒχÚË‚‡ ̨ÚÒˇ ÚÓÎ ̧ÍÓ ÍÓÌ‚ÂÈÂÌ ̊ ÒËÒÚÂÏ ̊. Õ‡ ̄ ÒÔÓÒÓ· ÔÓÁ‚ÓΡÂÚ ‚ ̊ ̃ËÒÎˇÚ ̧ ÔÓËÁ‚Ó‰ËÚÂÎ ̧ÌÓÒÚ ̧ Î ̨·ÓÈ ‡ÒËÌıÓÌÌÓÈ ÒËÒÚÂÏ ̊, ‰Îˇ ÍÓÚÓÓÈ Á‡‰‡Ì ̊ ‚ÂÏÂ̇ ‚ ̊ÔÓÎÌÂÌˡ ÒÓ· ̊ÚËÈ. ƒ‡ÌÌ ̊È ‚ÓÔÓÒ Ú·ÛÂÚ ‰ÓÔÓÎÌËÚÂÎ ̧Ì ̊ı ËÒÒΉӂ‡ÌËÈ, ÔÓ ̋ÚÓÏÛ Ôӂ‰ÂÌÌ ̊È ̋ÍÒÔÂËÏÂÌÚ ÏÓÊÌÓ Ò ̃ËÚ‡Ú ̧ ÛÒÎÓ‚ÌÓ ÛÒÔ ̄Ì ̊Ï.
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  16. Start
    27826
    Prefix
    ¬ ÔÂÒÔÂÍÚË‚Â ËÒÒΉӂ‡ÌË ӈÂÌÓÍ ‚ÂÏÂÌË ‰Îˇ ‡ÁÎÓÊÂÌˡ ÓÔÂ‡ˆËÈ ‚ ÍÓÏÔÓÁËˆË ̨ ÓÔÂ‡ˆËÈ, ÍÓÚÓ ̊ ÏÓ„ÛÚ · ̊Ú ̧ ÌÂÁ‡‚ËÒËÏ ̊. ƒÎˇ ËÁÛ ̃ÂÌˡ ̋ÚÓ„Ó ‚ÓÔÓÒ‡ · ̊ÎÓ · ̊ ıÓÓ ̄Ó ÛÒÚ‡ÌÓ‚ËÚ ̧ Ò‚ˇÁ ̧ ÏÂÊ‰Û ‡ÒËÌıÓÌÌ ̊ÏË ÒËÒÚÂχÏË Ò ÙÛÌ͈ËÂÈ ‚ÂÏÂÌË Ë ‚ÂÏÂÌÌ ̊ÏË ÏÌÓ„ÓÏÂÌ ̊ÏË ‡‚ÚÓχڇÏË, ‚‚‰ÂÌÌ ̊ÏË √Û·Ó
    Exact
    [15]
    Suffix
    . –‡·ÓÚ‡ ‚ ̊ÔÓÎÌÂ̇ ‚ ‡Ï͇ı ÔÓ„‡ÏÏ ̊ ÒÚ‡ÚÂ„Ë ̃ÂÒÍÓ„Ó ‡Á‚ËÚˡ „ÓÒÛ‰‡ÒÚ‚ÂÌÌ ̊ı Ó·‡ÁÓ‚‡ÚÂÎ ̧Ì ̊ı Û ̃ÂʉÂÌËÈ ‚ ̊Ò ̄Â„Ó ÔÓÙÂÒÒËÓ̇Π̧ÌÓ„Ó Ó·‡ÁÓ‚‡Ìˡ, π 2011-œ–-054. —ÔËÒÓÍ ÎËÚÂ‡ÚÛ ̊ 1.Bednarczyk M.
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