G. File. The relation of two patterns with comparable languages. In R. Cori M. Wirsing, editor, Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science (STACS '88), volume 294 of Lecture Notes in Computer Science, pages 184-192, Bordeaux, France, February 1988. Springer.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....problem Inst(p 1 ) Inst(p 2 ) is trivial: the equivalence holds i p 1 and p 2 are equal modulo a variable renaming. The latter is however true only in the NE case, and for the E case the decidability status of the equivalence problem Inst(p 1 ) Inst(p 2 ) is open. We also point out to paper [Fil88] for some results about the inclusion problem Inst(p 1 ) Inst(p 2 ) in the E and NE case. Proposition 7. In the word case, problem P3 is undecidable even if S consists of a single pattern. Formally, the undecidability result of [JSSY93] for problem P3 does not imply the undecidability of ....

G. File. The relation of two patterns with comparable languages. In R. Cori M. Wirsing, editor, Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science (STACS '88), volume 294 of Lecture Notes in Computer Science, pages 184-192, Bordeaux, France, February 1988. Springer.

....pattern languages. For example, in the case of general pattern languages the word problem is NP 1 We study so called non erasing substitutions. It is also possible to consider erasing substitutions where variables may be replaced by empty strings, leading to a different class of languages [7,29,30]. complete [2] and the inclusion problem is undecidable [15] but both problems are decidable in linear time for one variable pattern languages. On the other hand, PAT 1 is still incomparable to the regular and context free languages. A finite set S = fs 0 ; s 1 ; s r g A of ....

G. Fil'e, The relation of two patterns with comparable languages, in: R. Cori and M. Wirsing, eds., Proc. STACS 88, Lecture Notes in Computer Science, Vol. 294 (Springer, Berlin, 1988) 184--192.

.... k s n 1 2 L( g, and then S n 1 = fQ 2 S 0 n 1 (8Q 0 2 S 0 n 1 ) Q 0 6ae Q]g. 7 We study so called non erasing substitutions. It is also possible to consider erasing substitutions where variables may be replaced by empty strings, leading to a different class of languages (cf. Fil e [15]) 25 Note that S 0 can be effectively obtained from s 0 , since every pattern with s 0 2 L( must satisfy j j js 0 j. Thus, there are only finitely many candidate patterns with s 0 2 L( which can be effectively constructed. Since membership is uniformly decidable, we are done. ....

G. Fil'e, The relation of two patterns with comparable languages, In (R. Cori and M. Wirsing, Eds.), Proceedings of the 5th Ann. Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Vol. 294, pp. 184--192, SpringerVerlag, Berlin, 1988.

....s 0 2 L( g. We proceed inductively; for n 0, we define S 0 n 1 = fQ 2 S n s n 1 2 L(Q)g[fQ[f g Q 2 S n s n 1 62 L(Q) jQj k s n 1 2 L( g, and then Sn 1 = fQ 2 S 0 n 1 (8Q 0 2 S 0 n 1 ) Q 0 6ae Q]g. may be replaced by empty strings, leading to a different class of languages (cf. Fil e (1988)) Note that S 0 can be effectively obtained from s 0 , since every pattern with s 0 2 L( must satisfy j j js 0 j. Thus, there are only finitely many candidate patterns with s 0 2 L( which can be effectively constructed. Since membership is uniformly decidable, we are done. ....

Fil'e G. 1988. The relation of two patterns with comparable languages. In Proc. 5th Ann. Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 294, pp. 184--192, Springer-Verlag.

.... k s n 1 2 L( g, and then S n 1 = fQ 2 S 0 n 1 (8Q 0 2 S 0 n 1 ) Q 0 6ae Q]g. 7 We study so called non erasing substitutions. It is also possible to consider erasing substitutions where variables may be replaced by empty strings, leading to a different class of languages (cf. Fil e [15]) Incremental Concept Learning for Bounded Data Mining 25 Note that S 0 can be effectively obtained from s 0 , since every pattern with s 0 2 L( must satisfy j j js 0 j. Thus, there are only finitely many candidate patterns with s 0 2 L( which can be effectively constructed. Since ....

G. Fil'e, The relation of two patterns with comparable languages, In (R. Cori and M. Wirsing, Eds.), Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Vol. 294, pp. 184--192, SpringerVerlag, Berlin, 1988.

....sample, obtained as input. Let S = fs 0 ; s 1 ; s r g; we set n = P r j=0 js j j, and refer to n as the size of sample S. 3 We study non erasing substitutions. Erasing substitutions have been also considered, variables may be replaced by ) leading to a different language class (cf. [5]) PAT as well as PAT 1 constitute an indexable class L of uniformly recursive languages, i.e. there are an effective enumeration (L j ) j2IN of L and a recursive function f such that for all j 2 IN and all s 2 A 3 we have f(j; s) 1 if s 2 L j , and f(j; s) 0 otherwise. Except in Section ....

G. Fil'e. The relation of two patterns with comparable languages. In Proc. 5th Ann. Symp. Theoretical Aspects of Computer Science, LNCS 294, pp. 184--192, Berlin, 1988. Springer-Verlag.

....it belongs to L or not. Furthermore, every infinite sequence t = s j ) j2IN of strings such that 1 We study so called non erasing substitutions. It is also possible to consider erasing substitutions where variables may be replaced by empty strings, leading to a different class of languages [6]. 6 Thomas Erlebach, Peter Rossmanith, Hans Stadtherr, Angelika Steger, and Thomas Zeugmann range(t) fs j j 2 INg = L is said to be a text for L, or, synonymously, a positive presentation. By Text(L) we denote the set of all texts for L. Furthermore, let t be a text, and let n 2 IN. We set t n ....

G. Fil'e. The relation of two patterns with comparable languages. In R. Cori and M. Wirsing, editors, Proceedings of the 5th Ann. Symposium on Theoretical Aspects of Computer Science (STACS 88) (Bordeaux, France), LNCS 294, pages 184--192, Berlin, 1988. Springer-Verlag.

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