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By Kulikov A. S.

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N and xA = xal ... n. 1, Ind = {{a}, {b}, {c}, {a,b}}. 1, if X = {21. E Vev*I(3]L E Vev·)~ EX}. ,ab, abc, abca}. 1. Simple Properties of Vector Sequences 25 For every f!!. }). Every element of Vev* can be uniquely decomposed in a special manner. For every f!!. E Vev* \ {d, a sequence of sets (A b ... , Ale)' k 2: 1, is said to be a left-normal form (abbreviated In-form) of f!!. if and only if the following conditions are satisfied: (1) (Vi=1, ... EInd (2) f!!. = A1· .. '& (3) if k > 1, then (Vi = 2, ...

9 Let N = (S,T,F,Mo) be a smd-net with SMD(N) = {N1! ,Nn } where Ni = (Si,Ti,Fi,Mt) fori = 1, .. ,n. Then: (1) (Vt E T)card(et) = cardW) = card({Nilt E Ti})' Chapter 2. Formal Theory of Basic COSY 52 {N1 ,N2 } is a state machine decomposition of N, and {Ng ,N4 } is also a state machine decomposition of N. Note that for instance {N1 ,N2 ,Ng ,N4 } is not a state machine decomposition of N because of (2) of the definition. 11. 2. 12. Contact free non smd-net (2) (VM E [Mo) )card(M) (3) N is contact-free.

2, in particular we can use ind, the independency relation defined by EVl, ... l. E V F S we can define PO~... Sometimes we shall write ind(Pr), Ind(Pr) if the explicit name Pr is necessary. e. l. E V F S and i, j ;::: 1 such that (a(i), b(i») (j. PO~.. £ = (e,C). l. E V F S(Pr3), POi!!. is a total order. Now, we describe some simple properties of VFS. 6 (1) Pref(VFS) = VFS. l. ) E FSi,i = 1, ... ,n}. Proof. (1) Clearly VFS ~ Pref(VFS). l. 1L E V F S. l. = (Zl, ... , Yn). From the definition of VFS it follows that ZiYi E FSi , for i = 1, ...

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A 2E4-time algorithm for MAX-CUT by Kulikov A. S.


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