R. Fraiss'e, Sur les Classifications des Systems de relations, Publications Sc. d. l'Universite D'Alager 1:I (1954).  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... MSO formulas of quantifier depth r is fixed for all these large enough trees, giving us the asymptotic values 1 (for MSO sentences that are TRUE on F having T r as a subtree) and 0 (for MSO sentences that are FALSE on F having T r as a subtree) This approach used the pebble games developed in [Fr54, Eh61, Fa75, La77], see [EbF95] Then following the results suggested by Buchi, in [Mc a] it was proven that given a successor relation, all order invariant MSO queries exhibit the same eventually periodic behavior as regular languages (accepted by deterministic finite automata) This result led to the following ....

R. Fraiss'e, Sur les Classifications des Systems de relations, Publications Sc. d. l'Universite D'Alager 1:I (1954).

....much simpler. Thus, we think our paper describes a method for proving completeness which can be more easily adapted to other variants of feature logic than the method of quantifier elimination. The next section briefly reviews the theory CFT from [13] and Section 3 reviews the method of Fraiss e [8] and Ehrenfeucht [7] The core of the paper is Section 4, where we prove the completeness of CFT with the method of Section 3. yval xval yval 2 point circle 2 7 center radius type nat or 0 1 s def 1 2 2 3 point xval yval xval 2 red point name 3 color Fig. 1. Examples of (in Fact Rational) ....

....constrained by Phi is denoted as con( Phi) Hence, for a determinant ffi , con(ffi) det(ffi) Proposition2. For every solved form oe we have 8(V ffi Gamma con(ffi) 9con(ffi) ffi Note that the existence is no longer unique in case of a solved form. 3 Ehrenfeucht Fraiss e Games Fraiss e [8] gives a definition of elementary equivalence in terms of mappings between structures. Any two isomorphic structures are elementarily equivalent, but there are of course elementarily equivalent structures which are not isomorphic. Hence, to characterize elementary equivalence algebraically we have ....

Roland Fraiss'e. Sur les classifications des systems de relations. Publications Sci. de l'Universit'e d'Alger, I:35--182, June 1954.

....method of quantifier elimination. We will come back to a comparison of the different methods in Section 7. After summarizing some background material in the next section, Section 3 briefly reviews the theory CFT from [22] and some of its basic properties. Section 4 reviews the method of Fraiss e [12] and Ehrenfeucht [11] In Section 5, we discuss the path constraints we need for the formulation of the strategy. The core of the paper is Section 6, where we prove the completeness of CFT with the method of Section 4. We conclude with a brief comparison to other methods. 2 Preliminaries We ....

....S 0 = Ax xffg xfx Ax 0 x 0 ffg x 0 fx 0 Since Fr(x; x 0 ) is empty, we get CFT j= S 0 (x 6 : x 0 false) If we replace in S 0 however Ax by Bx for some B 6= A, then x : x 0 clashes with S 0 and the lemma does not apply. 4 Ehrenfeucht Fraiss e Games Fraiss e [12] gives a definition of elementary equivalence in terms of mappings between structures. In this section we just summarize this method, more detailed expositions can be found e.g. in [13, 18] Any two isomorphic structures are elementary equivalent, but there are of course elementary equivalent ....

Roland Fraiss'e. Sur les classifications des systems de relations. Publications Sci. de l'Universit'e d'Alger, I:35--182, June 1954.

....it has been shown (cf. Fact 1.3.4) that no fixed L k suffices to characterize the graphs of color class size 4. 1.6 Lower Bounds In this section we will show that L k is not expressive enough to characterize graphs efficiently. We will use the combinatorial games of Ehrenfeucht and Fraisse [10, 12] as modified for L k (see [18, 7, 29] All of the results in this section could be proved by induction on the complexity of the sentences in question; but, we find that the games offer more intuitive arguments. Let G and H be two graphs, and let k be a natural number. Define the L k game on G ....

R. Fraiss'e, "Sur les Classifications des Systems de Relations," Publ. Sci. Univ. Alger I (1954).

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